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TheAlgorithms/Python | 4,763 | from __future__ import annotations | ### **Describe your change:**
from __future__ import annotations
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [ ] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [ ] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [ ] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| cclauss | "2021-09-14T22:54:26Z" | "2021-09-22T21:11:51Z" | dc07a850763d8154e012c9d1be7f8fe78326e8fb | 15d1cfabb15903c5e9d4d103e2390876efb3f85f | from __future__ import annotations. ### **Describe your change:**
from __future__ import annotations
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [ ] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [ ] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [ ] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| def apply_table(inp, table):
"""
>>> apply_table("0123456789", list(range(10)))
'9012345678'
>>> apply_table("0123456789", list(range(9, -1, -1)))
'8765432109'
"""
res = ""
for i in table:
res += inp[i - 1]
return res
def left_shift(data):
"""
>>> left_shift("0123456789")
'1234567890'
"""
return data[1:] + data[0]
def XOR(a, b):
"""
>>> XOR("01010101", "00001111")
'01011010'
"""
res = ""
for i in range(len(a)):
if a[i] == b[i]:
res += "0"
else:
res += "1"
return res
def apply_sbox(s, data):
row = int("0b" + data[0] + data[-1], 2)
col = int("0b" + data[1:3], 2)
return bin(s[row][col])[2:]
def function(expansion, s0, s1, key, message):
left = message[:4]
right = message[4:]
temp = apply_table(right, expansion)
temp = XOR(temp, key)
l = apply_sbox(s0, temp[:4]) # noqa: E741
r = apply_sbox(s1, temp[4:])
l = "0" * (2 - len(l)) + l # noqa: E741
r = "0" * (2 - len(r)) + r
temp = apply_table(l + r, p4_table)
temp = XOR(left, temp)
return temp + right
if __name__ == "__main__":
key = input("Enter 10 bit key: ")
message = input("Enter 8 bit message: ")
p8_table = [6, 3, 7, 4, 8, 5, 10, 9]
p10_table = [3, 5, 2, 7, 4, 10, 1, 9, 8, 6]
p4_table = [2, 4, 3, 1]
IP = [2, 6, 3, 1, 4, 8, 5, 7]
IP_inv = [4, 1, 3, 5, 7, 2, 8, 6]
expansion = [4, 1, 2, 3, 2, 3, 4, 1]
s0 = [[1, 0, 3, 2], [3, 2, 1, 0], [0, 2, 1, 3], [3, 1, 3, 2]]
s1 = [[0, 1, 2, 3], [2, 0, 1, 3], [3, 0, 1, 0], [2, 1, 0, 3]]
# key generation
temp = apply_table(key, p10_table)
left = temp[:5]
right = temp[5:]
left = left_shift(left)
right = left_shift(right)
key1 = apply_table(left + right, p8_table)
left = left_shift(left)
right = left_shift(right)
left = left_shift(left)
right = left_shift(right)
key2 = apply_table(left + right, p8_table)
# encryption
temp = apply_table(message, IP)
temp = function(expansion, s0, s1, key1, temp)
temp = temp[4:] + temp[:4]
temp = function(expansion, s0, s1, key2, temp)
CT = apply_table(temp, IP_inv)
print("Cipher text is:", CT)
# decryption
temp = apply_table(CT, IP)
temp = function(expansion, s0, s1, key2, temp)
temp = temp[4:] + temp[:4]
temp = function(expansion, s0, s1, key1, temp)
PT = apply_table(temp, IP_inv)
print("Plain text after decypting is:", PT)
| def apply_table(inp, table):
"""
>>> apply_table("0123456789", list(range(10)))
'9012345678'
>>> apply_table("0123456789", list(range(9, -1, -1)))
'8765432109'
"""
res = ""
for i in table:
res += inp[i - 1]
return res
def left_shift(data):
"""
>>> left_shift("0123456789")
'1234567890'
"""
return data[1:] + data[0]
def XOR(a, b):
"""
>>> XOR("01010101", "00001111")
'01011010'
"""
res = ""
for i in range(len(a)):
if a[i] == b[i]:
res += "0"
else:
res += "1"
return res
def apply_sbox(s, data):
row = int("0b" + data[0] + data[-1], 2)
col = int("0b" + data[1:3], 2)
return bin(s[row][col])[2:]
def function(expansion, s0, s1, key, message):
left = message[:4]
right = message[4:]
temp = apply_table(right, expansion)
temp = XOR(temp, key)
l = apply_sbox(s0, temp[:4]) # noqa: E741
r = apply_sbox(s1, temp[4:])
l = "0" * (2 - len(l)) + l # noqa: E741
r = "0" * (2 - len(r)) + r
temp = apply_table(l + r, p4_table)
temp = XOR(left, temp)
return temp + right
if __name__ == "__main__":
key = input("Enter 10 bit key: ")
message = input("Enter 8 bit message: ")
p8_table = [6, 3, 7, 4, 8, 5, 10, 9]
p10_table = [3, 5, 2, 7, 4, 10, 1, 9, 8, 6]
p4_table = [2, 4, 3, 1]
IP = [2, 6, 3, 1, 4, 8, 5, 7]
IP_inv = [4, 1, 3, 5, 7, 2, 8, 6]
expansion = [4, 1, 2, 3, 2, 3, 4, 1]
s0 = [[1, 0, 3, 2], [3, 2, 1, 0], [0, 2, 1, 3], [3, 1, 3, 2]]
s1 = [[0, 1, 2, 3], [2, 0, 1, 3], [3, 0, 1, 0], [2, 1, 0, 3]]
# key generation
temp = apply_table(key, p10_table)
left = temp[:5]
right = temp[5:]
left = left_shift(left)
right = left_shift(right)
key1 = apply_table(left + right, p8_table)
left = left_shift(left)
right = left_shift(right)
left = left_shift(left)
right = left_shift(right)
key2 = apply_table(left + right, p8_table)
# encryption
temp = apply_table(message, IP)
temp = function(expansion, s0, s1, key1, temp)
temp = temp[4:] + temp[:4]
temp = function(expansion, s0, s1, key2, temp)
CT = apply_table(temp, IP_inv)
print("Cipher text is:", CT)
# decryption
temp = apply_table(CT, IP)
temp = function(expansion, s0, s1, key2, temp)
temp = temp[4:] + temp[:4]
temp = function(expansion, s0, s1, key1, temp)
PT = apply_table(temp, IP_inv)
print("Plain text after decypting is:", PT)
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Project Euler Problem 3: https://projecteuler.net/problem=3
Largest prime factor
The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143?
References:
- https://en.wikipedia.org/wiki/Prime_number#Unique_factorization
"""
import math
def isprime(num: int) -> bool:
"""
Returns boolean representing primality of given number num.
>>> isprime(2)
True
>>> isprime(3)
True
>>> isprime(27)
False
>>> isprime(2999)
True
>>> isprime(0)
Traceback (most recent call last):
...
ValueError: Parameter num must be greater than or equal to two.
>>> isprime(1)
Traceback (most recent call last):
...
ValueError: Parameter num must be greater than or equal to two.
"""
if num <= 1:
raise ValueError("Parameter num must be greater than or equal to two.")
if num == 2:
return True
elif num % 2 == 0:
return False
for i in range(3, int(math.sqrt(num)) + 1, 2):
if num % i == 0:
return False
return True
def solution(n: int = 600851475143) -> int:
"""
Returns the largest prime factor of a given number n.
>>> solution(13195)
29
>>> solution(10)
5
>>> solution(17)
17
>>> solution(3.4)
3
>>> solution(0)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater than or equal to one.
>>> solution(-17)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater than or equal to one.
>>> solution([])
Traceback (most recent call last):
...
TypeError: Parameter n must be int or castable to int.
>>> solution("asd")
Traceback (most recent call last):
...
TypeError: Parameter n must be int or castable to int.
"""
try:
n = int(n)
except (TypeError, ValueError):
raise TypeError("Parameter n must be int or castable to int.")
if n <= 0:
raise ValueError("Parameter n must be greater than or equal to one.")
max_number = 0
if isprime(n):
return n
while n % 2 == 0:
n //= 2
if isprime(n):
return n
for i in range(3, int(math.sqrt(n)) + 1, 2):
if n % i == 0:
if isprime(n / i):
max_number = n / i
break
elif isprime(i):
max_number = i
return max_number
if __name__ == "__main__":
print(f"{solution() = }")
| """
Project Euler Problem 3: https://projecteuler.net/problem=3
Largest prime factor
The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143?
References:
- https://en.wikipedia.org/wiki/Prime_number#Unique_factorization
"""
import math
def isprime(num: int) -> bool:
"""
Returns boolean representing primality of given number num.
>>> isprime(2)
True
>>> isprime(3)
True
>>> isprime(27)
False
>>> isprime(2999)
True
>>> isprime(0)
Traceback (most recent call last):
...
ValueError: Parameter num must be greater than or equal to two.
>>> isprime(1)
Traceback (most recent call last):
...
ValueError: Parameter num must be greater than or equal to two.
"""
if num <= 1:
raise ValueError("Parameter num must be greater than or equal to two.")
if num == 2:
return True
elif num % 2 == 0:
return False
for i in range(3, int(math.sqrt(num)) + 1, 2):
if num % i == 0:
return False
return True
def solution(n: int = 600851475143) -> int:
"""
Returns the largest prime factor of a given number n.
>>> solution(13195)
29
>>> solution(10)
5
>>> solution(17)
17
>>> solution(3.4)
3
>>> solution(0)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater than or equal to one.
>>> solution(-17)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater than or equal to one.
>>> solution([])
Traceback (most recent call last):
...
TypeError: Parameter n must be int or castable to int.
>>> solution("asd")
Traceback (most recent call last):
...
TypeError: Parameter n must be int or castable to int.
"""
try:
n = int(n)
except (TypeError, ValueError):
raise TypeError("Parameter n must be int or castable to int.")
if n <= 0:
raise ValueError("Parameter n must be greater than or equal to one.")
max_number = 0
if isprime(n):
return n
while n % 2 == 0:
n //= 2
if isprime(n):
return n
for i in range(3, int(math.sqrt(n)) + 1, 2):
if n % i == 0:
if isprime(n // i):
max_number = n // i
break
elif isprime(i):
max_number = i
return max_number
if __name__ == "__main__":
print(f"{solution() = }")
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Project Euler Problem 3: https://projecteuler.net/problem=3
Largest prime factor
The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143?
References:
- https://en.wikipedia.org/wiki/Prime_number#Unique_factorization
"""
def solution(n: int = 600851475143) -> int:
"""
Returns the largest prime factor of a given number n.
>>> solution(13195)
29
>>> solution(10)
5
>>> solution(17)
17
>>> solution(3.4)
3
>>> solution(0)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater than or equal to one.
>>> solution(-17)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater than or equal to one.
>>> solution([])
Traceback (most recent call last):
...
TypeError: Parameter n must be int or castable to int.
>>> solution("asd")
Traceback (most recent call last):
...
TypeError: Parameter n must be int or castable to int.
"""
try:
n = int(n)
except (TypeError, ValueError):
raise TypeError("Parameter n must be int or castable to int.")
if n <= 0:
raise ValueError("Parameter n must be greater than or equal to one.")
i = 2
ans = 0
if n == 2:
return 2
while n > 2:
while n % i != 0:
i += 1
ans = i
while n % i == 0:
n = n / i
i += 1
return int(ans)
if __name__ == "__main__":
print(f"{solution() = }")
| """
Project Euler Problem 3: https://projecteuler.net/problem=3
Largest prime factor
The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143?
References:
- https://en.wikipedia.org/wiki/Prime_number#Unique_factorization
"""
def solution(n: int = 600851475143) -> int:
"""
Returns the largest prime factor of a given number n.
>>> solution(13195)
29
>>> solution(10)
5
>>> solution(17)
17
>>> solution(3.4)
3
>>> solution(0)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater than or equal to one.
>>> solution(-17)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater than or equal to one.
>>> solution([])
Traceback (most recent call last):
...
TypeError: Parameter n must be int or castable to int.
>>> solution("asd")
Traceback (most recent call last):
...
TypeError: Parameter n must be int or castable to int.
"""
try:
n = int(n)
except (TypeError, ValueError):
raise TypeError("Parameter n must be int or castable to int.")
if n <= 0:
raise ValueError("Parameter n must be greater than or equal to one.")
i = 2
ans = 0
if n == 2:
return 2
while n > 2:
while n % i != 0:
i += 1
ans = i
while n % i == 0:
n = n // i
i += 1
return int(ans)
if __name__ == "__main__":
print(f"{solution() = }")
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Project Euler Problem 7: https://projecteuler.net/problem=7
10001st prime
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we
can see that the 6th prime is 13.
What is the 10001st prime number?
References:
- https://en.wikipedia.org/wiki/Prime_number
"""
def isprime(number: int) -> bool:
"""
Determines whether the given number is prime or not
>>> isprime(2)
True
>>> isprime(15)
False
>>> isprime(29)
True
"""
for i in range(2, int(number ** 0.5) + 1):
if number % i == 0:
return False
return True
def solution(nth: int = 10001) -> int:
"""
Returns the n-th prime number.
>>> solution(6)
13
>>> solution(1)
2
>>> solution(3)
5
>>> solution(20)
71
>>> solution(50)
229
>>> solution(100)
541
>>> solution(3.4)
5
>>> solution(0)
Traceback (most recent call last):
...
ValueError: Parameter nth must be greater than or equal to one.
>>> solution(-17)
Traceback (most recent call last):
...
ValueError: Parameter nth must be greater than or equal to one.
>>> solution([])
Traceback (most recent call last):
...
TypeError: Parameter nth must be int or castable to int.
>>> solution("asd")
Traceback (most recent call last):
...
TypeError: Parameter nth must be int or castable to int.
"""
try:
nth = int(nth)
except (TypeError, ValueError):
raise TypeError("Parameter nth must be int or castable to int.") from None
if nth <= 0:
raise ValueError("Parameter nth must be greater than or equal to one.")
primes = []
num = 2
while len(primes) < nth:
if isprime(num):
primes.append(num)
num += 1
else:
num += 1
return primes[len(primes) - 1]
if __name__ == "__main__":
print(f"{solution() = }")
| """
Project Euler Problem 7: https://projecteuler.net/problem=7
10001st prime
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we
can see that the 6th prime is 13.
What is the 10001st prime number?
References:
- https://en.wikipedia.org/wiki/Prime_number
"""
def isprime(number: int) -> bool:
"""
Determines whether the given number is prime or not
>>> isprime(2)
True
>>> isprime(15)
False
>>> isprime(29)
True
"""
for i in range(2, int(number ** 0.5) + 1):
if number % i == 0:
return False
return True
def solution(nth: int = 10001) -> int:
"""
Returns the n-th prime number.
>>> solution(6)
13
>>> solution(1)
2
>>> solution(3)
5
>>> solution(20)
71
>>> solution(50)
229
>>> solution(100)
541
>>> solution(3.4)
5
>>> solution(0)
Traceback (most recent call last):
...
ValueError: Parameter nth must be greater than or equal to one.
>>> solution(-17)
Traceback (most recent call last):
...
ValueError: Parameter nth must be greater than or equal to one.
>>> solution([])
Traceback (most recent call last):
...
TypeError: Parameter nth must be int or castable to int.
>>> solution("asd")
Traceback (most recent call last):
...
TypeError: Parameter nth must be int or castable to int.
"""
try:
nth = int(nth)
except (TypeError, ValueError):
raise TypeError("Parameter nth must be int or castable to int.") from None
if nth <= 0:
raise ValueError("Parameter nth must be greater than or equal to one.")
primes: list[int] = []
num = 2
while len(primes) < nth:
if isprime(num):
primes.append(num)
num += 1
else:
num += 1
return primes[len(primes) - 1]
if __name__ == "__main__":
print(f"{solution() = }")
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Project Euler Problem 8: https://projecteuler.net/problem=8
Largest product in a series
The four adjacent digits in the 1000-digit number that have the greatest
product are 9 × 9 × 8 × 9 = 5832.
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
Find the thirteen adjacent digits in the 1000-digit number that have the
greatest product. What is the value of this product?
"""
from functools import reduce
N = (
"73167176531330624919225119674426574742355349194934"
"96983520312774506326239578318016984801869478851843"
"85861560789112949495459501737958331952853208805511"
"12540698747158523863050715693290963295227443043557"
"66896648950445244523161731856403098711121722383113"
"62229893423380308135336276614282806444486645238749"
"30358907296290491560440772390713810515859307960866"
"70172427121883998797908792274921901699720888093776"
"65727333001053367881220235421809751254540594752243"
"52584907711670556013604839586446706324415722155397"
"53697817977846174064955149290862569321978468622482"
"83972241375657056057490261407972968652414535100474"
"82166370484403199890008895243450658541227588666881"
"16427171479924442928230863465674813919123162824586"
"17866458359124566529476545682848912883142607690042"
"24219022671055626321111109370544217506941658960408"
"07198403850962455444362981230987879927244284909188"
"84580156166097919133875499200524063689912560717606"
"05886116467109405077541002256983155200055935729725"
"71636269561882670428252483600823257530420752963450"
)
def solution(n: str = N) -> int:
"""
Find the thirteen adjacent digits in the 1000-digit number n that have
the greatest product and returns it.
>>> solution("13978431290823798458352374")
609638400
>>> solution("13978431295823798458352374")
2612736000
>>> solution("1397843129582379841238352374")
209018880
"""
return max(
reduce(lambda x, y: int(x) * int(y), n[i : i + 13]) for i in range(len(n) - 12)
)
if __name__ == "__main__":
print(f"{solution() = }")
| """
Project Euler Problem 8: https://projecteuler.net/problem=8
Largest product in a series
The four adjacent digits in the 1000-digit number that have the greatest
product are 9 × 9 × 8 × 9 = 5832.
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
Find the thirteen adjacent digits in the 1000-digit number that have the
greatest product. What is the value of this product?
"""
from functools import reduce
N = (
"73167176531330624919225119674426574742355349194934"
"96983520312774506326239578318016984801869478851843"
"85861560789112949495459501737958331952853208805511"
"12540698747158523863050715693290963295227443043557"
"66896648950445244523161731856403098711121722383113"
"62229893423380308135336276614282806444486645238749"
"30358907296290491560440772390713810515859307960866"
"70172427121883998797908792274921901699720888093776"
"65727333001053367881220235421809751254540594752243"
"52584907711670556013604839586446706324415722155397"
"53697817977846174064955149290862569321978468622482"
"83972241375657056057490261407972968652414535100474"
"82166370484403199890008895243450658541227588666881"
"16427171479924442928230863465674813919123162824586"
"17866458359124566529476545682848912883142607690042"
"24219022671055626321111109370544217506941658960408"
"07198403850962455444362981230987879927244284909188"
"84580156166097919133875499200524063689912560717606"
"05886116467109405077541002256983155200055935729725"
"71636269561882670428252483600823257530420752963450"
)
def solution(n: str = N) -> int:
"""
Find the thirteen adjacent digits in the 1000-digit number n that have
the greatest product and returns it.
>>> solution("13978431290823798458352374")
609638400
>>> solution("13978431295823798458352374")
2612736000
>>> solution("1397843129582379841238352374")
209018880
"""
return max(
# mypy cannot properly interpret reduce
int(reduce(lambda x, y: str(int(x) * int(y)), n[i : i + 13]))
for i in range(len(n) - 12)
)
if __name__ == "__main__":
print(f"{solution() = }")
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Project Euler Problem 9: https://projecteuler.net/problem=9
Special Pythagorean triplet
A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
a^2 + b^2 = c^2
For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product a*b*c.
References:
- https://en.wikipedia.org/wiki/Pythagorean_triple
"""
def solution() -> int:
"""
Returns the product of a,b,c which are Pythagorean Triplet that satisfies
the following:
1. a < b < c
2. a**2 + b**2 = c**2
3. a + b + c = 1000
>>> solution()
31875000
"""
for a in range(300):
for b in range(a + 1, 400):
for c in range(b + 1, 500):
if (a + b + c) == 1000:
if (a ** 2) + (b ** 2) == (c ** 2):
return a * b * c
def solution_fast() -> int:
"""
Returns the product of a,b,c which are Pythagorean Triplet that satisfies
the following:
1. a < b < c
2. a**2 + b**2 = c**2
3. a + b + c = 1000
>>> solution_fast()
31875000
"""
for a in range(300):
for b in range(400):
c = 1000 - a - b
if a < b < c and (a ** 2) + (b ** 2) == (c ** 2):
return a * b * c
def benchmark() -> None:
"""
Benchmark code comparing two different version function.
"""
import timeit
print(
timeit.timeit("solution()", setup="from __main__ import solution", number=1000)
)
print(
timeit.timeit(
"solution_fast()", setup="from __main__ import solution_fast", number=1000
)
)
if __name__ == "__main__":
print(f"{solution() = }")
| """
Project Euler Problem 9: https://projecteuler.net/problem=9
Special Pythagorean triplet
A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
a^2 + b^2 = c^2
For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product a*b*c.
References:
- https://en.wikipedia.org/wiki/Pythagorean_triple
"""
def solution() -> int:
"""
Returns the product of a,b,c which are Pythagorean Triplet that satisfies
the following:
1. a < b < c
2. a**2 + b**2 = c**2
3. a + b + c = 1000
>>> solution()
31875000
"""
for a in range(300):
for b in range(a + 1, 400):
for c in range(b + 1, 500):
if (a + b + c) == 1000:
if (a ** 2) + (b ** 2) == (c ** 2):
return a * b * c
return -1
def solution_fast() -> int:
"""
Returns the product of a,b,c which are Pythagorean Triplet that satisfies
the following:
1. a < b < c
2. a**2 + b**2 = c**2
3. a + b + c = 1000
>>> solution_fast()
31875000
"""
for a in range(300):
for b in range(400):
c = 1000 - a - b
if a < b < c and (a ** 2) + (b ** 2) == (c ** 2):
return a * b * c
return -1
def benchmark() -> None:
"""
Benchmark code comparing two different version function.
"""
import timeit
print(
timeit.timeit("solution()", setup="from __main__ import solution", number=1000)
)
print(
timeit.timeit(
"solution_fast()", setup="from __main__ import solution_fast", number=1000
)
)
if __name__ == "__main__":
print(f"{solution() = }")
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Problem 14: https://projecteuler.net/problem=14
Problem Statement:
The following iterative sequence is defined for the set of positive integers:
n → n/2 (n is even)
n → 3n + 1 (n is odd)
Using the rule above and starting with 13, we generate the following sequence:
13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
It can be seen that this sequence (starting at 13 and finishing at 1) contains
10 terms. Although it has not been proved yet (Collatz Problem), it is thought
that all starting numbers finish at 1.
Which starting number, under one million, produces the longest chain?
"""
def solution(n: int = 1000000) -> int:
"""Returns the number under n that generates the longest sequence using the
formula:
n → n/2 (n is even)
n → 3n + 1 (n is odd)
# The code below has been commented due to slow execution affecting Travis.
# >>> solution(1000000)
# 837799
>>> solution(200)
171
>>> solution(5000)
3711
>>> solution(15000)
13255
"""
largest_number = 0
pre_counter = 0
for input1 in range(n):
counter = 1
number = input1
while number > 1:
if number % 2 == 0:
number /= 2
counter += 1
else:
number = (3 * number) + 1
counter += 1
if counter > pre_counter:
largest_number = input1
pre_counter = counter
return largest_number
if __name__ == "__main__":
print(solution(int(input().strip())))
| """
Problem 14: https://projecteuler.net/problem=14
Problem Statement:
The following iterative sequence is defined for the set of positive integers:
n → n/2 (n is even)
n → 3n + 1 (n is odd)
Using the rule above and starting with 13, we generate the following sequence:
13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
It can be seen that this sequence (starting at 13 and finishing at 1) contains
10 terms. Although it has not been proved yet (Collatz Problem), it is thought
that all starting numbers finish at 1.
Which starting number, under one million, produces the longest chain?
"""
def solution(n: int = 1000000) -> int:
"""Returns the number under n that generates the longest sequence using the
formula:
n → n/2 (n is even)
n → 3n + 1 (n is odd)
# The code below has been commented due to slow execution affecting Travis.
# >>> solution(1000000)
# 837799
>>> solution(200)
171
>>> solution(5000)
3711
>>> solution(15000)
13255
"""
largest_number = 0
pre_counter = 0
for input1 in range(n):
counter = 1
number = input1
while number > 1:
if number % 2 == 0:
number //= 2
counter += 1
else:
number = (3 * number) + 1
counter += 1
if counter > pre_counter:
largest_number = input1
pre_counter = counter
return largest_number
if __name__ == "__main__":
print(solution(int(input().strip())))
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
The Fibonacci sequence is defined by the recurrence relation:
Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.
Hence the first 12 terms will be:
F1 = 1
F2 = 1
F3 = 2
F4 = 3
F5 = 5
F6 = 8
F7 = 13
F8 = 21
F9 = 34
F10 = 55
F11 = 89
F12 = 144
The 12th term, F12, is the first term to contain three digits.
What is the index of the first term in the Fibonacci sequence to contain 1000
digits?
"""
def fibonacci_generator() -> int:
"""
A generator that produces numbers in the Fibonacci sequence
>>> generator = fibonacci_generator()
>>> next(generator)
1
>>> next(generator)
2
>>> next(generator)
3
>>> next(generator)
5
>>> next(generator)
8
"""
a, b = 0, 1
while True:
a, b = b, a + b
yield b
def solution(n: int = 1000) -> int:
"""Returns the index of the first term in the Fibonacci sequence to contain
n digits.
>>> solution(1000)
4782
>>> solution(100)
476
>>> solution(50)
237
>>> solution(3)
12
"""
answer = 1
gen = fibonacci_generator()
while len(str(next(gen))) < n:
answer += 1
return answer + 1
if __name__ == "__main__":
print(solution(int(str(input()).strip())))
| """
The Fibonacci sequence is defined by the recurrence relation:
Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.
Hence the first 12 terms will be:
F1 = 1
F2 = 1
F3 = 2
F4 = 3
F5 = 5
F6 = 8
F7 = 13
F8 = 21
F9 = 34
F10 = 55
F11 = 89
F12 = 144
The 12th term, F12, is the first term to contain three digits.
What is the index of the first term in the Fibonacci sequence to contain 1000
digits?
"""
from typing import Generator
def fibonacci_generator() -> Generator[int, None, None]:
"""
A generator that produces numbers in the Fibonacci sequence
>>> generator = fibonacci_generator()
>>> next(generator)
1
>>> next(generator)
2
>>> next(generator)
3
>>> next(generator)
5
>>> next(generator)
8
"""
a, b = 0, 1
while True:
a, b = b, a + b
yield b
def solution(n: int = 1000) -> int:
"""Returns the index of the first term in the Fibonacci sequence to contain
n digits.
>>> solution(1000)
4782
>>> solution(100)
476
>>> solution(50)
237
>>> solution(3)
12
"""
answer = 1
gen = fibonacci_generator()
while len(str(next(gen))) < n:
answer += 1
return answer + 1
if __name__ == "__main__":
print(solution(int(str(input()).strip())))
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Euler Problem 26
https://projecteuler.net/problem=26
Problem Statement:
A unit fraction contains 1 in the numerator. The decimal representation of the
unit fractions with denominators 2 to 10 are given:
1/2 = 0.5
1/3 = 0.(3)
1/4 = 0.25
1/5 = 0.2
1/6 = 0.1(6)
1/7 = 0.(142857)
1/8 = 0.125
1/9 = 0.(1)
1/10 = 0.1
Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be
seen that 1/7 has a 6-digit recurring cycle.
Find the value of d < 1000 for which 1/d contains the longest recurring cycle
in its decimal fraction part.
"""
def solution(numerator: int = 1, digit: int = 1000) -> int:
"""
Considering any range can be provided,
because as per the problem, the digit d < 1000
>>> solution(1, 10)
7
>>> solution(10, 100)
97
>>> solution(10, 1000)
983
"""
the_digit = 1
longest_list_length = 0
for divide_by_number in range(numerator, digit + 1):
has_been_divided = []
now_divide = numerator
for division_cycle in range(1, digit + 1):
if now_divide in has_been_divided:
if longest_list_length < len(has_been_divided):
longest_list_length = len(has_been_divided)
the_digit = divide_by_number
else:
has_been_divided.append(now_divide)
now_divide = now_divide * 10 % divide_by_number
return the_digit
# Tests
if __name__ == "__main__":
import doctest
doctest.testmod()
| """
Euler Problem 26
https://projecteuler.net/problem=26
Problem Statement:
A unit fraction contains 1 in the numerator. The decimal representation of the
unit fractions with denominators 2 to 10 are given:
1/2 = 0.5
1/3 = 0.(3)
1/4 = 0.25
1/5 = 0.2
1/6 = 0.1(6)
1/7 = 0.(142857)
1/8 = 0.125
1/9 = 0.(1)
1/10 = 0.1
Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be
seen that 1/7 has a 6-digit recurring cycle.
Find the value of d < 1000 for which 1/d contains the longest recurring cycle
in its decimal fraction part.
"""
def solution(numerator: int = 1, digit: int = 1000) -> int:
"""
Considering any range can be provided,
because as per the problem, the digit d < 1000
>>> solution(1, 10)
7
>>> solution(10, 100)
97
>>> solution(10, 1000)
983
"""
the_digit = 1
longest_list_length = 0
for divide_by_number in range(numerator, digit + 1):
has_been_divided: list[int] = []
now_divide = numerator
for division_cycle in range(1, digit + 1):
if now_divide in has_been_divided:
if longest_list_length < len(has_been_divided):
longest_list_length = len(has_been_divided)
the_digit = divide_by_number
else:
has_been_divided.append(now_divide)
now_divide = now_divide * 10 % divide_by_number
return the_digit
# Tests
if __name__ == "__main__":
import doctest
doctest.testmod()
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
The number 3797 has an interesting property. Being prime itself, it is possible
to continuously remove digits from left to right, and remain prime at each stage:
3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.
Find the sum of the only eleven primes that are both truncatable from left to right
and right to left.
NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
"""
from __future__ import annotations
seive = [True] * 1000001
seive[1] = False
i = 2
while i * i <= 1000000:
if seive[i]:
for j in range(i * i, 1000001, i):
seive[j] = False
i += 1
def is_prime(n: int) -> bool:
"""
Returns True if n is prime,
False otherwise, for 1 <= n <= 1000000
>>> is_prime(87)
False
>>> is_prime(1)
False
>>> is_prime(25363)
False
"""
return seive[n]
def list_truncated_nums(n: int) -> list[int]:
"""
Returns a list of all left and right truncated numbers of n
>>> list_truncated_nums(927628)
[927628, 27628, 92762, 7628, 9276, 628, 927, 28, 92, 8, 9]
>>> list_truncated_nums(467)
[467, 67, 46, 7, 4]
>>> list_truncated_nums(58)
[58, 8, 5]
"""
str_num = str(n)
list_nums = [n]
for i in range(1, len(str_num)):
list_nums.append(int(str_num[i:]))
list_nums.append(int(str_num[:-i]))
return list_nums
def validate(n: int) -> bool:
"""
To optimize the approach, we will rule out the numbers above 1000,
whose first or last three digits are not prime
>>> validate(74679)
False
>>> validate(235693)
False
>>> validate(3797)
True
"""
if len(str(n)) > 3:
if not is_prime(int(str(n)[-3:])) or not is_prime(int(str(n)[:3])):
return False
return True
def compute_truncated_primes(count: int = 11) -> list[int]:
"""
Returns the list of truncated primes
>>> compute_truncated_primes(11)
[23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397]
"""
list_truncated_primes = []
num = 13
while len(list_truncated_primes) != count:
if validate(num):
list_nums = list_truncated_nums(num)
if all(is_prime(i) for i in list_nums):
list_truncated_primes.append(num)
num += 2
return list_truncated_primes
def solution() -> int:
"""
Returns the sum of truncated primes
"""
return sum(compute_truncated_primes(11))
if __name__ == "__main__":
print(f"{sum(compute_truncated_primes(11)) = }")
| """
The number 3797 has an interesting property. Being prime itself, it is possible
to continuously remove digits from left to right, and remain prime at each stage:
3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.
Find the sum of the only eleven primes that are both truncatable from left to right
and right to left.
NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
"""
from __future__ import annotations
seive = [True] * 1000001
seive[1] = False
i = 2
while i * i <= 1000000:
if seive[i]:
for j in range(i * i, 1000001, i):
seive[j] = False
i += 1
def is_prime(n: int) -> bool:
"""
Returns True if n is prime,
False otherwise, for 1 <= n <= 1000000
>>> is_prime(87)
False
>>> is_prime(1)
False
>>> is_prime(25363)
False
"""
return seive[n]
def list_truncated_nums(n: int) -> list[int]:
"""
Returns a list of all left and right truncated numbers of n
>>> list_truncated_nums(927628)
[927628, 27628, 92762, 7628, 9276, 628, 927, 28, 92, 8, 9]
>>> list_truncated_nums(467)
[467, 67, 46, 7, 4]
>>> list_truncated_nums(58)
[58, 8, 5]
"""
str_num = str(n)
list_nums = [n]
for i in range(1, len(str_num)):
list_nums.append(int(str_num[i:]))
list_nums.append(int(str_num[:-i]))
return list_nums
def validate(n: int) -> bool:
"""
To optimize the approach, we will rule out the numbers above 1000,
whose first or last three digits are not prime
>>> validate(74679)
False
>>> validate(235693)
False
>>> validate(3797)
True
"""
if len(str(n)) > 3:
if not is_prime(int(str(n)[-3:])) or not is_prime(int(str(n)[:3])):
return False
return True
def compute_truncated_primes(count: int = 11) -> list[int]:
"""
Returns the list of truncated primes
>>> compute_truncated_primes(11)
[23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397]
"""
list_truncated_primes: list[int] = []
num = 13
while len(list_truncated_primes) != count:
if validate(num):
list_nums = list_truncated_nums(num)
if all(is_prime(i) for i in list_nums):
list_truncated_primes.append(num)
num += 2
return list_truncated_primes
def solution() -> int:
"""
Returns the sum of truncated primes
"""
return sum(compute_truncated_primes(11))
if __name__ == "__main__":
print(f"{sum(compute_truncated_primes(11)) = }")
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Problem 44: https://projecteuler.net/problem=44
Pentagonal numbers are generated by the formula, Pn=n(3n−1)/2. The first ten
pentagonal numbers are:
1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...
It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference,
70 − 22 = 48, is not pentagonal.
Find the pair of pentagonal numbers, Pj and Pk, for which their sum and difference
are pentagonal and D = |Pk − Pj| is minimised; what is the value of D?
"""
def is_pentagonal(n: int) -> bool:
"""
Returns True if n is pentagonal, False otherwise.
>>> is_pentagonal(330)
True
>>> is_pentagonal(7683)
False
>>> is_pentagonal(2380)
True
"""
root = (1 + 24 * n) ** 0.5
return ((1 + root) / 6) % 1 == 0
def solution(limit: int = 5000) -> int:
"""
Returns the minimum difference of two pentagonal numbers P1 and P2 such that
P1 + P2 is pentagonal and P2 - P1 is pentagonal.
>>> solution(5000)
5482660
"""
pentagonal_nums = [(i * (3 * i - 1)) // 2 for i in range(1, limit)]
for i, pentagonal_i in enumerate(pentagonal_nums):
for j in range(i, len(pentagonal_nums)):
pentagonal_j = pentagonal_nums[j]
a = pentagonal_i + pentagonal_j
b = pentagonal_j - pentagonal_i
if is_pentagonal(a) and is_pentagonal(b):
return b
if __name__ == "__main__":
print(f"{solution() = }")
| """
Problem 44: https://projecteuler.net/problem=44
Pentagonal numbers are generated by the formula, Pn=n(3n−1)/2. The first ten
pentagonal numbers are:
1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...
It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference,
70 − 22 = 48, is not pentagonal.
Find the pair of pentagonal numbers, Pj and Pk, for which their sum and difference
are pentagonal and D = |Pk − Pj| is minimised; what is the value of D?
"""
def is_pentagonal(n: int) -> bool:
"""
Returns True if n is pentagonal, False otherwise.
>>> is_pentagonal(330)
True
>>> is_pentagonal(7683)
False
>>> is_pentagonal(2380)
True
"""
root = (1 + 24 * n) ** 0.5
return ((1 + root) / 6) % 1 == 0
def solution(limit: int = 5000) -> int:
"""
Returns the minimum difference of two pentagonal numbers P1 and P2 such that
P1 + P2 is pentagonal and P2 - P1 is pentagonal.
>>> solution(5000)
5482660
"""
pentagonal_nums = [(i * (3 * i - 1)) // 2 for i in range(1, limit)]
for i, pentagonal_i in enumerate(pentagonal_nums):
for j in range(i, len(pentagonal_nums)):
pentagonal_j = pentagonal_nums[j]
a = pentagonal_i + pentagonal_j
b = pentagonal_j - pentagonal_i
if is_pentagonal(a) and is_pentagonal(b):
return b
return -1
if __name__ == "__main__":
print(f"{solution() = }")
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Problem 46: https://projecteuler.net/problem=46
It was proposed by Christian Goldbach that every odd composite number can be
written as the sum of a prime and twice a square.
9 = 7 + 2 × 12
15 = 7 + 2 × 22
21 = 3 + 2 × 32
25 = 7 + 2 × 32
27 = 19 + 2 × 22
33 = 31 + 2 × 12
It turns out that the conjecture was false.
What is the smallest odd composite that cannot be written as the sum of a
prime and twice a square?
"""
from __future__ import annotations
seive = [True] * 100001
i = 2
while i * i <= 100000:
if seive[i]:
for j in range(i * i, 100001, i):
seive[j] = False
i += 1
def is_prime(n: int) -> bool:
"""
Returns True if n is prime,
False otherwise, for 2 <= n <= 100000
>>> is_prime(87)
False
>>> is_prime(23)
True
>>> is_prime(25363)
False
"""
return seive[n]
odd_composites = [num for num in range(3, len(seive), 2) if not is_prime(num)]
def compute_nums(n: int) -> list[int]:
"""
Returns a list of first n odd composite numbers which do
not follow the conjecture.
>>> compute_nums(1)
[5777]
>>> compute_nums(2)
[5777, 5993]
>>> compute_nums(0)
Traceback (most recent call last):
...
ValueError: n must be >= 0
>>> compute_nums("a")
Traceback (most recent call last):
...
ValueError: n must be an integer
>>> compute_nums(1.1)
Traceback (most recent call last):
...
ValueError: n must be an integer
"""
if not isinstance(n, int):
raise ValueError("n must be an integer")
if n <= 0:
raise ValueError("n must be >= 0")
list_nums = []
for num in range(len(odd_composites)):
i = 0
while 2 * i * i <= odd_composites[num]:
rem = odd_composites[num] - 2 * i * i
if is_prime(rem):
break
i += 1
else:
list_nums.append(odd_composites[num])
if len(list_nums) == n:
return list_nums
def solution() -> int:
"""Return the solution to the problem"""
return compute_nums(1)[0]
if __name__ == "__main__":
print(f"{solution() = }")
| """
Problem 46: https://projecteuler.net/problem=46
It was proposed by Christian Goldbach that every odd composite number can be
written as the sum of a prime and twice a square.
9 = 7 + 2 × 12
15 = 7 + 2 × 22
21 = 3 + 2 × 32
25 = 7 + 2 × 32
27 = 19 + 2 × 22
33 = 31 + 2 × 12
It turns out that the conjecture was false.
What is the smallest odd composite that cannot be written as the sum of a
prime and twice a square?
"""
from __future__ import annotations
seive = [True] * 100001
i = 2
while i * i <= 100000:
if seive[i]:
for j in range(i * i, 100001, i):
seive[j] = False
i += 1
def is_prime(n: int) -> bool:
"""
Returns True if n is prime,
False otherwise, for 2 <= n <= 100000
>>> is_prime(87)
False
>>> is_prime(23)
True
>>> is_prime(25363)
False
"""
return seive[n]
odd_composites = [num for num in range(3, len(seive), 2) if not is_prime(num)]
def compute_nums(n: int) -> list[int]:
"""
Returns a list of first n odd composite numbers which do
not follow the conjecture.
>>> compute_nums(1)
[5777]
>>> compute_nums(2)
[5777, 5993]
>>> compute_nums(0)
Traceback (most recent call last):
...
ValueError: n must be >= 0
>>> compute_nums("a")
Traceback (most recent call last):
...
ValueError: n must be an integer
>>> compute_nums(1.1)
Traceback (most recent call last):
...
ValueError: n must be an integer
"""
if not isinstance(n, int):
raise ValueError("n must be an integer")
if n <= 0:
raise ValueError("n must be >= 0")
list_nums = []
for num in range(len(odd_composites)):
i = 0
while 2 * i * i <= odd_composites[num]:
rem = odd_composites[num] - 2 * i * i
if is_prime(rem):
break
i += 1
else:
list_nums.append(odd_composites[num])
if len(list_nums) == n:
return list_nums
return []
def solution() -> int:
"""Return the solution to the problem"""
return compute_nums(1)[0]
if __name__ == "__main__":
print(f"{solution() = }")
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
https://projecteuler.net/problem=51
Prime digit replacements
Problem 51
By replacing the 1st digit of the 2-digit number *3, it turns out that six of
the nine possible values: 13, 23, 43, 53, 73, and 83, are all prime.
By replacing the 3rd and 4th digits of 56**3 with the same digit, this 5-digit
number is the first example having seven primes among the ten generated numbers,
yielding the family: 56003, 56113, 56333, 56443, 56663, 56773, and 56993.
Consequently 56003, being the first member of this family, is the smallest prime
with this property.
Find the smallest prime which, by replacing part of the number (not necessarily
adjacent digits) with the same digit, is part of an eight prime value family.
"""
from __future__ import annotations
from collections import Counter
def prime_sieve(n: int) -> list[int]:
"""
Sieve of Erotosthenes
Function to return all the prime numbers up to a certain number
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
>>> prime_sieve(3)
[2]
>>> prime_sieve(50)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
"""
is_prime = [True] * n
is_prime[0] = False
is_prime[1] = False
is_prime[2] = True
for i in range(3, int(n ** 0.5 + 1), 2):
index = i * 2
while index < n:
is_prime[index] = False
index = index + i
primes = [2]
for i in range(3, n, 2):
if is_prime[i]:
primes.append(i)
return primes
def digit_replacements(number: int) -> list[list[int]]:
"""
Returns all the possible families of digit replacements in a number which
contains at least one repeating digit
>>> digit_replacements(544)
[[500, 511, 522, 533, 544, 555, 566, 577, 588, 599]]
>>> digit_replacements(3112)
[[3002, 3112, 3222, 3332, 3442, 3552, 3662, 3772, 3882, 3992]]
"""
number = str(number)
replacements = []
digits = ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9"]
for duplicate in Counter(number) - Counter(set(number)):
family = [int(number.replace(duplicate, digit)) for digit in digits]
replacements.append(family)
return replacements
def solution(family_length: int = 8) -> int:
"""
Returns the solution of the problem
>>> solution(2)
229399
>>> solution(3)
221311
"""
numbers_checked = set()
# Filter primes with less than 3 replaceable digits
primes = {
x for x in set(prime_sieve(1_000_000)) if len(str(x)) - len(set(str(x))) >= 3
}
for prime in primes:
if prime in numbers_checked:
continue
replacements = digit_replacements(prime)
for family in replacements:
numbers_checked.update(family)
primes_in_family = primes.intersection(family)
if len(primes_in_family) != family_length:
continue
return min(primes_in_family)
if __name__ == "__main__":
print(solution())
| """
https://projecteuler.net/problem=51
Prime digit replacements
Problem 51
By replacing the 1st digit of the 2-digit number *3, it turns out that six of
the nine possible values: 13, 23, 43, 53, 73, and 83, are all prime.
By replacing the 3rd and 4th digits of 56**3 with the same digit, this 5-digit
number is the first example having seven primes among the ten generated numbers,
yielding the family: 56003, 56113, 56333, 56443, 56663, 56773, and 56993.
Consequently 56003, being the first member of this family, is the smallest prime
with this property.
Find the smallest prime which, by replacing part of the number (not necessarily
adjacent digits) with the same digit, is part of an eight prime value family.
"""
from __future__ import annotations
from collections import Counter
def prime_sieve(n: int) -> list[int]:
"""
Sieve of Erotosthenes
Function to return all the prime numbers up to a certain number
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
>>> prime_sieve(3)
[2]
>>> prime_sieve(50)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
"""
is_prime = [True] * n
is_prime[0] = False
is_prime[1] = False
is_prime[2] = True
for i in range(3, int(n ** 0.5 + 1), 2):
index = i * 2
while index < n:
is_prime[index] = False
index = index + i
primes = [2]
for i in range(3, n, 2):
if is_prime[i]:
primes.append(i)
return primes
def digit_replacements(number: int) -> list[list[int]]:
"""
Returns all the possible families of digit replacements in a number which
contains at least one repeating digit
>>> digit_replacements(544)
[[500, 511, 522, 533, 544, 555, 566, 577, 588, 599]]
>>> digit_replacements(3112)
[[3002, 3112, 3222, 3332, 3442, 3552, 3662, 3772, 3882, 3992]]
"""
number_str = str(number)
replacements = []
digits = ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9"]
for duplicate in Counter(number_str) - Counter(set(number_str)):
family = [int(number_str.replace(duplicate, digit)) for digit in digits]
replacements.append(family)
return replacements
def solution(family_length: int = 8) -> int:
"""
Returns the solution of the problem
>>> solution(2)
229399
>>> solution(3)
221311
"""
numbers_checked = set()
# Filter primes with less than 3 replaceable digits
primes = {
x for x in set(prime_sieve(1_000_000)) if len(str(x)) - len(set(str(x))) >= 3
}
for prime in primes:
if prime in numbers_checked:
continue
replacements = digit_replacements(prime)
for family in replacements:
numbers_checked.update(family)
primes_in_family = primes.intersection(family)
if len(primes_in_family) != family_length:
continue
return min(primes_in_family)
return -1
if __name__ == "__main__":
print(solution())
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Project Euler Problem 074: https://projecteuler.net/problem=74
Starting from any positive integer number
it is possible to attain another one summing the factorial of its digits.
Repeating this step, we can build chains of numbers.
It is not difficult to prove that EVERY starting number
will eventually get stuck in a loop.
The request is to find how many numbers less than one million
produce a chain with exactly 60 non repeating items.
Solution approach:
This solution simply consists in a loop that generates
the chains of non repeating items.
The generation of the chain stops before a repeating item
or if the size of the chain is greater then the desired one.
After generating each chain, the length is checked and the
counter increases.
"""
factorial_cache = {}
factorial_sum_cache = {}
def factorial(a: int) -> int:
"""Returns the factorial of the input a
>>> factorial(5)
120
>>> factorial(6)
720
>>> factorial(0)
1
"""
# The factorial function is not defined for negative numbers
if a < 0:
raise ValueError("Invalid negative input!", a)
if a in factorial_cache:
return factorial_cache[a]
# The case of 0! is handled separately
if a == 0:
factorial_cache[a] = 1
else:
# use a temporary support variable to store the computation
temporary_number = a
temporary_computation = 1
while temporary_number > 0:
temporary_computation *= temporary_number
temporary_number -= 1
factorial_cache[a] = temporary_computation
return factorial_cache[a]
def factorial_sum(a: int) -> int:
"""Function to perform the sum of the factorial
of all the digits in a
>>> factorial_sum(69)
363600
"""
if a in factorial_sum_cache:
return factorial_sum_cache[a]
# Prepare a variable to hold the computation
fact_sum = 0
""" Convert a in string to iterate on its digits
convert the digit back into an int
and add its factorial to fact_sum.
"""
for i in str(a):
fact_sum += factorial(int(i))
factorial_sum_cache[a] = fact_sum
return fact_sum
def solution(chain_length: int = 60, number_limit: int = 1000000) -> int:
"""Returns the number of numbers that produce
chains with exactly 60 non repeating elements.
>>> solution(10, 1000)
26
"""
# the counter for the chains with the exact desired length
chain_counter = 0
for i in range(1, number_limit + 1):
# The temporary list will contain the elements of the chain
chain_set = {i}
len_chain_set = 1
last_chain_element = i
# The new element of the chain
new_chain_element = factorial_sum(last_chain_element)
# Stop computing the chain when you find a repeating item
# or the length it greater then the desired one.
while new_chain_element not in chain_set and len_chain_set <= chain_length:
chain_set.add(new_chain_element)
len_chain_set += 1
last_chain_element = new_chain_element
new_chain_element = factorial_sum(last_chain_element)
# If the while exited because the chain list contains the exact amount
# of elements increase the counter
if len_chain_set == chain_length:
chain_counter += 1
return chain_counter
if __name__ == "__main__":
import doctest
doctest.testmod()
print(f"{solution()}")
| """
Project Euler Problem 074: https://projecteuler.net/problem=74
Starting from any positive integer number
it is possible to attain another one summing the factorial of its digits.
Repeating this step, we can build chains of numbers.
It is not difficult to prove that EVERY starting number
will eventually get stuck in a loop.
The request is to find how many numbers less than one million
produce a chain with exactly 60 non repeating items.
Solution approach:
This solution simply consists in a loop that generates
the chains of non repeating items.
The generation of the chain stops before a repeating item
or if the size of the chain is greater then the desired one.
After generating each chain, the length is checked and the
counter increases.
"""
factorial_cache: dict[int, int] = {}
factorial_sum_cache: dict[int, int] = {}
def factorial(a: int) -> int:
"""Returns the factorial of the input a
>>> factorial(5)
120
>>> factorial(6)
720
>>> factorial(0)
1
"""
# The factorial function is not defined for negative numbers
if a < 0:
raise ValueError("Invalid negative input!", a)
if a in factorial_cache:
return factorial_cache[a]
# The case of 0! is handled separately
if a == 0:
factorial_cache[a] = 1
else:
# use a temporary support variable to store the computation
temporary_number = a
temporary_computation = 1
while temporary_number > 0:
temporary_computation *= temporary_number
temporary_number -= 1
factorial_cache[a] = temporary_computation
return factorial_cache[a]
def factorial_sum(a: int) -> int:
"""Function to perform the sum of the factorial
of all the digits in a
>>> factorial_sum(69)
363600
"""
if a in factorial_sum_cache:
return factorial_sum_cache[a]
# Prepare a variable to hold the computation
fact_sum = 0
""" Convert a in string to iterate on its digits
convert the digit back into an int
and add its factorial to fact_sum.
"""
for i in str(a):
fact_sum += factorial(int(i))
factorial_sum_cache[a] = fact_sum
return fact_sum
def solution(chain_length: int = 60, number_limit: int = 1000000) -> int:
"""Returns the number of numbers that produce
chains with exactly 60 non repeating elements.
>>> solution(10, 1000)
26
"""
# the counter for the chains with the exact desired length
chain_counter = 0
for i in range(1, number_limit + 1):
# The temporary list will contain the elements of the chain
chain_set = {i}
len_chain_set = 1
last_chain_element = i
# The new element of the chain
new_chain_element = factorial_sum(last_chain_element)
# Stop computing the chain when you find a repeating item
# or the length it greater then the desired one.
while new_chain_element not in chain_set and len_chain_set <= chain_length:
chain_set.add(new_chain_element)
len_chain_set += 1
last_chain_element = new_chain_element
new_chain_element = factorial_sum(last_chain_element)
# If the while exited because the chain list contains the exact amount
# of elements increase the counter
if len_chain_set == chain_length:
chain_counter += 1
return chain_counter
if __name__ == "__main__":
import doctest
doctest.testmod()
print(f"{solution()}")
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Project Euler Problem 80: https://projecteuler.net/problem=80
Author: Sandeep Gupta
Problem statement: For the first one hundred natural numbers, find the total of
the digital sums of the first one hundred decimal digits for all the irrational
square roots.
Time: 5 October 2020, 18:30
"""
import decimal
def solution() -> int:
"""
To evaluate the sum, Used decimal python module to calculate the decimal
places up to 100, the most important thing would be take calculate
a few extra places for decimal otherwise there will be rounding
error.
>>> solution()
40886
"""
answer = 0
decimal_context = decimal.Context(prec=105)
for i in range(2, 100):
number = decimal.Decimal(i)
sqrt_number = number.sqrt(decimal_context)
if len(str(sqrt_number)) > 1:
answer += int(str(sqrt_number)[0])
sqrt_number = str(sqrt_number)[2:101]
answer += sum(int(x) for x in sqrt_number)
return answer
if __name__ == "__main__":
import doctest
doctest.testmod()
| """
Project Euler Problem 80: https://projecteuler.net/problem=80
Author: Sandeep Gupta
Problem statement: For the first one hundred natural numbers, find the total of
the digital sums of the first one hundred decimal digits for all the irrational
square roots.
Time: 5 October 2020, 18:30
"""
import decimal
def solution() -> int:
"""
To evaluate the sum, Used decimal python module to calculate the decimal
places up to 100, the most important thing would be take calculate
a few extra places for decimal otherwise there will be rounding
error.
>>> solution()
40886
"""
answer = 0
decimal_context = decimal.Context(prec=105)
for i in range(2, 100):
number = decimal.Decimal(i)
sqrt_number = number.sqrt(decimal_context)
if len(str(sqrt_number)) > 1:
answer += int(str(sqrt_number)[0])
sqrt_number_str = str(sqrt_number)[2:101]
answer += sum(int(x) for x in sqrt_number_str)
return answer
if __name__ == "__main__":
import doctest
doctest.testmod()
print(f"{solution() = }")
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Problem:
Comparing two numbers written in index form like 2'11 and 3'7 is not difficult, as any
calculator would confirm that 2^11 = 2048 < 3^7 = 2187.
However, confirming that 632382^518061 > 519432^525806 would be much more difficult, as
both numbers contain over three million digits.
Using base_exp.txt, a 22K text file containing one thousand lines with a base/exponent
pair on each line, determine which line number has the greatest numerical value.
NOTE: The first two lines in the file represent the numbers in the example given above.
"""
import os
from math import log10
def solution(data_file: str = "base_exp.txt") -> int:
"""
>>> solution()
709
"""
largest = [0, 0]
for i, line in enumerate(open(os.path.join(os.path.dirname(__file__), data_file))):
a, x = list(map(int, line.split(",")))
if x * log10(a) > largest[0]:
largest = [x * log10(a), i + 1]
return largest[1]
if __name__ == "__main__":
print(solution())
| """
Problem:
Comparing two numbers written in index form like 2'11 and 3'7 is not difficult, as any
calculator would confirm that 2^11 = 2048 < 3^7 = 2187.
However, confirming that 632382^518061 > 519432^525806 would be much more difficult, as
both numbers contain over three million digits.
Using base_exp.txt, a 22K text file containing one thousand lines with a base/exponent
pair on each line, determine which line number has the greatest numerical value.
NOTE: The first two lines in the file represent the numbers in the example given above.
"""
import os
from math import log10
def solution(data_file: str = "base_exp.txt") -> int:
"""
>>> solution()
709
"""
largest: float = 0
result = 0
for i, line in enumerate(open(os.path.join(os.path.dirname(__file__), data_file))):
a, x = list(map(int, line.split(",")))
if x * log10(a) > largest:
largest = x * log10(a)
result = i + 1
return result
if __name__ == "__main__":
print(solution())
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
If we are presented with the first k terms of a sequence it is impossible to say with
certainty the value of the next term, as there are infinitely many polynomial functions
that can model the sequence.
As an example, let us consider the sequence of cube
numbers. This is defined by the generating function,
u(n) = n3: 1, 8, 27, 64, 125, 216, ...
Suppose we were only given the first two terms of this sequence. Working on the
principle that "simple is best" we should assume a linear relationship and predict the
next term to be 15 (common difference 7). Even if we were presented with the first three
terms, by the same principle of simplicity, a quadratic relationship should be
assumed.
We shall define OP(k, n) to be the nth term of the optimum polynomial
generating function for the first k terms of a sequence. It should be clear that
OP(k, n) will accurately generate the terms of the sequence for n ≤ k, and potentially
the first incorrect term (FIT) will be OP(k, k+1); in which case we shall call it a
bad OP (BOP).
As a basis, if we were only given the first term of sequence, it would be most
sensible to assume constancy; that is, for n ≥ 2, OP(1, n) = u(1).
Hence we obtain the
following OPs for the cubic sequence:
OP(1, n) = 1 1, 1, 1, 1, ...
OP(2, n) = 7n-6 1, 8, 15, ...
OP(3, n) = 6n^2-11n+6 1, 8, 27, 58, ...
OP(4, n) = n^3 1, 8, 27, 64, 125, ...
Clearly no BOPs exist for k ≥ 4.
By considering the sum of FITs generated by the BOPs (indicated in red above), we
obtain 1 + 15 + 58 = 74.
Consider the following tenth degree polynomial generating function:
1 - n + n^2 - n^3 + n^4 - n^5 + n^6 - n^7 + n^8 - n^9 + n^10
Find the sum of FITs for the BOPs.
"""
from __future__ import annotations
from typing import Callable, Union
Matrix = list[list[Union[float, int]]]
def solve(matrix: Matrix, vector: Matrix) -> Matrix:
"""
Solve the linear system of equations Ax = b (A = "matrix", b = "vector")
for x using Gaussian elimination and back substitution. We assume that A
is an invertible square matrix and that b is a column vector of the
same height.
>>> solve([[1, 0], [0, 1]], [[1],[2]])
[[1.0], [2.0]]
>>> solve([[2, 1, -1],[-3, -1, 2],[-2, 1, 2]],[[8], [-11],[-3]])
[[2.0], [3.0], [-1.0]]
"""
size: int = len(matrix)
augmented: Matrix = [[0 for _ in range(size + 1)] for _ in range(size)]
row: int
row2: int
col: int
col2: int
pivot_row: int
ratio: float
for row in range(size):
for col in range(size):
augmented[row][col] = matrix[row][col]
augmented[row][size] = vector[row][0]
row = 0
col = 0
while row < size and col < size:
# pivoting
pivot_row = max((abs(augmented[row2][col]), row2) for row2 in range(col, size))[
1
]
if augmented[pivot_row][col] == 0:
col += 1
continue
else:
augmented[row], augmented[pivot_row] = augmented[pivot_row], augmented[row]
for row2 in range(row + 1, size):
ratio = augmented[row2][col] / augmented[row][col]
augmented[row2][col] = 0
for col2 in range(col + 1, size + 1):
augmented[row2][col2] -= augmented[row][col2] * ratio
row += 1
col += 1
# back substitution
for col in range(1, size):
for row in range(col):
ratio = augmented[row][col] / augmented[col][col]
for col2 in range(col, size + 1):
augmented[row][col2] -= augmented[col][col2] * ratio
# round to get rid of numbers like 2.000000000000004
return [
[round(augmented[row][size] / augmented[row][row], 10)] for row in range(size)
]
def interpolate(y_list: list[int]) -> Callable[[int], int]:
"""
Given a list of data points (1,y0),(2,y1), ..., return a function that
interpolates the data points. We find the coefficients of the interpolating
polynomial by solving a system of linear equations corresponding to
x = 1, 2, 3...
>>> interpolate([1])(3)
1
>>> interpolate([1, 8])(3)
15
>>> interpolate([1, 8, 27])(4)
58
>>> interpolate([1, 8, 27, 64])(6)
216
"""
size: int = len(y_list)
matrix: Matrix = [[0 for _ in range(size)] for _ in range(size)]
vector: Matrix = [[0] for _ in range(size)]
coeffs: Matrix
x_val: int
y_val: int
col: int
for x_val, y_val in enumerate(y_list):
for col in range(size):
matrix[x_val][col] = (x_val + 1) ** (size - col - 1)
vector[x_val][0] = y_val
coeffs = solve(matrix, vector)
def interpolated_func(var: int) -> int:
"""
>>> interpolate([1])(3)
1
>>> interpolate([1, 8])(3)
15
>>> interpolate([1, 8, 27])(4)
58
>>> interpolate([1, 8, 27, 64])(6)
216
"""
return sum(
round(coeffs[x_val][0]) * (var ** (size - x_val - 1))
for x_val in range(size)
)
return interpolated_func
def question_function(variable: int) -> int:
"""
The generating function u as specified in the question.
>>> question_function(0)
1
>>> question_function(1)
1
>>> question_function(5)
8138021
>>> question_function(10)
9090909091
"""
return (
1
- variable
+ variable ** 2
- variable ** 3
+ variable ** 4
- variable ** 5
+ variable ** 6
- variable ** 7
+ variable ** 8
- variable ** 9
+ variable ** 10
)
def solution(func: Callable[[int], int] = question_function, order: int = 10) -> int:
"""
Find the sum of the FITs of the BOPS. For each interpolating polynomial of order
1, 2, ... , 10, find the first x such that the value of the polynomial at x does
not equal u(x).
>>> solution(lambda n: n ** 3, 3)
74
"""
data_points: list[int] = [func(x_val) for x_val in range(1, order + 1)]
polynomials: list[Callable[[int], int]] = [
interpolate(data_points[:max_coeff]) for max_coeff in range(1, order + 1)
]
ret: int = 0
poly: int
x_val: int
for poly in polynomials:
x_val = 1
while func(x_val) == poly(x_val):
x_val += 1
ret += poly(x_val)
return ret
if __name__ == "__main__":
print(f"{solution() = }")
| """
If we are presented with the first k terms of a sequence it is impossible to say with
certainty the value of the next term, as there are infinitely many polynomial functions
that can model the sequence.
As an example, let us consider the sequence of cube
numbers. This is defined by the generating function,
u(n) = n3: 1, 8, 27, 64, 125, 216, ...
Suppose we were only given the first two terms of this sequence. Working on the
principle that "simple is best" we should assume a linear relationship and predict the
next term to be 15 (common difference 7). Even if we were presented with the first three
terms, by the same principle of simplicity, a quadratic relationship should be
assumed.
We shall define OP(k, n) to be the nth term of the optimum polynomial
generating function for the first k terms of a sequence. It should be clear that
OP(k, n) will accurately generate the terms of the sequence for n ≤ k, and potentially
the first incorrect term (FIT) will be OP(k, k+1); in which case we shall call it a
bad OP (BOP).
As a basis, if we were only given the first term of sequence, it would be most
sensible to assume constancy; that is, for n ≥ 2, OP(1, n) = u(1).
Hence we obtain the
following OPs for the cubic sequence:
OP(1, n) = 1 1, 1, 1, 1, ...
OP(2, n) = 7n-6 1, 8, 15, ...
OP(3, n) = 6n^2-11n+6 1, 8, 27, 58, ...
OP(4, n) = n^3 1, 8, 27, 64, 125, ...
Clearly no BOPs exist for k ≥ 4.
By considering the sum of FITs generated by the BOPs (indicated in red above), we
obtain 1 + 15 + 58 = 74.
Consider the following tenth degree polynomial generating function:
1 - n + n^2 - n^3 + n^4 - n^5 + n^6 - n^7 + n^8 - n^9 + n^10
Find the sum of FITs for the BOPs.
"""
from __future__ import annotations
from typing import Callable, Union
Matrix = list[list[Union[float, int]]]
def solve(matrix: Matrix, vector: Matrix) -> Matrix:
"""
Solve the linear system of equations Ax = b (A = "matrix", b = "vector")
for x using Gaussian elimination and back substitution. We assume that A
is an invertible square matrix and that b is a column vector of the
same height.
>>> solve([[1, 0], [0, 1]], [[1],[2]])
[[1.0], [2.0]]
>>> solve([[2, 1, -1],[-3, -1, 2],[-2, 1, 2]],[[8], [-11],[-3]])
[[2.0], [3.0], [-1.0]]
"""
size: int = len(matrix)
augmented: Matrix = [[0 for _ in range(size + 1)] for _ in range(size)]
row: int
row2: int
col: int
col2: int
pivot_row: int
ratio: float
for row in range(size):
for col in range(size):
augmented[row][col] = matrix[row][col]
augmented[row][size] = vector[row][0]
row = 0
col = 0
while row < size and col < size:
# pivoting
pivot_row = max((abs(augmented[row2][col]), row2) for row2 in range(col, size))[
1
]
if augmented[pivot_row][col] == 0:
col += 1
continue
else:
augmented[row], augmented[pivot_row] = augmented[pivot_row], augmented[row]
for row2 in range(row + 1, size):
ratio = augmented[row2][col] / augmented[row][col]
augmented[row2][col] = 0
for col2 in range(col + 1, size + 1):
augmented[row2][col2] -= augmented[row][col2] * ratio
row += 1
col += 1
# back substitution
for col in range(1, size):
for row in range(col):
ratio = augmented[row][col] / augmented[col][col]
for col2 in range(col, size + 1):
augmented[row][col2] -= augmented[col][col2] * ratio
# round to get rid of numbers like 2.000000000000004
return [
[round(augmented[row][size] / augmented[row][row], 10)] for row in range(size)
]
def interpolate(y_list: list[int]) -> Callable[[int], int]:
"""
Given a list of data points (1,y0),(2,y1), ..., return a function that
interpolates the data points. We find the coefficients of the interpolating
polynomial by solving a system of linear equations corresponding to
x = 1, 2, 3...
>>> interpolate([1])(3)
1
>>> interpolate([1, 8])(3)
15
>>> interpolate([1, 8, 27])(4)
58
>>> interpolate([1, 8, 27, 64])(6)
216
"""
size: int = len(y_list)
matrix: Matrix = [[0 for _ in range(size)] for _ in range(size)]
vector: Matrix = [[0] for _ in range(size)]
coeffs: Matrix
x_val: int
y_val: int
col: int
for x_val, y_val in enumerate(y_list):
for col in range(size):
matrix[x_val][col] = (x_val + 1) ** (size - col - 1)
vector[x_val][0] = y_val
coeffs = solve(matrix, vector)
def interpolated_func(var: int) -> int:
"""
>>> interpolate([1])(3)
1
>>> interpolate([1, 8])(3)
15
>>> interpolate([1, 8, 27])(4)
58
>>> interpolate([1, 8, 27, 64])(6)
216
"""
return sum(
round(coeffs[x_val][0]) * (var ** (size - x_val - 1))
for x_val in range(size)
)
return interpolated_func
def question_function(variable: int) -> int:
"""
The generating function u as specified in the question.
>>> question_function(0)
1
>>> question_function(1)
1
>>> question_function(5)
8138021
>>> question_function(10)
9090909091
"""
return (
1
- variable
+ variable ** 2
- variable ** 3
+ variable ** 4
- variable ** 5
+ variable ** 6
- variable ** 7
+ variable ** 8
- variable ** 9
+ variable ** 10
)
def solution(func: Callable[[int], int] = question_function, order: int = 10) -> int:
"""
Find the sum of the FITs of the BOPS. For each interpolating polynomial of order
1, 2, ... , 10, find the first x such that the value of the polynomial at x does
not equal u(x).
>>> solution(lambda n: n ** 3, 3)
74
"""
data_points: list[int] = [func(x_val) for x_val in range(1, order + 1)]
polynomials: list[Callable[[int], int]] = [
interpolate(data_points[:max_coeff]) for max_coeff in range(1, order + 1)
]
ret: int = 0
poly: Callable[[int], int]
x_val: int
for poly in polynomials:
x_val = 1
while func(x_val) == poly(x_val):
x_val += 1
ret += poly(x_val)
return ret
if __name__ == "__main__":
print(f"{solution() = }")
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Project Euler Problem 188: https://projecteuler.net/problem=188
The hyperexponentiation of a number
The hyperexponentiation or tetration of a number a by a positive integer b,
denoted by a↑↑b or b^a, is recursively defined by:
a↑↑1 = a,
a↑↑(k+1) = a(a↑↑k).
Thus we have e.g. 3↑↑2 = 3^3 = 27, hence 3↑↑3 = 3^27 = 7625597484987 and
3↑↑4 is roughly 103.6383346400240996*10^12.
Find the last 8 digits of 1777↑↑1855.
References:
- https://en.wikipedia.org/wiki/Tetration
"""
# small helper function for modular exponentiation
def _modexpt(base: int, exponent: int, modulo_value: int) -> int:
"""
Returns the modular exponentiation, that is the value
of `base ** exponent % modulo_value`, without calculating
the actual number.
>>> _modexpt(2, 4, 10)
6
>>> _modexpt(2, 1024, 100)
16
>>> _modexpt(13, 65535, 7)
6
"""
if exponent == 1:
return base
if exponent % 2 == 0:
x = _modexpt(base, exponent / 2, modulo_value) % modulo_value
return (x * x) % modulo_value
else:
return (base * _modexpt(base, exponent - 1, modulo_value)) % modulo_value
def solution(base: int = 1777, height: int = 1855, digits: int = 8) -> int:
"""
Returns the last 8 digits of the hyperexponentiation of base by
height, i.e. the number base↑↑height:
>>> solution(base=3, height=2)
27
>>> solution(base=3, height=3)
97484987
>>> solution(base=123, height=456, digits=4)
2547
"""
# calculate base↑↑height by right-assiciative repeated modular
# exponentiation
result = base
for i in range(1, height):
result = _modexpt(base, result, 10 ** digits)
return result
if __name__ == "__main__":
print(f"{solution() = }")
| """
Project Euler Problem 188: https://projecteuler.net/problem=188
The hyperexponentiation of a number
The hyperexponentiation or tetration of a number a by a positive integer b,
denoted by a↑↑b or b^a, is recursively defined by:
a↑↑1 = a,
a↑↑(k+1) = a(a↑↑k).
Thus we have e.g. 3↑↑2 = 3^3 = 27, hence 3↑↑3 = 3^27 = 7625597484987 and
3↑↑4 is roughly 103.6383346400240996*10^12.
Find the last 8 digits of 1777↑↑1855.
References:
- https://en.wikipedia.org/wiki/Tetration
"""
# small helper function for modular exponentiation (fast exponentiation algorithm)
def _modexpt(base: int, exponent: int, modulo_value: int) -> int:
"""
Returns the modular exponentiation, that is the value
of `base ** exponent % modulo_value`, without calculating
the actual number.
>>> _modexpt(2, 4, 10)
6
>>> _modexpt(2, 1024, 100)
16
>>> _modexpt(13, 65535, 7)
6
"""
if exponent == 1:
return base
if exponent % 2 == 0:
x = _modexpt(base, exponent // 2, modulo_value) % modulo_value
return (x * x) % modulo_value
else:
return (base * _modexpt(base, exponent - 1, modulo_value)) % modulo_value
def solution(base: int = 1777, height: int = 1855, digits: int = 8) -> int:
"""
Returns the last 8 digits of the hyperexponentiation of base by
height, i.e. the number base↑↑height:
>>> solution(base=3, height=2)
27
>>> solution(base=3, height=3)
97484987
>>> solution(base=123, height=456, digits=4)
2547
"""
# calculate base↑↑height by right-assiciative repeated modular
# exponentiation
result = base
for i in range(1, height):
result = _modexpt(base, result, 10 ** digits)
return result
if __name__ == "__main__":
print(f"{solution() = }")
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Prize Strings
Problem 191
A particular school offers cash rewards to children with good attendance and
punctuality. If they are absent for three consecutive days or late on more
than one occasion then they forfeit their prize.
During an n-day period a trinary string is formed for each child consisting
of L's (late), O's (on time), and A's (absent).
Although there are eighty-one trinary strings for a 4-day period that can be
formed, exactly forty-three strings would lead to a prize:
OOOO OOOA OOOL OOAO OOAA OOAL OOLO OOLA OAOO OAOA
OAOL OAAO OAAL OALO OALA OLOO OLOA OLAO OLAA AOOO
AOOA AOOL AOAO AOAA AOAL AOLO AOLA AAOO AAOA AAOL
AALO AALA ALOO ALOA ALAO ALAA LOOO LOOA LOAO LOAA
LAOO LAOA LAAO
How many "prize" strings exist over a 30-day period?
References:
- The original Project Euler project page:
https://projecteuler.net/problem=191
"""
cache = {}
def _calculate(days: int, absent: int, late: int) -> int:
"""
A small helper function for the recursion, mainly to have
a clean interface for the solution() function below.
It should get called with the number of days (corresponding
to the desired length of the 'prize strings'), and the
initial values for the number of consecutive absent days and
number of total late days.
>>> _calculate(days=4, absent=0, late=0)
43
>>> _calculate(days=30, absent=2, late=0)
0
>>> _calculate(days=30, absent=1, late=0)
98950096
"""
# if we are absent twice, or late 3 consecutive days,
# no further prize strings are possible
if late == 3 or absent == 2:
return 0
# if we have no days left, and have not failed any other rules,
# we have a prize string
if days == 0:
return 1
# No easy solution, so now we need to do the recursive calculation
# First, check if the combination is already in the cache, and
# if yes, return the stored value from there since we already
# know the number of possible prize strings from this point on
key = (days, absent, late)
if key in cache:
return cache[key]
# now we calculate the three possible ways that can unfold from
# this point on, depending on our attendance today
# 1) if we are late (but not absent), the "absent" counter stays as
# it is, but the "late" counter increases by one
state_late = _calculate(days - 1, absent, late + 1)
# 2) if we are absent, the "absent" counter increases by 1, and the
# "late" counter resets to 0
state_absent = _calculate(days - 1, absent + 1, 0)
# 3) if we are on time, this resets the "late" counter and keeps the
# absent counter
state_ontime = _calculate(days - 1, absent, 0)
prizestrings = state_late + state_absent + state_ontime
cache[key] = prizestrings
return prizestrings
def solution(days: int = 30) -> int:
"""
Returns the number of possible prize strings for a particular number
of days, using a simple recursive function with caching to speed it up.
>>> solution()
1918080160
>>> solution(4)
43
"""
return _calculate(days, absent=0, late=0)
if __name__ == "__main__":
print(solution())
| """
Prize Strings
Problem 191
A particular school offers cash rewards to children with good attendance and
punctuality. If they are absent for three consecutive days or late on more
than one occasion then they forfeit their prize.
During an n-day period a trinary string is formed for each child consisting
of L's (late), O's (on time), and A's (absent).
Although there are eighty-one trinary strings for a 4-day period that can be
formed, exactly forty-three strings would lead to a prize:
OOOO OOOA OOOL OOAO OOAA OOAL OOLO OOLA OAOO OAOA
OAOL OAAO OAAL OALO OALA OLOO OLOA OLAO OLAA AOOO
AOOA AOOL AOAO AOAA AOAL AOLO AOLA AAOO AAOA AAOL
AALO AALA ALOO ALOA ALAO ALAA LOOO LOOA LOAO LOAA
LAOO LAOA LAAO
How many "prize" strings exist over a 30-day period?
References:
- The original Project Euler project page:
https://projecteuler.net/problem=191
"""
cache: dict[tuple[int, int, int], int] = {}
def _calculate(days: int, absent: int, late: int) -> int:
"""
A small helper function for the recursion, mainly to have
a clean interface for the solution() function below.
It should get called with the number of days (corresponding
to the desired length of the 'prize strings'), and the
initial values for the number of consecutive absent days and
number of total late days.
>>> _calculate(days=4, absent=0, late=0)
43
>>> _calculate(days=30, absent=2, late=0)
0
>>> _calculate(days=30, absent=1, late=0)
98950096
"""
# if we are absent twice, or late 3 consecutive days,
# no further prize strings are possible
if late == 3 or absent == 2:
return 0
# if we have no days left, and have not failed any other rules,
# we have a prize string
if days == 0:
return 1
# No easy solution, so now we need to do the recursive calculation
# First, check if the combination is already in the cache, and
# if yes, return the stored value from there since we already
# know the number of possible prize strings from this point on
key = (days, absent, late)
if key in cache:
return cache[key]
# now we calculate the three possible ways that can unfold from
# this point on, depending on our attendance today
# 1) if we are late (but not absent), the "absent" counter stays as
# it is, but the "late" counter increases by one
state_late = _calculate(days - 1, absent, late + 1)
# 2) if we are absent, the "absent" counter increases by 1, and the
# "late" counter resets to 0
state_absent = _calculate(days - 1, absent + 1, 0)
# 3) if we are on time, this resets the "late" counter and keeps the
# absent counter
state_ontime = _calculate(days - 1, absent, 0)
prizestrings = state_late + state_absent + state_ontime
cache[key] = prizestrings
return prizestrings
def solution(days: int = 30) -> int:
"""
Returns the number of possible prize strings for a particular number
of days, using a simple recursive function with caching to speed it up.
>>> solution()
1918080160
>>> solution(4)
43
"""
return _calculate(days, absent=0, late=0)
if __name__ == "__main__":
print(solution())
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Project Euler Problem 207: https://projecteuler.net/problem=207
Problem Statement:
For some positive integers k, there exists an integer partition of the form
4**t = 2**t + k, where 4**t, 2**t, and k are all positive integers and t is a real
number. The first two such partitions are 4**1 = 2**1 + 2 and
4**1.5849625... = 2**1.5849625... + 6.
Partitions where t is also an integer are called perfect.
For any m ≥ 1 let P(m) be the proportion of such partitions that are perfect with
k ≤ m.
Thus P(6) = 1/2.
In the following table are listed some values of P(m)
P(5) = 1/1
P(10) = 1/2
P(15) = 2/3
P(20) = 1/2
P(25) = 1/2
P(30) = 2/5
...
P(180) = 1/4
P(185) = 3/13
Find the smallest m for which P(m) < 1/12345
Solution:
Equation 4**t = 2**t + k solved for t gives:
t = log2(sqrt(4*k+1)/2 + 1/2)
For t to be real valued, sqrt(4*k+1) must be an integer which is implemented in
function check_t_real(k). For a perfect partition t must be an integer.
To speed up significantly the search for partitions, instead of incrementing k by one
per iteration, the next valid k is found by k = (i**2 - 1) / 4 with an integer i and
k has to be a positive integer. If this is the case a partition is found. The partition
is perfect if t os an integer. The integer i is increased with increment 1 until the
proportion perfect partitions / total partitions drops under the given value.
"""
import math
def check_partition_perfect(positive_integer: int) -> bool:
"""
Check if t = f(positive_integer) = log2(sqrt(4*positive_integer+1)/2 + 1/2) is a
real number.
>>> check_partition_perfect(2)
True
>>> check_partition_perfect(6)
False
"""
exponent = math.log2(math.sqrt(4 * positive_integer + 1) / 2 + 1 / 2)
return exponent == int(exponent)
def solution(max_proportion: float = 1 / 12345) -> int:
"""
Find m for which the proportion of perfect partitions to total partitions is lower
than max_proportion
>>> solution(1) > 5
True
>>> solution(1/2) > 10
True
>>> solution(3 / 13) > 185
True
"""
total_partitions = 0
perfect_partitions = 0
integer = 3
while True:
partition_candidate = (integer ** 2 - 1) / 4
# if candidate is an integer, then there is a partition for k
if partition_candidate == int(partition_candidate):
partition_candidate = int(partition_candidate)
total_partitions += 1
if check_partition_perfect(partition_candidate):
perfect_partitions += 1
if perfect_partitions > 0:
if perfect_partitions / total_partitions < max_proportion:
return partition_candidate
integer += 1
if __name__ == "__main__":
print(f"{solution() = }")
| """
Project Euler Problem 207: https://projecteuler.net/problem=207
Problem Statement:
For some positive integers k, there exists an integer partition of the form
4**t = 2**t + k, where 4**t, 2**t, and k are all positive integers and t is a real
number. The first two such partitions are 4**1 = 2**1 + 2 and
4**1.5849625... = 2**1.5849625... + 6.
Partitions where t is also an integer are called perfect.
For any m ≥ 1 let P(m) be the proportion of such partitions that are perfect with
k ≤ m.
Thus P(6) = 1/2.
In the following table are listed some values of P(m)
P(5) = 1/1
P(10) = 1/2
P(15) = 2/3
P(20) = 1/2
P(25) = 1/2
P(30) = 2/5
...
P(180) = 1/4
P(185) = 3/13
Find the smallest m for which P(m) < 1/12345
Solution:
Equation 4**t = 2**t + k solved for t gives:
t = log2(sqrt(4*k+1)/2 + 1/2)
For t to be real valued, sqrt(4*k+1) must be an integer which is implemented in
function check_t_real(k). For a perfect partition t must be an integer.
To speed up significantly the search for partitions, instead of incrementing k by one
per iteration, the next valid k is found by k = (i**2 - 1) / 4 with an integer i and
k has to be a positive integer. If this is the case a partition is found. The partition
is perfect if t os an integer. The integer i is increased with increment 1 until the
proportion perfect partitions / total partitions drops under the given value.
"""
import math
def check_partition_perfect(positive_integer: int) -> bool:
"""
Check if t = f(positive_integer) = log2(sqrt(4*positive_integer+1)/2 + 1/2) is a
real number.
>>> check_partition_perfect(2)
True
>>> check_partition_perfect(6)
False
"""
exponent = math.log2(math.sqrt(4 * positive_integer + 1) / 2 + 1 / 2)
return exponent == int(exponent)
def solution(max_proportion: float = 1 / 12345) -> int:
"""
Find m for which the proportion of perfect partitions to total partitions is lower
than max_proportion
>>> solution(1) > 5
True
>>> solution(1/2) > 10
True
>>> solution(3 / 13) > 185
True
"""
total_partitions = 0
perfect_partitions = 0
integer = 3
while True:
partition_candidate = (integer ** 2 - 1) / 4
# if candidate is an integer, then there is a partition for k
if partition_candidate == int(partition_candidate):
partition_candidate = int(partition_candidate)
total_partitions += 1
if check_partition_perfect(partition_candidate):
perfect_partitions += 1
if perfect_partitions > 0:
if perfect_partitions / total_partitions < max_proportion:
return int(partition_candidate)
integer += 1
if __name__ == "__main__":
print(f"{solution() = }")
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Sum of digits sequence
Problem 551
Let a(0), a(1),... be an integer sequence defined by:
a(0) = 1
for n >= 1, a(n) is the sum of the digits of all preceding terms
The sequence starts with 1, 1, 2, 4, 8, ...
You are given a(10^6) = 31054319.
Find a(10^15)
"""
ks = [k for k in range(2, 20 + 1)]
base = [10 ** k for k in range(ks[-1] + 1)]
memo = {}
def next_term(a_i, k, i, n):
"""
Calculates and updates a_i in-place to either the n-th term or the
smallest term for which c > 10^k when the terms are written in the form:
a(i) = b * 10^k + c
For any a(i), if digitsum(b) and c have the same value, the difference
between subsequent terms will be the same until c >= 10^k. This difference
is cached to greatly speed up the computation.
Arguments:
a_i -- array of digits starting from the one's place that represent
the i-th term in the sequence
k -- k when terms are written in the from a(i) = b*10^k + c.
Term are calulcated until c > 10^k or the n-th term is reached.
i -- position along the sequence
n -- term to calculate up to if k is large enough
Return: a tuple of difference between ending term and starting term, and
the number of terms calculated. ex. if starting term is a_0=1, and
ending term is a_10=62, then (61, 9) is returned.
"""
# ds_b - digitsum(b)
ds_b = sum(a_i[j] for j in range(k, len(a_i)))
c = sum(a_i[j] * base[j] for j in range(min(len(a_i), k)))
diff, dn = 0, 0
max_dn = n - i
sub_memo = memo.get(ds_b)
if sub_memo is not None:
jumps = sub_memo.get(c)
if jumps is not None and len(jumps) > 0:
# find and make the largest jump without going over
max_jump = -1
for _k in range(len(jumps) - 1, -1, -1):
if jumps[_k][2] <= k and jumps[_k][1] <= max_dn:
max_jump = _k
break
if max_jump >= 0:
diff, dn, _kk = jumps[max_jump]
# since the difference between jumps is cached, add c
new_c = diff + c
for j in range(min(k, len(a_i))):
new_c, a_i[j] = divmod(new_c, 10)
if new_c > 0:
add(a_i, k, new_c)
else:
sub_memo[c] = []
else:
sub_memo = {c: []}
memo[ds_b] = sub_memo
if dn >= max_dn or c + diff >= base[k]:
return diff, dn
if k > ks[0]:
while True:
# keep doing smaller jumps
_diff, terms_jumped = next_term(a_i, k - 1, i + dn, n)
diff += _diff
dn += terms_jumped
if dn >= max_dn or c + diff >= base[k]:
break
else:
# would be too small a jump, just compute sequential terms instead
_diff, terms_jumped = compute(a_i, k, i + dn, n)
diff += _diff
dn += terms_jumped
jumps = sub_memo[c]
# keep jumps sorted by # of terms skipped
j = 0
while j < len(jumps):
if jumps[j][1] > dn:
break
j += 1
# cache the jump for this value digitsum(b) and c
sub_memo[c].insert(j, (diff, dn, k))
return (diff, dn)
def compute(a_i, k, i, n):
"""
same as next_term(a_i, k, i, n) but computes terms without memoizing results.
"""
if i >= n:
return 0, i
if k > len(a_i):
a_i.extend([0 for _ in range(k - len(a_i))])
# note: a_i -> b * 10^k + c
# ds_b -> digitsum(b)
# ds_c -> digitsum(c)
start_i = i
ds_b, ds_c, diff = 0, 0, 0
for j in range(len(a_i)):
if j >= k:
ds_b += a_i[j]
else:
ds_c += a_i[j]
while i < n:
i += 1
addend = ds_c + ds_b
diff += addend
ds_c = 0
for j in range(k):
s = a_i[j] + addend
addend, a_i[j] = divmod(s, 10)
ds_c += a_i[j]
if addend > 0:
break
if addend > 0:
add(a_i, k, addend)
return diff, i - start_i
def add(digits, k, addend):
"""
adds addend to digit array given in digits
starting at index k
"""
for j in range(k, len(digits)):
s = digits[j] + addend
if s >= 10:
quotient, digits[j] = divmod(s, 10)
addend = addend // 10 + quotient
else:
digits[j] = s
addend = addend // 10
if addend == 0:
break
while addend > 0:
addend, digit = divmod(addend, 10)
digits.append(digit)
def solution(n: int = 10 ** 15) -> int:
"""
returns n-th term of sequence
>>> solution(10)
62
>>> solution(10**6)
31054319
>>> solution(10**15)
73597483551591773
"""
digits = [1]
i = 1
dn = 0
while True:
diff, terms_jumped = next_term(digits, 20, i + dn, n)
dn += terms_jumped
if dn == n - i:
break
a_n = 0
for j in range(len(digits)):
a_n += digits[j] * 10 ** j
return a_n
if __name__ == "__main__":
print(f"{solution() = }")
| """
Sum of digits sequence
Problem 551
Let a(0), a(1),... be an integer sequence defined by:
a(0) = 1
for n >= 1, a(n) is the sum of the digits of all preceding terms
The sequence starts with 1, 1, 2, 4, 8, ...
You are given a(10^6) = 31054319.
Find a(10^15)
"""
ks = [k for k in range(2, 20 + 1)]
base = [10 ** k for k in range(ks[-1] + 1)]
memo: dict[int, dict[int, list[list[int]]]] = {}
def next_term(a_i, k, i, n):
"""
Calculates and updates a_i in-place to either the n-th term or the
smallest term for which c > 10^k when the terms are written in the form:
a(i) = b * 10^k + c
For any a(i), if digitsum(b) and c have the same value, the difference
between subsequent terms will be the same until c >= 10^k. This difference
is cached to greatly speed up the computation.
Arguments:
a_i -- array of digits starting from the one's place that represent
the i-th term in the sequence
k -- k when terms are written in the from a(i) = b*10^k + c.
Term are calulcated until c > 10^k or the n-th term is reached.
i -- position along the sequence
n -- term to calculate up to if k is large enough
Return: a tuple of difference between ending term and starting term, and
the number of terms calculated. ex. if starting term is a_0=1, and
ending term is a_10=62, then (61, 9) is returned.
"""
# ds_b - digitsum(b)
ds_b = sum(a_i[j] for j in range(k, len(a_i)))
c = sum(a_i[j] * base[j] for j in range(min(len(a_i), k)))
diff, dn = 0, 0
max_dn = n - i
sub_memo = memo.get(ds_b)
if sub_memo is not None:
jumps = sub_memo.get(c)
if jumps is not None and len(jumps) > 0:
# find and make the largest jump without going over
max_jump = -1
for _k in range(len(jumps) - 1, -1, -1):
if jumps[_k][2] <= k and jumps[_k][1] <= max_dn:
max_jump = _k
break
if max_jump >= 0:
diff, dn, _kk = jumps[max_jump]
# since the difference between jumps is cached, add c
new_c = diff + c
for j in range(min(k, len(a_i))):
new_c, a_i[j] = divmod(new_c, 10)
if new_c > 0:
add(a_i, k, new_c)
else:
sub_memo[c] = []
else:
sub_memo = {c: []}
memo[ds_b] = sub_memo
if dn >= max_dn or c + diff >= base[k]:
return diff, dn
if k > ks[0]:
while True:
# keep doing smaller jumps
_diff, terms_jumped = next_term(a_i, k - 1, i + dn, n)
diff += _diff
dn += terms_jumped
if dn >= max_dn or c + diff >= base[k]:
break
else:
# would be too small a jump, just compute sequential terms instead
_diff, terms_jumped = compute(a_i, k, i + dn, n)
diff += _diff
dn += terms_jumped
jumps = sub_memo[c]
# keep jumps sorted by # of terms skipped
j = 0
while j < len(jumps):
if jumps[j][1] > dn:
break
j += 1
# cache the jump for this value digitsum(b) and c
sub_memo[c].insert(j, (diff, dn, k))
return (diff, dn)
def compute(a_i, k, i, n):
"""
same as next_term(a_i, k, i, n) but computes terms without memoizing results.
"""
if i >= n:
return 0, i
if k > len(a_i):
a_i.extend([0 for _ in range(k - len(a_i))])
# note: a_i -> b * 10^k + c
# ds_b -> digitsum(b)
# ds_c -> digitsum(c)
start_i = i
ds_b, ds_c, diff = 0, 0, 0
for j in range(len(a_i)):
if j >= k:
ds_b += a_i[j]
else:
ds_c += a_i[j]
while i < n:
i += 1
addend = ds_c + ds_b
diff += addend
ds_c = 0
for j in range(k):
s = a_i[j] + addend
addend, a_i[j] = divmod(s, 10)
ds_c += a_i[j]
if addend > 0:
break
if addend > 0:
add(a_i, k, addend)
return diff, i - start_i
def add(digits, k, addend):
"""
adds addend to digit array given in digits
starting at index k
"""
for j in range(k, len(digits)):
s = digits[j] + addend
if s >= 10:
quotient, digits[j] = divmod(s, 10)
addend = addend // 10 + quotient
else:
digits[j] = s
addend = addend // 10
if addend == 0:
break
while addend > 0:
addend, digit = divmod(addend, 10)
digits.append(digit)
def solution(n: int = 10 ** 15) -> int:
"""
returns n-th term of sequence
>>> solution(10)
62
>>> solution(10**6)
31054319
>>> solution(10**15)
73597483551591773
"""
digits = [1]
i = 1
dn = 0
while True:
diff, terms_jumped = next_term(digits, 20, i + dn, n)
dn += terms_jumped
if dn == n - i:
break
a_n = 0
for j in range(len(digits)):
a_n += digits[j] * 10 ** j
return a_n
if __name__ == "__main__":
print(f"{solution() = }")
| 1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Consider all integer combinations of ab for 2 <= a <= 5 and 2 <= b <= 5:
2^2=4, 2^3=8, 2^4=16, 2^5=32
3^2=9, 3^3=27, 3^4=81, 3^5=243
4^2=16, 4^3=64, 4^4=256, 4^5=1024
5^2=25, 5^3=125, 5^4=625, 5^5=3125
If they are then placed in numerical order, with any repeats removed, we get
the following sequence of 15 distinct terms:
4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
How many distinct terms are in the sequence generated by ab
for 2 <= a <= 100 and 2 <= b <= 100?
"""
def solution(n: int = 100) -> int:
"""Returns the number of distinct terms in the sequence generated by a^b
for 2 <= a <= 100 and 2 <= b <= 100.
>>> solution(100)
9183
>>> solution(50)
2184
>>> solution(20)
324
>>> solution(5)
15
>>> solution(2)
1
>>> solution(1)
0
"""
collectPowers = set()
currentPow = 0
N = n + 1 # maximum limit
for a in range(2, N):
for b in range(2, N):
currentPow = a ** b # calculates the current power
collectPowers.add(currentPow) # adds the result to the set
return len(collectPowers)
if __name__ == "__main__":
print("Number of terms ", solution(int(str(input()).strip())))
| """
Consider all integer combinations of ab for 2 <= a <= 5 and 2 <= b <= 5:
2^2=4, 2^3=8, 2^4=16, 2^5=32
3^2=9, 3^3=27, 3^4=81, 3^5=243
4^2=16, 4^3=64, 4^4=256, 4^5=1024
5^2=25, 5^3=125, 5^4=625, 5^5=3125
If they are then placed in numerical order, with any repeats removed, we get
the following sequence of 15 distinct terms:
4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
How many distinct terms are in the sequence generated by ab
for 2 <= a <= 100 and 2 <= b <= 100?
"""
def solution(n: int = 100) -> int:
"""Returns the number of distinct terms in the sequence generated by a^b
for 2 <= a <= 100 and 2 <= b <= 100.
>>> solution(100)
9183
>>> solution(50)
2184
>>> solution(20)
324
>>> solution(5)
15
>>> solution(2)
1
>>> solution(1)
0
"""
collectPowers = set()
currentPow = 0
N = n + 1 # maximum limit
for a in range(2, N):
for b in range(2, N):
currentPow = a ** b # calculates the current power
collectPowers.add(currentPow) # adds the result to the set
return len(collectPowers)
if __name__ == "__main__":
print("Number of terms ", solution(int(str(input()).strip())))
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| -1 |
||
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Problem 81: https://projecteuler.net/problem=81
In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right,
by only moving to the right and down, is indicated in bold red and is equal to 2427.
[131] 673 234 103 18
[201] [96] [342] 965 150
630 803 [746] [422] 111
537 699 497 [121] 956
805 732 524 [37] [331]
Find the minimal path sum from the top left to the bottom right by only moving right
and down in matrix.txt (https://projecteuler.net/project/resources/p081_matrix.txt),
a 31K text file containing an 80 by 80 matrix.
"""
import os
def solution(filename: str = "matrix.txt") -> int:
"""
Returns the minimal path sum from the top left to the bottom right of the matrix.
>>> solution()
427337
"""
with open(os.path.join(os.path.dirname(__file__), filename)) as in_file:
data = in_file.read()
grid = [[int(cell) for cell in row.split(",")] for row in data.strip().splitlines()]
dp = [[0 for cell in row] for row in grid]
n = len(grid[0])
dp = [[0 for i in range(n)] for j in range(n)]
dp[0][0] = grid[0][0]
for i in range(1, n):
dp[0][i] = grid[0][i] + dp[0][i - 1]
for i in range(1, n):
dp[i][0] = grid[i][0] + dp[i - 1][0]
for i in range(1, n):
for j in range(1, n):
dp[i][j] = grid[i][j] + min(dp[i - 1][j], dp[i][j - 1])
return dp[-1][-1]
if __name__ == "__main__":
print(f"{solution() = }")
| """
Problem 81: https://projecteuler.net/problem=81
In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right,
by only moving to the right and down, is indicated in bold red and is equal to 2427.
[131] 673 234 103 18
[201] [96] [342] 965 150
630 803 [746] [422] 111
537 699 497 [121] 956
805 732 524 [37] [331]
Find the minimal path sum from the top left to the bottom right by only moving right
and down in matrix.txt (https://projecteuler.net/project/resources/p081_matrix.txt),
a 31K text file containing an 80 by 80 matrix.
"""
import os
def solution(filename: str = "matrix.txt") -> int:
"""
Returns the minimal path sum from the top left to the bottom right of the matrix.
>>> solution()
427337
"""
with open(os.path.join(os.path.dirname(__file__), filename)) as in_file:
data = in_file.read()
grid = [[int(cell) for cell in row.split(",")] for row in data.strip().splitlines()]
dp = [[0 for cell in row] for row in grid]
n = len(grid[0])
dp = [[0 for i in range(n)] for j in range(n)]
dp[0][0] = grid[0][0]
for i in range(1, n):
dp[0][i] = grid[0][i] + dp[0][i - 1]
for i in range(1, n):
dp[i][0] = grid[i][0] + dp[i - 1][0]
for i in range(1, n):
for j in range(1, n):
dp[i][j] = grid[i][j] + min(dp[i - 1][j], dp[i][j - 1])
return dp[-1][-1]
if __name__ == "__main__":
print(f"{solution() = }")
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
The Reverse Polish Nation also known as Polish postfix notation
or simply postfix notation.
https://en.wikipedia.org/wiki/Reverse_Polish_notation
Classic examples of simple stack implementations
Valid operators are +, -, *, /.
Each operand may be an integer or another expression.
"""
from __future__ import annotations
from typing import Any
def evaluate_postfix(postfix_notation: list) -> int:
"""
>>> evaluate_postfix(["2", "1", "+", "3", "*"])
9
>>> evaluate_postfix(["4", "13", "5", "/", "+"])
6
>>> evaluate_postfix([])
0
"""
if not postfix_notation:
return 0
operations = {"+", "-", "*", "/"}
stack: list[Any] = []
for token in postfix_notation:
if token in operations:
b, a = stack.pop(), stack.pop()
if token == "+":
stack.append(a + b)
elif token == "-":
stack.append(a - b)
elif token == "*":
stack.append(a * b)
else:
if a * b < 0 and a % b != 0:
stack.append(a // b + 1)
else:
stack.append(a // b)
else:
stack.append(int(token))
return stack.pop()
if __name__ == "__main__":
import doctest
doctest.testmod()
| """
The Reverse Polish Nation also known as Polish postfix notation
or simply postfix notation.
https://en.wikipedia.org/wiki/Reverse_Polish_notation
Classic examples of simple stack implementations
Valid operators are +, -, *, /.
Each operand may be an integer or another expression.
"""
from __future__ import annotations
from typing import Any
def evaluate_postfix(postfix_notation: list) -> int:
"""
>>> evaluate_postfix(["2", "1", "+", "3", "*"])
9
>>> evaluate_postfix(["4", "13", "5", "/", "+"])
6
>>> evaluate_postfix([])
0
"""
if not postfix_notation:
return 0
operations = {"+", "-", "*", "/"}
stack: list[Any] = []
for token in postfix_notation:
if token in operations:
b, a = stack.pop(), stack.pop()
if token == "+":
stack.append(a + b)
elif token == "-":
stack.append(a - b)
elif token == "*":
stack.append(a * b)
else:
if a * b < 0 and a % b != 0:
stack.append(a // b + 1)
else:
stack.append(a // b)
else:
stack.append(int(token))
return stack.pop()
if __name__ == "__main__":
import doctest
doctest.testmod()
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| def points_to_polynomial(coordinates: list[list[int]]) -> str:
"""
coordinates is a two dimensional matrix: [[x, y], [x, y], ...]
number of points you want to use
>>> print(points_to_polynomial([]))
The program cannot work out a fitting polynomial.
>>> print(points_to_polynomial([[]]))
The program cannot work out a fitting polynomial.
>>> print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
f(x)=x^2*0.0+x^1*-0.0+x^0*0.0
>>> print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
f(x)=x^2*0.0+x^1*-0.0+x^0*1.0
>>> print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
f(x)=x^2*0.0+x^1*-0.0+x^0*3.0
>>> print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
f(x)=x^2*0.0+x^1*1.0+x^0*0.0
>>> print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
f(x)=x^2*1.0+x^1*-0.0+x^0*0.0
>>> print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
f(x)=x^2*1.0+x^1*-0.0+x^0*2.0
>>> print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
f(x)=x^2*-1.0+x^1*-0.0+x^0*-2.0
>>> print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))
f(x)=x^2*5.0+x^1*-18.0+x^0*18.0
"""
try:
check = 1
more_check = 0
d = coordinates[0][0]
for j in range(len(coordinates)):
if j == 0:
continue
if d == coordinates[j][0]:
more_check += 1
solved = "x=" + str(coordinates[j][0])
if more_check == len(coordinates) - 1:
check = 2
break
elif more_check > 0 and more_check != len(coordinates) - 1:
check = 3
else:
check = 1
if len(coordinates) == 1 and coordinates[0][0] == 0:
check = 2
solved = "x=0"
except Exception:
check = 3
x = len(coordinates)
if check == 1:
count_of_line = 0
matrix: list[list[float]] = []
# put the x and x to the power values in a matrix
while count_of_line < x:
count_in_line = 0
a = coordinates[count_of_line][0]
count_line: list[float] = []
while count_in_line < x:
count_line.append(a ** (x - (count_in_line + 1)))
count_in_line += 1
matrix.append(count_line)
count_of_line += 1
count_of_line = 0
# put the y values into a vector
vector: list[float] = []
while count_of_line < x:
vector.append(coordinates[count_of_line][1])
count_of_line += 1
count = 0
while count < x:
zahlen = 0
while zahlen < x:
if count == zahlen:
zahlen += 1
if zahlen == x:
break
bruch = matrix[zahlen][count] / matrix[count][count]
for counting_columns, item in enumerate(matrix[count]):
# manipulating all the values in the matrix
matrix[zahlen][counting_columns] -= item * bruch
# manipulating the values in the vector
vector[zahlen] -= vector[count] * bruch
zahlen += 1
count += 1
count = 0
# make solutions
solution: list[str] = []
while count < x:
solution.append(str(vector[count] / matrix[count][count]))
count += 1
count = 0
solved = "f(x)="
while count < x:
remove_e: list[str] = solution[count].split("E")
if len(remove_e) > 1:
solution[count] = remove_e[0] + "*10^" + remove_e[1]
solved += "x^" + str(x - (count + 1)) + "*" + str(solution[count])
if count + 1 != x:
solved += "+"
count += 1
return solved
elif check == 2:
return solved
else:
return "The program cannot work out a fitting polynomial."
if __name__ == "__main__":
print(points_to_polynomial([]))
print(points_to_polynomial([[]]))
print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))
| def points_to_polynomial(coordinates: list[list[int]]) -> str:
"""
coordinates is a two dimensional matrix: [[x, y], [x, y], ...]
number of points you want to use
>>> print(points_to_polynomial([]))
The program cannot work out a fitting polynomial.
>>> print(points_to_polynomial([[]]))
The program cannot work out a fitting polynomial.
>>> print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
f(x)=x^2*0.0+x^1*-0.0+x^0*0.0
>>> print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
f(x)=x^2*0.0+x^1*-0.0+x^0*1.0
>>> print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
f(x)=x^2*0.0+x^1*-0.0+x^0*3.0
>>> print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
f(x)=x^2*0.0+x^1*1.0+x^0*0.0
>>> print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
f(x)=x^2*1.0+x^1*-0.0+x^0*0.0
>>> print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
f(x)=x^2*1.0+x^1*-0.0+x^0*2.0
>>> print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
f(x)=x^2*-1.0+x^1*-0.0+x^0*-2.0
>>> print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))
f(x)=x^2*5.0+x^1*-18.0+x^0*18.0
"""
try:
check = 1
more_check = 0
d = coordinates[0][0]
for j in range(len(coordinates)):
if j == 0:
continue
if d == coordinates[j][0]:
more_check += 1
solved = "x=" + str(coordinates[j][0])
if more_check == len(coordinates) - 1:
check = 2
break
elif more_check > 0 and more_check != len(coordinates) - 1:
check = 3
else:
check = 1
if len(coordinates) == 1 and coordinates[0][0] == 0:
check = 2
solved = "x=0"
except Exception:
check = 3
x = len(coordinates)
if check == 1:
count_of_line = 0
matrix: list[list[float]] = []
# put the x and x to the power values in a matrix
while count_of_line < x:
count_in_line = 0
a = coordinates[count_of_line][0]
count_line: list[float] = []
while count_in_line < x:
count_line.append(a ** (x - (count_in_line + 1)))
count_in_line += 1
matrix.append(count_line)
count_of_line += 1
count_of_line = 0
# put the y values into a vector
vector: list[float] = []
while count_of_line < x:
vector.append(coordinates[count_of_line][1])
count_of_line += 1
count = 0
while count < x:
zahlen = 0
while zahlen < x:
if count == zahlen:
zahlen += 1
if zahlen == x:
break
bruch = matrix[zahlen][count] / matrix[count][count]
for counting_columns, item in enumerate(matrix[count]):
# manipulating all the values in the matrix
matrix[zahlen][counting_columns] -= item * bruch
# manipulating the values in the vector
vector[zahlen] -= vector[count] * bruch
zahlen += 1
count += 1
count = 0
# make solutions
solution: list[str] = []
while count < x:
solution.append(str(vector[count] / matrix[count][count]))
count += 1
count = 0
solved = "f(x)="
while count < x:
remove_e: list[str] = solution[count].split("E")
if len(remove_e) > 1:
solution[count] = remove_e[0] + "*10^" + remove_e[1]
solved += "x^" + str(x - (count + 1)) + "*" + str(solution[count])
if count + 1 != x:
solved += "+"
count += 1
return solved
elif check == 2:
return solved
else:
return "The program cannot work out a fitting polynomial."
if __name__ == "__main__":
print(points_to_polynomial([]))
print(points_to_polynomial([[]]))
print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
This is a pure Python implementation of the bogosort algorithm,
also known as permutation sort, stupid sort, slowsort, shotgun sort, or monkey sort.
Bogosort generates random permutations until it guesses the correct one.
More info on: https://en.wikipedia.org/wiki/Bogosort
For doctests run following command:
python -m doctest -v bogo_sort.py
or
python3 -m doctest -v bogo_sort.py
For manual testing run:
python bogo_sort.py
"""
import random
def bogo_sort(collection):
"""Pure implementation of the bogosort algorithm in Python
:param collection: some mutable ordered collection with heterogeneous
comparable items inside
:return: the same collection ordered by ascending
Examples:
>>> bogo_sort([0, 5, 3, 2, 2])
[0, 2, 2, 3, 5]
>>> bogo_sort([])
[]
>>> bogo_sort([-2, -5, -45])
[-45, -5, -2]
"""
def is_sorted(collection):
if len(collection) < 2:
return True
for i in range(len(collection) - 1):
if collection[i] > collection[i + 1]:
return False
return True
while not is_sorted(collection):
random.shuffle(collection)
return collection
if __name__ == "__main__":
user_input = input("Enter numbers separated by a comma:\n").strip()
unsorted = [int(item) for item in user_input.split(",")]
print(bogo_sort(unsorted))
| """
This is a pure Python implementation of the bogosort algorithm,
also known as permutation sort, stupid sort, slowsort, shotgun sort, or monkey sort.
Bogosort generates random permutations until it guesses the correct one.
More info on: https://en.wikipedia.org/wiki/Bogosort
For doctests run following command:
python -m doctest -v bogo_sort.py
or
python3 -m doctest -v bogo_sort.py
For manual testing run:
python bogo_sort.py
"""
import random
def bogo_sort(collection):
"""Pure implementation of the bogosort algorithm in Python
:param collection: some mutable ordered collection with heterogeneous
comparable items inside
:return: the same collection ordered by ascending
Examples:
>>> bogo_sort([0, 5, 3, 2, 2])
[0, 2, 2, 3, 5]
>>> bogo_sort([])
[]
>>> bogo_sort([-2, -5, -45])
[-45, -5, -2]
"""
def is_sorted(collection):
if len(collection) < 2:
return True
for i in range(len(collection) - 1):
if collection[i] > collection[i + 1]:
return False
return True
while not is_sorted(collection):
random.shuffle(collection)
return collection
if __name__ == "__main__":
user_input = input("Enter numbers separated by a comma:\n").strip()
unsorted = [int(item) for item in user_input.split(",")]
print(bogo_sort(unsorted))
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """Absolute Value."""
def abs_val(num):
"""
Find the absolute value of a number.
>>> abs_val(-5.1)
5.1
>>> abs_val(-5) == abs_val(5)
True
>>> abs_val(0)
0
"""
return -num if num < 0 else num
def test_abs_val():
"""
>>> test_abs_val()
"""
assert 0 == abs_val(0)
assert 34 == abs_val(34)
assert 100000000000 == abs_val(-100000000000)
if __name__ == "__main__":
print(abs_val(-34)) # --> 34
| """Absolute Value."""
def abs_val(num):
"""
Find the absolute value of a number.
>>> abs_val(-5.1)
5.1
>>> abs_val(-5) == abs_val(5)
True
>>> abs_val(0)
0
"""
return -num if num < 0 else num
def test_abs_val():
"""
>>> test_abs_val()
"""
assert 0 == abs_val(0)
assert 34 == abs_val(34)
assert 100000000000 == abs_val(-100000000000)
if __name__ == "__main__":
print(abs_val(-34)) # --> 34
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| -1 |
||
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| END = "#"
class Trie:
def __init__(self):
self._trie = {}
def insert_word(self, text):
trie = self._trie
for char in text:
if char not in trie:
trie[char] = {}
trie = trie[char]
trie[END] = True
def find_word(self, prefix):
trie = self._trie
for char in prefix:
if char in trie:
trie = trie[char]
else:
return []
return self._elements(trie)
def _elements(self, d):
result = []
for c, v in d.items():
if c == END:
sub_result = [" "]
else:
sub_result = [c + s for s in self._elements(v)]
result.extend(sub_result)
return tuple(result)
trie = Trie()
words = ("depart", "detergent", "daring", "dog", "deer", "deal")
for word in words:
trie.insert_word(word)
def autocomplete_using_trie(s):
"""
>>> trie = Trie()
>>> for word in words:
... trie.insert_word(word)
...
>>> matches = autocomplete_using_trie("de")
"detergent " in matches
True
"dog " in matches
False
"""
suffixes = trie.find_word(s)
return tuple(s + w for w in suffixes)
def main():
print(autocomplete_using_trie("de"))
if __name__ == "__main__":
main()
| END = "#"
class Trie:
def __init__(self):
self._trie = {}
def insert_word(self, text):
trie = self._trie
for char in text:
if char not in trie:
trie[char] = {}
trie = trie[char]
trie[END] = True
def find_word(self, prefix):
trie = self._trie
for char in prefix:
if char in trie:
trie = trie[char]
else:
return []
return self._elements(trie)
def _elements(self, d):
result = []
for c, v in d.items():
if c == END:
sub_result = [" "]
else:
sub_result = [c + s for s in self._elements(v)]
result.extend(sub_result)
return tuple(result)
trie = Trie()
words = ("depart", "detergent", "daring", "dog", "deer", "deal")
for word in words:
trie.insert_word(word)
def autocomplete_using_trie(s):
"""
>>> trie = Trie()
>>> for word in words:
... trie.insert_word(word)
...
>>> matches = autocomplete_using_trie("de")
"detergent " in matches
True
"dog " in matches
False
"""
suffixes = trie.find_word(s)
return tuple(s + w for w in suffixes)
def main():
print(autocomplete_using_trie("de"))
if __name__ == "__main__":
main()
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| -1 |
||
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| -1 |
||
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| import random
from .binary_exp_mod import bin_exp_mod
# This is a probabilistic check to test primality, useful for big numbers!
# if it's a prime, it will return true
# if it's not a prime, the chance of it returning true is at most 1/4**prec
def is_prime(n, prec=1000):
"""
>>> from .prime_check import prime_check
>>> all(is_prime(i) == prime_check(i) for i in range(1000))
True
"""
if n < 2:
return False
if n % 2 == 0:
return n == 2
# this means n is odd
d = n - 1
exp = 0
while d % 2 == 0:
d /= 2
exp += 1
# n - 1=d*(2**exp)
count = 0
while count < prec:
a = random.randint(2, n - 1)
b = bin_exp_mod(a, d, n)
if b != 1:
flag = True
for i in range(exp):
if b == n - 1:
flag = False
break
b = b * b
b %= n
if flag:
return False
count += 1
return True
if __name__ == "__main__":
n = abs(int(input("Enter bound : ").strip()))
print("Here's the list of primes:")
print(", ".join(str(i) for i in range(n + 1) if is_prime(i)))
| import random
from .binary_exp_mod import bin_exp_mod
# This is a probabilistic check to test primality, useful for big numbers!
# if it's a prime, it will return true
# if it's not a prime, the chance of it returning true is at most 1/4**prec
def is_prime(n, prec=1000):
"""
>>> from .prime_check import prime_check
>>> all(is_prime(i) == prime_check(i) for i in range(1000))
True
"""
if n < 2:
return False
if n % 2 == 0:
return n == 2
# this means n is odd
d = n - 1
exp = 0
while d % 2 == 0:
d /= 2
exp += 1
# n - 1=d*(2**exp)
count = 0
while count < prec:
a = random.randint(2, n - 1)
b = bin_exp_mod(a, d, n)
if b != 1:
flag = True
for i in range(exp):
if b == n - 1:
flag = False
break
b = b * b
b %= n
if flag:
return False
count += 1
return True
if __name__ == "__main__":
n = abs(int(input("Enter bound : ").strip()))
print("Here's the list of primes:")
print(", ".join(str(i) for i in range(n + 1) if is_prime(i)))
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
The function below will convert any binary string to the octal equivalent.
>>> bin_to_octal("1111")
'17'
>>> bin_to_octal("101010101010011")
'52523'
>>> bin_to_octal("")
Traceback (most recent call last):
...
ValueError: Empty string was passed to the function
>>> bin_to_octal("a-1")
Traceback (most recent call last):
...
ValueError: Non-binary value was passed to the function
"""
def bin_to_octal(bin_string: str) -> str:
if not all(char in "01" for char in bin_string):
raise ValueError("Non-binary value was passed to the function")
if not bin_string:
raise ValueError("Empty string was passed to the function")
oct_string = ""
while len(bin_string) % 3 != 0:
bin_string = "0" + bin_string
bin_string_in_3_list = [
bin_string[index : index + 3]
for index in range(len(bin_string))
if index % 3 == 0
]
for bin_group in bin_string_in_3_list:
oct_val = 0
for index, val in enumerate(bin_group):
oct_val += int(2 ** (2 - index) * int(val))
oct_string += str(oct_val)
return oct_string
if __name__ == "__main__":
from doctest import testmod
testmod()
| """
The function below will convert any binary string to the octal equivalent.
>>> bin_to_octal("1111")
'17'
>>> bin_to_octal("101010101010011")
'52523'
>>> bin_to_octal("")
Traceback (most recent call last):
...
ValueError: Empty string was passed to the function
>>> bin_to_octal("a-1")
Traceback (most recent call last):
...
ValueError: Non-binary value was passed to the function
"""
def bin_to_octal(bin_string: str) -> str:
if not all(char in "01" for char in bin_string):
raise ValueError("Non-binary value was passed to the function")
if not bin_string:
raise ValueError("Empty string was passed to the function")
oct_string = ""
while len(bin_string) % 3 != 0:
bin_string = "0" + bin_string
bin_string_in_3_list = [
bin_string[index : index + 3]
for index in range(len(bin_string))
if index % 3 == 0
]
for bin_group in bin_string_in_3_list:
oct_val = 0
for index, val in enumerate(bin_group):
oct_val += int(2 ** (2 - index) * int(val))
oct_string += str(oct_val)
return oct_string
if __name__ == "__main__":
from doctest import testmod
testmod()
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
author : Mayank Kumar Jha (mk9440)
"""
from __future__ import annotations
def find_max_sub_array(A, low, high):
if low == high:
return low, high, A[low]
else:
mid = (low + high) // 2
left_low, left_high, left_sum = find_max_sub_array(A, low, mid)
right_low, right_high, right_sum = find_max_sub_array(A, mid + 1, high)
cross_left, cross_right, cross_sum = find_max_cross_sum(A, low, mid, high)
if left_sum >= right_sum and left_sum >= cross_sum:
return left_low, left_high, left_sum
elif right_sum >= left_sum and right_sum >= cross_sum:
return right_low, right_high, right_sum
else:
return cross_left, cross_right, cross_sum
def find_max_cross_sum(A, low, mid, high):
left_sum, max_left = -999999999, -1
right_sum, max_right = -999999999, -1
summ = 0
for i in range(mid, low - 1, -1):
summ += A[i]
if summ > left_sum:
left_sum = summ
max_left = i
summ = 0
for i in range(mid + 1, high + 1):
summ += A[i]
if summ > right_sum:
right_sum = summ
max_right = i
return max_left, max_right, (left_sum + right_sum)
def max_sub_array(nums: list[int]) -> int:
"""
Finds the contiguous subarray which has the largest sum and return its sum.
>>> max_sub_array([-2, 1, -3, 4, -1, 2, 1, -5, 4])
6
An empty (sub)array has sum 0.
>>> max_sub_array([])
0
If all elements are negative, the largest subarray would be the empty array,
having the sum 0.
>>> max_sub_array([-1, -2, -3])
0
>>> max_sub_array([5, -2, -3])
5
>>> max_sub_array([31, -41, 59, 26, -53, 58, 97, -93, -23, 84])
187
"""
best = 0
current = 0
for i in nums:
current += i
if current < 0:
current = 0
best = max(best, current)
return best
if __name__ == "__main__":
"""
A random simulation of this algorithm.
"""
import time
from random import randint
from matplotlib import pyplot as plt
inputs = [10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
tim = []
for i in inputs:
li = [randint(1, i) for j in range(i)]
strt = time.time()
(find_max_sub_array(li, 0, len(li) - 1))
end = time.time()
tim.append(end - strt)
print("No of Inputs Time Taken")
for i in range(len(inputs)):
print(inputs[i], "\t\t", tim[i])
plt.plot(inputs, tim)
plt.xlabel("Number of Inputs")
plt.ylabel("Time taken in seconds ")
plt.show()
| """
author : Mayank Kumar Jha (mk9440)
"""
from __future__ import annotations
def find_max_sub_array(A, low, high):
if low == high:
return low, high, A[low]
else:
mid = (low + high) // 2
left_low, left_high, left_sum = find_max_sub_array(A, low, mid)
right_low, right_high, right_sum = find_max_sub_array(A, mid + 1, high)
cross_left, cross_right, cross_sum = find_max_cross_sum(A, low, mid, high)
if left_sum >= right_sum and left_sum >= cross_sum:
return left_low, left_high, left_sum
elif right_sum >= left_sum and right_sum >= cross_sum:
return right_low, right_high, right_sum
else:
return cross_left, cross_right, cross_sum
def find_max_cross_sum(A, low, mid, high):
left_sum, max_left = -999999999, -1
right_sum, max_right = -999999999, -1
summ = 0
for i in range(mid, low - 1, -1):
summ += A[i]
if summ > left_sum:
left_sum = summ
max_left = i
summ = 0
for i in range(mid + 1, high + 1):
summ += A[i]
if summ > right_sum:
right_sum = summ
max_right = i
return max_left, max_right, (left_sum + right_sum)
def max_sub_array(nums: list[int]) -> int:
"""
Finds the contiguous subarray which has the largest sum and return its sum.
>>> max_sub_array([-2, 1, -3, 4, -1, 2, 1, -5, 4])
6
An empty (sub)array has sum 0.
>>> max_sub_array([])
0
If all elements are negative, the largest subarray would be the empty array,
having the sum 0.
>>> max_sub_array([-1, -2, -3])
0
>>> max_sub_array([5, -2, -3])
5
>>> max_sub_array([31, -41, 59, 26, -53, 58, 97, -93, -23, 84])
187
"""
best = 0
current = 0
for i in nums:
current += i
if current < 0:
current = 0
best = max(best, current)
return best
if __name__ == "__main__":
"""
A random simulation of this algorithm.
"""
import time
from random import randint
from matplotlib import pyplot as plt
inputs = [10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
tim = []
for i in inputs:
li = [randint(1, i) for j in range(i)]
strt = time.time()
(find_max_sub_array(li, 0, len(li) - 1))
end = time.time()
tim.append(end - strt)
print("No of Inputs Time Taken")
for i in range(len(inputs)):
print(inputs[i], "\t\t", tim[i])
plt.plot(inputs, tim)
plt.xlabel("Number of Inputs")
plt.ylabel("Time taken in seconds ")
plt.show()
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| # Implementation of Circular Queue (using Python lists)
class CircularQueue:
"""Circular FIFO queue with a fixed capacity"""
def __init__(self, n: int):
self.n = n
self.array = [None] * self.n
self.front = 0 # index of the first element
self.rear = 0
self.size = 0
def __len__(self) -> int:
"""
>>> cq = CircularQueue(5)
>>> len(cq)
0
>>> cq.enqueue("A") # doctest: +ELLIPSIS
<data_structures.queue.circular_queue.CircularQueue object at ...
>>> len(cq)
1
"""
return self.size
def is_empty(self) -> bool:
"""
>>> cq = CircularQueue(5)
>>> cq.is_empty()
True
>>> cq.enqueue("A").is_empty()
False
"""
return self.size == 0
def first(self):
"""
>>> cq = CircularQueue(5)
>>> cq.first()
False
>>> cq.enqueue("A").first()
'A'
"""
return False if self.is_empty() else self.array[self.front]
def enqueue(self, data):
"""
This function insert an element in the queue using self.rear value as an index
>>> cq = CircularQueue(5)
>>> cq.enqueue("A") # doctest: +ELLIPSIS
<data_structures.queue.circular_queue.CircularQueue object at ...
>>> (cq.size, cq.first())
(1, 'A')
>>> cq.enqueue("B") # doctest: +ELLIPSIS
<data_structures.queue.circular_queue.CircularQueue object at ...
>>> (cq.size, cq.first())
(2, 'A')
"""
if self.size >= self.n:
raise Exception("QUEUE IS FULL")
self.array[self.rear] = data
self.rear = (self.rear + 1) % self.n
self.size += 1
return self
def dequeue(self):
"""
This function removes an element from the queue using on self.front value as an
index
>>> cq = CircularQueue(5)
>>> cq.dequeue()
Traceback (most recent call last):
...
Exception: UNDERFLOW
>>> cq.enqueue("A").enqueue("B").dequeue()
'A'
>>> (cq.size, cq.first())
(1, 'B')
>>> cq.dequeue()
'B'
>>> cq.dequeue()
Traceback (most recent call last):
...
Exception: UNDERFLOW
"""
if self.size == 0:
raise Exception("UNDERFLOW")
temp = self.array[self.front]
self.array[self.front] = None
self.front = (self.front + 1) % self.n
self.size -= 1
return temp
| # Implementation of Circular Queue (using Python lists)
class CircularQueue:
"""Circular FIFO queue with a fixed capacity"""
def __init__(self, n: int):
self.n = n
self.array = [None] * self.n
self.front = 0 # index of the first element
self.rear = 0
self.size = 0
def __len__(self) -> int:
"""
>>> cq = CircularQueue(5)
>>> len(cq)
0
>>> cq.enqueue("A") # doctest: +ELLIPSIS
<data_structures.queue.circular_queue.CircularQueue object at ...
>>> len(cq)
1
"""
return self.size
def is_empty(self) -> bool:
"""
>>> cq = CircularQueue(5)
>>> cq.is_empty()
True
>>> cq.enqueue("A").is_empty()
False
"""
return self.size == 0
def first(self):
"""
>>> cq = CircularQueue(5)
>>> cq.first()
False
>>> cq.enqueue("A").first()
'A'
"""
return False if self.is_empty() else self.array[self.front]
def enqueue(self, data):
"""
This function insert an element in the queue using self.rear value as an index
>>> cq = CircularQueue(5)
>>> cq.enqueue("A") # doctest: +ELLIPSIS
<data_structures.queue.circular_queue.CircularQueue object at ...
>>> (cq.size, cq.first())
(1, 'A')
>>> cq.enqueue("B") # doctest: +ELLIPSIS
<data_structures.queue.circular_queue.CircularQueue object at ...
>>> (cq.size, cq.first())
(2, 'A')
"""
if self.size >= self.n:
raise Exception("QUEUE IS FULL")
self.array[self.rear] = data
self.rear = (self.rear + 1) % self.n
self.size += 1
return self
def dequeue(self):
"""
This function removes an element from the queue using on self.front value as an
index
>>> cq = CircularQueue(5)
>>> cq.dequeue()
Traceback (most recent call last):
...
Exception: UNDERFLOW
>>> cq.enqueue("A").enqueue("B").dequeue()
'A'
>>> (cq.size, cq.first())
(1, 'B')
>>> cq.dequeue()
'B'
>>> cq.dequeue()
Traceback (most recent call last):
...
Exception: UNDERFLOW
"""
if self.size == 0:
raise Exception("UNDERFLOW")
temp = self.array[self.front]
self.array[self.front] = None
self.front = (self.front + 1) % self.n
self.size -= 1
return temp
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Problem 20: https://projecteuler.net/problem=20
n! means n × (n − 1) × ... × 3 × 2 × 1
For example, 10! = 10 × 9 × ... × 3 × 2 × 1 = 3628800,
and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.
Find the sum of the digits in the number 100!
"""
from math import factorial
def solution(num: int = 100) -> int:
"""Returns the sum of the digits in the factorial of num
>>> solution(1000)
10539
>>> solution(200)
1404
>>> solution(100)
648
>>> solution(50)
216
>>> solution(10)
27
>>> solution(5)
3
>>> solution(3)
6
>>> solution(2)
2
>>> solution(1)
1
>>> solution(0)
1
"""
return sum(map(int, str(factorial(num))))
if __name__ == "__main__":
print(solution(int(input("Enter the Number: ").strip())))
| """
Problem 20: https://projecteuler.net/problem=20
n! means n × (n − 1) × ... × 3 × 2 × 1
For example, 10! = 10 × 9 × ... × 3 × 2 × 1 = 3628800,
and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.
Find the sum of the digits in the number 100!
"""
from math import factorial
def solution(num: int = 100) -> int:
"""Returns the sum of the digits in the factorial of num
>>> solution(1000)
10539
>>> solution(200)
1404
>>> solution(100)
648
>>> solution(50)
216
>>> solution(10)
27
>>> solution(5)
3
>>> solution(3)
6
>>> solution(2)
2
>>> solution(1)
1
>>> solution(0)
1
"""
return sum(map(int, str(factorial(num))))
if __name__ == "__main__":
print(solution(int(input("Enter the Number: ").strip())))
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| # Created by sarathkaul on 17/11/19
# Modified by Arkadip Bhattacharya(@darkmatter18) on 20/04/2020
from collections import defaultdict
def word_occurence(sentence: str) -> dict:
"""
>>> from collections import Counter
>>> SENTENCE = "a b A b c b d b d e f e g e h e i e j e 0"
>>> occurence_dict = word_occurence(SENTENCE)
>>> all(occurence_dict[word] == count for word, count
... in Counter(SENTENCE.split()).items())
True
>>> dict(word_occurence("Two spaces"))
{'Two': 1, 'spaces': 1}
"""
occurrence: dict = defaultdict(int)
# Creating a dictionary containing count of each word
for word in sentence.split():
occurrence[word] += 1
return occurrence
if __name__ == "__main__":
for word, count in word_occurence("INPUT STRING").items():
print(f"{word}: {count}")
| # Created by sarathkaul on 17/11/19
# Modified by Arkadip Bhattacharya(@darkmatter18) on 20/04/2020
from collections import defaultdict
def word_occurence(sentence: str) -> dict:
"""
>>> from collections import Counter
>>> SENTENCE = "a b A b c b d b d e f e g e h e i e j e 0"
>>> occurence_dict = word_occurence(SENTENCE)
>>> all(occurence_dict[word] == count for word, count
... in Counter(SENTENCE.split()).items())
True
>>> dict(word_occurence("Two spaces"))
{'Two': 1, 'spaces': 1}
"""
occurrence: dict = defaultdict(int)
# Creating a dictionary containing count of each word
for word in sentence.split():
occurrence[word] += 1
return occurrence
if __name__ == "__main__":
for word, count in word_occurence("INPUT STRING").items():
print(f"{word}: {count}")
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| -1 |
||
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Implementation Burke's algorithm (dithering)
"""
import numpy as np
from cv2 import destroyAllWindows, imread, imshow, waitKey
class Burkes:
"""
Burke's algorithm is using for converting grayscale image to black and white version
Source: Source: https://en.wikipedia.org/wiki/Dither
Note:
* Best results are given with threshold= ~1/2 * max greyscale value.
* This implementation get RGB image and converts it to greyscale in runtime.
"""
def __init__(self, input_img, threshold: int):
self.min_threshold = 0
# max greyscale value for #FFFFFF
self.max_threshold = int(self.get_greyscale(255, 255, 255))
if not self.min_threshold < threshold < self.max_threshold:
raise ValueError(f"Factor value should be from 0 to {self.max_threshold}")
self.input_img = input_img
self.threshold = threshold
self.width, self.height = self.input_img.shape[1], self.input_img.shape[0]
# error table size (+4 columns and +1 row) greater than input image because of
# lack of if statements
self.error_table = [
[0 for _ in range(self.height + 4)] for __ in range(self.width + 1)
]
self.output_img = np.ones((self.width, self.height, 3), np.uint8) * 255
@classmethod
def get_greyscale(cls, blue: int, green: int, red: int) -> float:
"""
>>> Burkes.get_greyscale(3, 4, 5)
3.753
"""
return 0.114 * blue + 0.587 * green + 0.2126 * red
def process(self) -> None:
for y in range(self.height):
for x in range(self.width):
greyscale = int(self.get_greyscale(*self.input_img[y][x]))
if self.threshold > greyscale + self.error_table[y][x]:
self.output_img[y][x] = (0, 0, 0)
current_error = greyscale + self.error_table[x][y]
else:
self.output_img[y][x] = (255, 255, 255)
current_error = greyscale + self.error_table[x][y] - 255
"""
Burkes error propagation (`*` is current pixel):
* 8/32 4/32
2/32 4/32 8/32 4/32 2/32
"""
self.error_table[y][x + 1] += int(8 / 32 * current_error)
self.error_table[y][x + 2] += int(4 / 32 * current_error)
self.error_table[y + 1][x] += int(8 / 32 * current_error)
self.error_table[y + 1][x + 1] += int(4 / 32 * current_error)
self.error_table[y + 1][x + 2] += int(2 / 32 * current_error)
self.error_table[y + 1][x - 1] += int(4 / 32 * current_error)
self.error_table[y + 1][x - 2] += int(2 / 32 * current_error)
if __name__ == "__main__":
# create Burke's instances with original images in greyscale
burkes_instances = [
Burkes(imread("image_data/lena.jpg", 1), threshold)
for threshold in (1, 126, 130, 140)
]
for burkes in burkes_instances:
burkes.process()
for burkes in burkes_instances:
imshow(
f"Original image with dithering threshold: {burkes.threshold}",
burkes.output_img,
)
waitKey(0)
destroyAllWindows()
| """
Implementation Burke's algorithm (dithering)
"""
import numpy as np
from cv2 import destroyAllWindows, imread, imshow, waitKey
class Burkes:
"""
Burke's algorithm is using for converting grayscale image to black and white version
Source: Source: https://en.wikipedia.org/wiki/Dither
Note:
* Best results are given with threshold= ~1/2 * max greyscale value.
* This implementation get RGB image and converts it to greyscale in runtime.
"""
def __init__(self, input_img, threshold: int):
self.min_threshold = 0
# max greyscale value for #FFFFFF
self.max_threshold = int(self.get_greyscale(255, 255, 255))
if not self.min_threshold < threshold < self.max_threshold:
raise ValueError(f"Factor value should be from 0 to {self.max_threshold}")
self.input_img = input_img
self.threshold = threshold
self.width, self.height = self.input_img.shape[1], self.input_img.shape[0]
# error table size (+4 columns and +1 row) greater than input image because of
# lack of if statements
self.error_table = [
[0 for _ in range(self.height + 4)] for __ in range(self.width + 1)
]
self.output_img = np.ones((self.width, self.height, 3), np.uint8) * 255
@classmethod
def get_greyscale(cls, blue: int, green: int, red: int) -> float:
"""
>>> Burkes.get_greyscale(3, 4, 5)
3.753
"""
return 0.114 * blue + 0.587 * green + 0.2126 * red
def process(self) -> None:
for y in range(self.height):
for x in range(self.width):
greyscale = int(self.get_greyscale(*self.input_img[y][x]))
if self.threshold > greyscale + self.error_table[y][x]:
self.output_img[y][x] = (0, 0, 0)
current_error = greyscale + self.error_table[x][y]
else:
self.output_img[y][x] = (255, 255, 255)
current_error = greyscale + self.error_table[x][y] - 255
"""
Burkes error propagation (`*` is current pixel):
* 8/32 4/32
2/32 4/32 8/32 4/32 2/32
"""
self.error_table[y][x + 1] += int(8 / 32 * current_error)
self.error_table[y][x + 2] += int(4 / 32 * current_error)
self.error_table[y + 1][x] += int(8 / 32 * current_error)
self.error_table[y + 1][x + 1] += int(4 / 32 * current_error)
self.error_table[y + 1][x + 2] += int(2 / 32 * current_error)
self.error_table[y + 1][x - 1] += int(4 / 32 * current_error)
self.error_table[y + 1][x - 2] += int(2 / 32 * current_error)
if __name__ == "__main__":
# create Burke's instances with original images in greyscale
burkes_instances = [
Burkes(imread("image_data/lena.jpg", 1), threshold)
for threshold in (1, 126, 130, 140)
]
for burkes in burkes_instances:
burkes.process()
for burkes in burkes_instances:
imshow(
f"Original image with dithering threshold: {burkes.threshold}",
burkes.output_img,
)
waitKey(0)
destroyAllWindows()
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """Implementation of Basic Math in Python."""
import math
def prime_factors(n: int) -> list:
"""Find Prime Factors.
>>> prime_factors(100)
[2, 2, 5, 5]
>>> prime_factors(0)
Traceback (most recent call last):
...
ValueError: Only positive integers have prime factors
>>> prime_factors(-10)
Traceback (most recent call last):
...
ValueError: Only positive integers have prime factors
"""
if n <= 0:
raise ValueError("Only positive integers have prime factors")
pf = []
while n % 2 == 0:
pf.append(2)
n = int(n / 2)
for i in range(3, int(math.sqrt(n)) + 1, 2):
while n % i == 0:
pf.append(i)
n = int(n / i)
if n > 2:
pf.append(n)
return pf
def number_of_divisors(n: int) -> int:
"""Calculate Number of Divisors of an Integer.
>>> number_of_divisors(100)
9
>>> number_of_divisors(0)
Traceback (most recent call last):
...
ValueError: Only positive numbers are accepted
>>> number_of_divisors(-10)
Traceback (most recent call last):
...
ValueError: Only positive numbers are accepted
"""
if n <= 0:
raise ValueError("Only positive numbers are accepted")
div = 1
temp = 1
while n % 2 == 0:
temp += 1
n = int(n / 2)
div *= temp
for i in range(3, int(math.sqrt(n)) + 1, 2):
temp = 1
while n % i == 0:
temp += 1
n = int(n / i)
div *= temp
return div
def sum_of_divisors(n: int) -> int:
"""Calculate Sum of Divisors.
>>> sum_of_divisors(100)
217
>>> sum_of_divisors(0)
Traceback (most recent call last):
...
ValueError: Only positive numbers are accepted
>>> sum_of_divisors(-10)
Traceback (most recent call last):
...
ValueError: Only positive numbers are accepted
"""
if n <= 0:
raise ValueError("Only positive numbers are accepted")
s = 1
temp = 1
while n % 2 == 0:
temp += 1
n = int(n / 2)
if temp > 1:
s *= (2 ** temp - 1) / (2 - 1)
for i in range(3, int(math.sqrt(n)) + 1, 2):
temp = 1
while n % i == 0:
temp += 1
n = int(n / i)
if temp > 1:
s *= (i ** temp - 1) / (i - 1)
return int(s)
def euler_phi(n: int) -> int:
"""Calculate Euler's Phi Function.
>>> euler_phi(100)
40
"""
s = n
for x in set(prime_factors(n)):
s *= (x - 1) / x
return int(s)
if __name__ == "__main__":
import doctest
doctest.testmod()
| """Implementation of Basic Math in Python."""
import math
def prime_factors(n: int) -> list:
"""Find Prime Factors.
>>> prime_factors(100)
[2, 2, 5, 5]
>>> prime_factors(0)
Traceback (most recent call last):
...
ValueError: Only positive integers have prime factors
>>> prime_factors(-10)
Traceback (most recent call last):
...
ValueError: Only positive integers have prime factors
"""
if n <= 0:
raise ValueError("Only positive integers have prime factors")
pf = []
while n % 2 == 0:
pf.append(2)
n = int(n / 2)
for i in range(3, int(math.sqrt(n)) + 1, 2):
while n % i == 0:
pf.append(i)
n = int(n / i)
if n > 2:
pf.append(n)
return pf
def number_of_divisors(n: int) -> int:
"""Calculate Number of Divisors of an Integer.
>>> number_of_divisors(100)
9
>>> number_of_divisors(0)
Traceback (most recent call last):
...
ValueError: Only positive numbers are accepted
>>> number_of_divisors(-10)
Traceback (most recent call last):
...
ValueError: Only positive numbers are accepted
"""
if n <= 0:
raise ValueError("Only positive numbers are accepted")
div = 1
temp = 1
while n % 2 == 0:
temp += 1
n = int(n / 2)
div *= temp
for i in range(3, int(math.sqrt(n)) + 1, 2):
temp = 1
while n % i == 0:
temp += 1
n = int(n / i)
div *= temp
return div
def sum_of_divisors(n: int) -> int:
"""Calculate Sum of Divisors.
>>> sum_of_divisors(100)
217
>>> sum_of_divisors(0)
Traceback (most recent call last):
...
ValueError: Only positive numbers are accepted
>>> sum_of_divisors(-10)
Traceback (most recent call last):
...
ValueError: Only positive numbers are accepted
"""
if n <= 0:
raise ValueError("Only positive numbers are accepted")
s = 1
temp = 1
while n % 2 == 0:
temp += 1
n = int(n / 2)
if temp > 1:
s *= (2 ** temp - 1) / (2 - 1)
for i in range(3, int(math.sqrt(n)) + 1, 2):
temp = 1
while n % i == 0:
temp += 1
n = int(n / i)
if temp > 1:
s *= (i ** temp - 1) / (i - 1)
return int(s)
def euler_phi(n: int) -> int:
"""Calculate Euler's Phi Function.
>>> euler_phi(100)
40
"""
s = n
for x in set(prime_factors(n)):
s *= (x - 1) / x
return int(s)
if __name__ == "__main__":
import doctest
doctest.testmod()
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| -1 |
||
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
In mathematics, the Lucas–Lehmer test (LLT) is a primality test for Mersenne
numbers. https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test
A Mersenne number is a number that is one less than a power of two.
That is M_p = 2^p - 1
https://en.wikipedia.org/wiki/Mersenne_prime
The Lucas–Lehmer test is the primality test used by the
Great Internet Mersenne Prime Search (GIMPS) to locate large primes.
"""
# Primality test 2^p - 1
# Return true if 2^p - 1 is prime
def lucas_lehmer_test(p: int) -> bool:
"""
>>> lucas_lehmer_test(p=7)
True
>>> lucas_lehmer_test(p=11)
False
# M_11 = 2^11 - 1 = 2047 = 23 * 89
"""
if p < 2:
raise ValueError("p should not be less than 2!")
elif p == 2:
return True
s = 4
M = (1 << p) - 1
for i in range(p - 2):
s = ((s * s) - 2) % M
return s == 0
if __name__ == "__main__":
print(lucas_lehmer_test(7))
print(lucas_lehmer_test(11))
| """
In mathematics, the Lucas–Lehmer test (LLT) is a primality test for Mersenne
numbers. https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test
A Mersenne number is a number that is one less than a power of two.
That is M_p = 2^p - 1
https://en.wikipedia.org/wiki/Mersenne_prime
The Lucas–Lehmer test is the primality test used by the
Great Internet Mersenne Prime Search (GIMPS) to locate large primes.
"""
# Primality test 2^p - 1
# Return true if 2^p - 1 is prime
def lucas_lehmer_test(p: int) -> bool:
"""
>>> lucas_lehmer_test(p=7)
True
>>> lucas_lehmer_test(p=11)
False
# M_11 = 2^11 - 1 = 2047 = 23 * 89
"""
if p < 2:
raise ValueError("p should not be less than 2!")
elif p == 2:
return True
s = 4
M = (1 << p) - 1
for i in range(p - 2):
s = ((s * s) - 2) % M
return s == 0
if __name__ == "__main__":
print(lucas_lehmer_test(7))
print(lucas_lehmer_test(11))
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| -1 |
||
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
https://en.wikipedia.org/wiki/Breadth-first_search
pseudo-code:
breadth_first_search(graph G, start vertex s):
// all nodes initially unexplored
mark s as explored
let Q = queue data structure, initialized with s
while Q is non-empty:
remove the first node of Q, call it v
for each edge(v, w): // for w in graph[v]
if w unexplored:
mark w as explored
add w to Q (at the end)
"""
from __future__ import annotations
G = {
"A": ["B", "C"],
"B": ["A", "D", "E"],
"C": ["A", "F"],
"D": ["B"],
"E": ["B", "F"],
"F": ["C", "E"],
}
def breadth_first_search(graph: dict, start: str) -> set[str]:
"""
>>> ''.join(sorted(breadth_first_search(G, 'A')))
'ABCDEF'
"""
explored = {start}
queue = [start]
while queue:
v = queue.pop(0) # queue.popleft()
for w in graph[v]:
if w not in explored:
explored.add(w)
queue.append(w)
return explored
if __name__ == "__main__":
print(breadth_first_search(G, "A"))
| """
https://en.wikipedia.org/wiki/Breadth-first_search
pseudo-code:
breadth_first_search(graph G, start vertex s):
// all nodes initially unexplored
mark s as explored
let Q = queue data structure, initialized with s
while Q is non-empty:
remove the first node of Q, call it v
for each edge(v, w): // for w in graph[v]
if w unexplored:
mark w as explored
add w to Q (at the end)
"""
from __future__ import annotations
G = {
"A": ["B", "C"],
"B": ["A", "D", "E"],
"C": ["A", "F"],
"D": ["B"],
"E": ["B", "F"],
"F": ["C", "E"],
}
def breadth_first_search(graph: dict, start: str) -> set[str]:
"""
>>> ''.join(sorted(breadth_first_search(G, 'A')))
'ABCDEF'
"""
explored = {start}
queue = [start]
while queue:
v = queue.pop(0) # queue.popleft()
for w in graph[v]:
if w not in explored:
explored.add(w)
queue.append(w)
return explored
if __name__ == "__main__":
print(breadth_first_search(G, "A"))
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| import heapq
import numpy as np
TPos = tuple[int, int]
class PriorityQueue:
def __init__(self):
self.elements = []
self.set = set()
def minkey(self):
if not self.empty():
return self.elements[0][0]
else:
return float("inf")
def empty(self):
return len(self.elements) == 0
def put(self, item, priority):
if item not in self.set:
heapq.heappush(self.elements, (priority, item))
self.set.add(item)
else:
# update
# print("update", item)
temp = []
(pri, x) = heapq.heappop(self.elements)
while x != item:
temp.append((pri, x))
(pri, x) = heapq.heappop(self.elements)
temp.append((priority, item))
for (pro, xxx) in temp:
heapq.heappush(self.elements, (pro, xxx))
def remove_element(self, item):
if item in self.set:
self.set.remove(item)
temp = []
(pro, x) = heapq.heappop(self.elements)
while x != item:
temp.append((pro, x))
(pro, x) = heapq.heappop(self.elements)
for (prito, yyy) in temp:
heapq.heappush(self.elements, (prito, yyy))
def top_show(self):
return self.elements[0][1]
def get(self):
(priority, item) = heapq.heappop(self.elements)
self.set.remove(item)
return (priority, item)
def consistent_heuristic(P: TPos, goal: TPos):
# euclidean distance
a = np.array(P)
b = np.array(goal)
return np.linalg.norm(a - b)
def heuristic_2(P: TPos, goal: TPos):
# integer division by time variable
return consistent_heuristic(P, goal) // t
def heuristic_1(P: TPos, goal: TPos):
# manhattan distance
return abs(P[0] - goal[0]) + abs(P[1] - goal[1])
def key(start: TPos, i: int, goal: TPos, g_function: dict[TPos, float]):
ans = g_function[start] + W1 * heuristics[i](start, goal)
return ans
def do_something(back_pointer, goal, start):
grid = np.chararray((n, n))
for i in range(n):
for j in range(n):
grid[i][j] = "*"
for i in range(n):
for j in range(n):
if (j, (n - 1) - i) in blocks:
grid[i][j] = "#"
grid[0][(n - 1)] = "-"
x = back_pointer[goal]
while x != start:
(x_c, y_c) = x
# print(x)
grid[(n - 1) - y_c][x_c] = "-"
x = back_pointer[x]
grid[(n - 1)][0] = "-"
for i in range(n):
for j in range(n):
if (i, j) == (0, n - 1):
print(grid[i][j], end=" ")
print("<-- End position", end=" ")
else:
print(grid[i][j], end=" ")
print()
print("^")
print("Start position")
print()
print("# is an obstacle")
print("- is the path taken by algorithm")
print("PATH TAKEN BY THE ALGORITHM IS:-")
x = back_pointer[goal]
while x != start:
print(x, end=" ")
x = back_pointer[x]
print(x)
quit()
def valid(p: TPos):
if p[0] < 0 or p[0] > n - 1:
return False
if p[1] < 0 or p[1] > n - 1:
return False
return True
def expand_state(
s,
j,
visited,
g_function,
close_list_anchor,
close_list_inad,
open_list,
back_pointer,
):
for itera in range(n_heuristic):
open_list[itera].remove_element(s)
# print("s", s)
# print("j", j)
(x, y) = s
left = (x - 1, y)
right = (x + 1, y)
up = (x, y + 1)
down = (x, y - 1)
for neighbours in [left, right, up, down]:
if neighbours not in blocks:
if valid(neighbours) and neighbours not in visited:
# print("neighbour", neighbours)
visited.add(neighbours)
back_pointer[neighbours] = -1
g_function[neighbours] = float("inf")
if valid(neighbours) and g_function[neighbours] > g_function[s] + 1:
g_function[neighbours] = g_function[s] + 1
back_pointer[neighbours] = s
if neighbours not in close_list_anchor:
open_list[0].put(neighbours, key(neighbours, 0, goal, g_function))
if neighbours not in close_list_inad:
for var in range(1, n_heuristic):
if key(neighbours, var, goal, g_function) <= W2 * key(
neighbours, 0, goal, g_function
):
open_list[j].put(
neighbours, key(neighbours, var, goal, g_function)
)
def make_common_ground():
some_list = []
for x in range(1, 5):
for y in range(1, 6):
some_list.append((x, y))
for x in range(15, 20):
some_list.append((x, 17))
for x in range(10, 19):
for y in range(1, 15):
some_list.append((x, y))
# L block
for x in range(1, 4):
for y in range(12, 19):
some_list.append((x, y))
for x in range(3, 13):
for y in range(16, 19):
some_list.append((x, y))
return some_list
heuristics = {0: consistent_heuristic, 1: heuristic_1, 2: heuristic_2}
blocks_blk = [
(0, 1),
(1, 1),
(2, 1),
(3, 1),
(4, 1),
(5, 1),
(6, 1),
(7, 1),
(8, 1),
(9, 1),
(10, 1),
(11, 1),
(12, 1),
(13, 1),
(14, 1),
(15, 1),
(16, 1),
(17, 1),
(18, 1),
(19, 1),
]
blocks_all = make_common_ground()
blocks = blocks_blk
# hyper parameters
W1 = 1
W2 = 1
n = 20
n_heuristic = 3 # one consistent and two other inconsistent
# start and end destination
start = (0, 0)
goal = (n - 1, n - 1)
t = 1
def multi_a_star(start: TPos, goal: TPos, n_heuristic: int):
g_function = {start: 0, goal: float("inf")}
back_pointer = {start: -1, goal: -1}
open_list = []
visited = set()
for i in range(n_heuristic):
open_list.append(PriorityQueue())
open_list[i].put(start, key(start, i, goal, g_function))
close_list_anchor: list[int] = []
close_list_inad: list[int] = []
while open_list[0].minkey() < float("inf"):
for i in range(1, n_heuristic):
# print(open_list[0].minkey(), open_list[i].minkey())
if open_list[i].minkey() <= W2 * open_list[0].minkey():
global t
t += 1
if g_function[goal] <= open_list[i].minkey():
if g_function[goal] < float("inf"):
do_something(back_pointer, goal, start)
else:
_, get_s = open_list[i].top_show()
visited.add(get_s)
expand_state(
get_s,
i,
visited,
g_function,
close_list_anchor,
close_list_inad,
open_list,
back_pointer,
)
close_list_inad.append(get_s)
else:
if g_function[goal] <= open_list[0].minkey():
if g_function[goal] < float("inf"):
do_something(back_pointer, goal, start)
else:
get_s = open_list[0].top_show()
visited.add(get_s)
expand_state(
get_s,
0,
visited,
g_function,
close_list_anchor,
close_list_inad,
open_list,
back_pointer,
)
close_list_anchor.append(get_s)
print("No path found to goal")
print()
for i in range(n - 1, -1, -1):
for j in range(n):
if (j, i) in blocks:
print("#", end=" ")
elif (j, i) in back_pointer:
if (j, i) == (n - 1, n - 1):
print("*", end=" ")
else:
print("-", end=" ")
else:
print("*", end=" ")
if (j, i) == (n - 1, n - 1):
print("<-- End position", end=" ")
print()
print("^")
print("Start position")
print()
print("# is an obstacle")
print("- is the path taken by algorithm")
if __name__ == "__main__":
multi_a_star(start, goal, n_heuristic)
| import heapq
import numpy as np
TPos = tuple[int, int]
class PriorityQueue:
def __init__(self):
self.elements = []
self.set = set()
def minkey(self):
if not self.empty():
return self.elements[0][0]
else:
return float("inf")
def empty(self):
return len(self.elements) == 0
def put(self, item, priority):
if item not in self.set:
heapq.heappush(self.elements, (priority, item))
self.set.add(item)
else:
# update
# print("update", item)
temp = []
(pri, x) = heapq.heappop(self.elements)
while x != item:
temp.append((pri, x))
(pri, x) = heapq.heappop(self.elements)
temp.append((priority, item))
for (pro, xxx) in temp:
heapq.heappush(self.elements, (pro, xxx))
def remove_element(self, item):
if item in self.set:
self.set.remove(item)
temp = []
(pro, x) = heapq.heappop(self.elements)
while x != item:
temp.append((pro, x))
(pro, x) = heapq.heappop(self.elements)
for (prito, yyy) in temp:
heapq.heappush(self.elements, (prito, yyy))
def top_show(self):
return self.elements[0][1]
def get(self):
(priority, item) = heapq.heappop(self.elements)
self.set.remove(item)
return (priority, item)
def consistent_heuristic(P: TPos, goal: TPos):
# euclidean distance
a = np.array(P)
b = np.array(goal)
return np.linalg.norm(a - b)
def heuristic_2(P: TPos, goal: TPos):
# integer division by time variable
return consistent_heuristic(P, goal) // t
def heuristic_1(P: TPos, goal: TPos):
# manhattan distance
return abs(P[0] - goal[0]) + abs(P[1] - goal[1])
def key(start: TPos, i: int, goal: TPos, g_function: dict[TPos, float]):
ans = g_function[start] + W1 * heuristics[i](start, goal)
return ans
def do_something(back_pointer, goal, start):
grid = np.chararray((n, n))
for i in range(n):
for j in range(n):
grid[i][j] = "*"
for i in range(n):
for j in range(n):
if (j, (n - 1) - i) in blocks:
grid[i][j] = "#"
grid[0][(n - 1)] = "-"
x = back_pointer[goal]
while x != start:
(x_c, y_c) = x
# print(x)
grid[(n - 1) - y_c][x_c] = "-"
x = back_pointer[x]
grid[(n - 1)][0] = "-"
for i in range(n):
for j in range(n):
if (i, j) == (0, n - 1):
print(grid[i][j], end=" ")
print("<-- End position", end=" ")
else:
print(grid[i][j], end=" ")
print()
print("^")
print("Start position")
print()
print("# is an obstacle")
print("- is the path taken by algorithm")
print("PATH TAKEN BY THE ALGORITHM IS:-")
x = back_pointer[goal]
while x != start:
print(x, end=" ")
x = back_pointer[x]
print(x)
quit()
def valid(p: TPos):
if p[0] < 0 or p[0] > n - 1:
return False
if p[1] < 0 or p[1] > n - 1:
return False
return True
def expand_state(
s,
j,
visited,
g_function,
close_list_anchor,
close_list_inad,
open_list,
back_pointer,
):
for itera in range(n_heuristic):
open_list[itera].remove_element(s)
# print("s", s)
# print("j", j)
(x, y) = s
left = (x - 1, y)
right = (x + 1, y)
up = (x, y + 1)
down = (x, y - 1)
for neighbours in [left, right, up, down]:
if neighbours not in blocks:
if valid(neighbours) and neighbours not in visited:
# print("neighbour", neighbours)
visited.add(neighbours)
back_pointer[neighbours] = -1
g_function[neighbours] = float("inf")
if valid(neighbours) and g_function[neighbours] > g_function[s] + 1:
g_function[neighbours] = g_function[s] + 1
back_pointer[neighbours] = s
if neighbours not in close_list_anchor:
open_list[0].put(neighbours, key(neighbours, 0, goal, g_function))
if neighbours not in close_list_inad:
for var in range(1, n_heuristic):
if key(neighbours, var, goal, g_function) <= W2 * key(
neighbours, 0, goal, g_function
):
open_list[j].put(
neighbours, key(neighbours, var, goal, g_function)
)
def make_common_ground():
some_list = []
for x in range(1, 5):
for y in range(1, 6):
some_list.append((x, y))
for x in range(15, 20):
some_list.append((x, 17))
for x in range(10, 19):
for y in range(1, 15):
some_list.append((x, y))
# L block
for x in range(1, 4):
for y in range(12, 19):
some_list.append((x, y))
for x in range(3, 13):
for y in range(16, 19):
some_list.append((x, y))
return some_list
heuristics = {0: consistent_heuristic, 1: heuristic_1, 2: heuristic_2}
blocks_blk = [
(0, 1),
(1, 1),
(2, 1),
(3, 1),
(4, 1),
(5, 1),
(6, 1),
(7, 1),
(8, 1),
(9, 1),
(10, 1),
(11, 1),
(12, 1),
(13, 1),
(14, 1),
(15, 1),
(16, 1),
(17, 1),
(18, 1),
(19, 1),
]
blocks_all = make_common_ground()
blocks = blocks_blk
# hyper parameters
W1 = 1
W2 = 1
n = 20
n_heuristic = 3 # one consistent and two other inconsistent
# start and end destination
start = (0, 0)
goal = (n - 1, n - 1)
t = 1
def multi_a_star(start: TPos, goal: TPos, n_heuristic: int):
g_function = {start: 0, goal: float("inf")}
back_pointer = {start: -1, goal: -1}
open_list = []
visited = set()
for i in range(n_heuristic):
open_list.append(PriorityQueue())
open_list[i].put(start, key(start, i, goal, g_function))
close_list_anchor: list[int] = []
close_list_inad: list[int] = []
while open_list[0].minkey() < float("inf"):
for i in range(1, n_heuristic):
# print(open_list[0].minkey(), open_list[i].minkey())
if open_list[i].minkey() <= W2 * open_list[0].minkey():
global t
t += 1
if g_function[goal] <= open_list[i].minkey():
if g_function[goal] < float("inf"):
do_something(back_pointer, goal, start)
else:
_, get_s = open_list[i].top_show()
visited.add(get_s)
expand_state(
get_s,
i,
visited,
g_function,
close_list_anchor,
close_list_inad,
open_list,
back_pointer,
)
close_list_inad.append(get_s)
else:
if g_function[goal] <= open_list[0].minkey():
if g_function[goal] < float("inf"):
do_something(back_pointer, goal, start)
else:
get_s = open_list[0].top_show()
visited.add(get_s)
expand_state(
get_s,
0,
visited,
g_function,
close_list_anchor,
close_list_inad,
open_list,
back_pointer,
)
close_list_anchor.append(get_s)
print("No path found to goal")
print()
for i in range(n - 1, -1, -1):
for j in range(n):
if (j, i) in blocks:
print("#", end=" ")
elif (j, i) in back_pointer:
if (j, i) == (n - 1, n - 1):
print("*", end=" ")
else:
print("-", end=" ")
else:
print("*", end=" ")
if (j, i) == (n - 1, n - 1):
print("<-- End position", end=" ")
print()
print("^")
print("Start position")
print()
print("# is an obstacle")
print("- is the path taken by algorithm")
if __name__ == "__main__":
multi_a_star(start, goal, n_heuristic)
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| -1 |
||
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| -1 |
||
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Project Euler Problem 74: https://projecteuler.net/problem=74
The number 145 is well known for the property that the sum of the factorial of its
digits is equal to 145:
1! + 4! + 5! = 1 + 24 + 120 = 145
Perhaps less well known is 169, in that it produces the longest chain of numbers that
link back to 169; it turns out that there are only three such loops that exist:
169 → 363601 → 1454 → 169
871 → 45361 → 871
872 → 45362 → 872
It is not difficult to prove that EVERY starting number will eventually get stuck in
a loop. For example,
69 → 363600 → 1454 → 169 → 363601 (→ 1454)
78 → 45360 → 871 → 45361 (→ 871)
540 → 145 (→ 145)
Starting with 69 produces a chain of five non-repeating terms, but the longest
non-repeating chain with a starting number below one million is sixty terms.
How many chains, with a starting number below one million, contain exactly sixty
non-repeating terms?
"""
DIGIT_FACTORIALS = {
"0": 1,
"1": 1,
"2": 2,
"3": 6,
"4": 24,
"5": 120,
"6": 720,
"7": 5040,
"8": 40320,
"9": 362880,
}
CACHE_SUM_DIGIT_FACTORIALS = {145: 145}
CHAIN_LENGTH_CACHE = {
145: 0,
169: 3,
36301: 3,
1454: 3,
871: 2,
45361: 2,
872: 2,
}
def sum_digit_factorials(n: int) -> int:
"""
Return the sum of the factorial of the digits of n.
>>> sum_digit_factorials(145)
145
>>> sum_digit_factorials(45361)
871
>>> sum_digit_factorials(540)
145
"""
if n in CACHE_SUM_DIGIT_FACTORIALS:
return CACHE_SUM_DIGIT_FACTORIALS[n]
ret = sum(DIGIT_FACTORIALS[let] for let in str(n))
CACHE_SUM_DIGIT_FACTORIALS[n] = ret
return ret
def chain_length(n: int, previous: set = None) -> int:
"""
Calculate the length of the chain of non-repeating terms starting with n.
Previous is a set containing the previous member of the chain.
>>> chain_length(10101)
11
>>> chain_length(555)
20
>>> chain_length(178924)
39
"""
previous = previous or set()
if n in CHAIN_LENGTH_CACHE:
return CHAIN_LENGTH_CACHE[n]
next_number = sum_digit_factorials(n)
if next_number in previous:
CHAIN_LENGTH_CACHE[n] = 0
return 0
else:
previous.add(n)
ret = 1 + chain_length(next_number, previous)
CHAIN_LENGTH_CACHE[n] = ret
return ret
def solution(num_terms: int = 60, max_start: int = 1000000) -> int:
"""
Return the number of chains with a starting number below one million which
contain exactly n non-repeating terms.
>>> solution(10,1000)
28
"""
return sum(1 for i in range(1, max_start) if chain_length(i) == num_terms)
if __name__ == "__main__":
print(f"{solution() = }")
| """
Project Euler Problem 74: https://projecteuler.net/problem=74
The number 145 is well known for the property that the sum of the factorial of its
digits is equal to 145:
1! + 4! + 5! = 1 + 24 + 120 = 145
Perhaps less well known is 169, in that it produces the longest chain of numbers that
link back to 169; it turns out that there are only three such loops that exist:
169 → 363601 → 1454 → 169
871 → 45361 → 871
872 → 45362 → 872
It is not difficult to prove that EVERY starting number will eventually get stuck in
a loop. For example,
69 → 363600 → 1454 → 169 → 363601 (→ 1454)
78 → 45360 → 871 → 45361 (→ 871)
540 → 145 (→ 145)
Starting with 69 produces a chain of five non-repeating terms, but the longest
non-repeating chain with a starting number below one million is sixty terms.
How many chains, with a starting number below one million, contain exactly sixty
non-repeating terms?
"""
DIGIT_FACTORIALS = {
"0": 1,
"1": 1,
"2": 2,
"3": 6,
"4": 24,
"5": 120,
"6": 720,
"7": 5040,
"8": 40320,
"9": 362880,
}
CACHE_SUM_DIGIT_FACTORIALS = {145: 145}
CHAIN_LENGTH_CACHE = {
145: 0,
169: 3,
36301: 3,
1454: 3,
871: 2,
45361: 2,
872: 2,
}
def sum_digit_factorials(n: int) -> int:
"""
Return the sum of the factorial of the digits of n.
>>> sum_digit_factorials(145)
145
>>> sum_digit_factorials(45361)
871
>>> sum_digit_factorials(540)
145
"""
if n in CACHE_SUM_DIGIT_FACTORIALS:
return CACHE_SUM_DIGIT_FACTORIALS[n]
ret = sum(DIGIT_FACTORIALS[let] for let in str(n))
CACHE_SUM_DIGIT_FACTORIALS[n] = ret
return ret
def chain_length(n: int, previous: set = None) -> int:
"""
Calculate the length of the chain of non-repeating terms starting with n.
Previous is a set containing the previous member of the chain.
>>> chain_length(10101)
11
>>> chain_length(555)
20
>>> chain_length(178924)
39
"""
previous = previous or set()
if n in CHAIN_LENGTH_CACHE:
return CHAIN_LENGTH_CACHE[n]
next_number = sum_digit_factorials(n)
if next_number in previous:
CHAIN_LENGTH_CACHE[n] = 0
return 0
else:
previous.add(n)
ret = 1 + chain_length(next_number, previous)
CHAIN_LENGTH_CACHE[n] = ret
return ret
def solution(num_terms: int = 60, max_start: int = 1000000) -> int:
"""
Return the number of chains with a starting number below one million which
contain exactly n non-repeating terms.
>>> solution(10,1000)
28
"""
return sum(1 for i in range(1, max_start) if chain_length(i) == num_terms)
if __name__ == "__main__":
print(f"{solution() = }")
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Project Euler Problem 7: https://projecteuler.net/problem=7
10001st prime
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we
can see that the 6th prime is 13.
What is the 10001st prime number?
References:
- https://en.wikipedia.org/wiki/Prime_number
"""
from math import sqrt
def is_prime(num: int) -> bool:
"""
Determines whether the given number is prime or not
>>> is_prime(2)
True
>>> is_prime(15)
False
>>> is_prime(29)
True
>>> is_prime(0)
False
"""
if num == 2:
return True
elif num % 2 == 0:
return False
else:
sq = int(sqrt(num)) + 1
for i in range(3, sq, 2):
if num % i == 0:
return False
return True
def solution(nth: int = 10001) -> int:
"""
Returns the n-th prime number.
>>> solution(6)
13
>>> solution(1)
2
>>> solution(3)
5
>>> solution(20)
71
>>> solution(50)
229
>>> solution(100)
541
"""
count = 0
number = 1
while count != nth and number < 3:
number += 1
if is_prime(number):
count += 1
while count != nth:
number += 2
if is_prime(number):
count += 1
return number
if __name__ == "__main__":
print(f"{solution() = }")
| """
Project Euler Problem 7: https://projecteuler.net/problem=7
10001st prime
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we
can see that the 6th prime is 13.
What is the 10001st prime number?
References:
- https://en.wikipedia.org/wiki/Prime_number
"""
from math import sqrt
def is_prime(num: int) -> bool:
"""
Determines whether the given number is prime or not
>>> is_prime(2)
True
>>> is_prime(15)
False
>>> is_prime(29)
True
>>> is_prime(0)
False
"""
if num == 2:
return True
elif num % 2 == 0:
return False
else:
sq = int(sqrt(num)) + 1
for i in range(3, sq, 2):
if num % i == 0:
return False
return True
def solution(nth: int = 10001) -> int:
"""
Returns the n-th prime number.
>>> solution(6)
13
>>> solution(1)
2
>>> solution(3)
5
>>> solution(20)
71
>>> solution(50)
229
>>> solution(100)
541
"""
count = 0
number = 1
while count != nth and number < 3:
number += 1
if is_prime(number):
count += 1
while count != nth:
number += 2
if is_prime(number):
count += 1
return number
if __name__ == "__main__":
print(f"{solution() = }")
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| -1 |
||
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Is IP v4 address valid?
A valid IP address must be four octets in the form of A.B.C.D,
where A,B,C and D are numbers from 0-254
for example: 192.168.23.1, 172.254.254.254 are valid IP address
192.168.255.0, 255.192.3.121 are invalid IP address
"""
def is_ip_v4_address_valid(ip_v4_address: str) -> bool:
"""
print "Valid IP address" If IP is valid.
or
print "Invalid IP address" If IP is invalid.
>>> is_ip_v4_address_valid("192.168.0.23")
True
>>> is_ip_v4_address_valid("192.255.15.8")
False
>>> is_ip_v4_address_valid("172.100.0.8")
True
>>> is_ip_v4_address_valid("254.255.0.255")
False
>>> is_ip_v4_address_valid("1.2.33333333.4")
False
>>> is_ip_v4_address_valid("1.2.-3.4")
False
>>> is_ip_v4_address_valid("1.2.3")
False
>>> is_ip_v4_address_valid("1.2.3.4.5")
False
>>> is_ip_v4_address_valid("1.2.A.4")
False
>>> is_ip_v4_address_valid("0.0.0.0")
True
>>> is_ip_v4_address_valid("1.2.3.")
False
"""
octets = [int(i) for i in ip_v4_address.split(".") if i.isdigit()]
return len(octets) == 4 and all(0 <= int(octet) <= 254 for octet in octets)
if __name__ == "__main__":
ip = input().strip()
valid_or_invalid = "valid" if is_ip_v4_address_valid(ip) else "invalid"
print(f"{ip} is a {valid_or_invalid} IP v4 address.")
| """
Is IP v4 address valid?
A valid IP address must be four octets in the form of A.B.C.D,
where A,B,C and D are numbers from 0-254
for example: 192.168.23.1, 172.254.254.254 are valid IP address
192.168.255.0, 255.192.3.121 are invalid IP address
"""
def is_ip_v4_address_valid(ip_v4_address: str) -> bool:
"""
print "Valid IP address" If IP is valid.
or
print "Invalid IP address" If IP is invalid.
>>> is_ip_v4_address_valid("192.168.0.23")
True
>>> is_ip_v4_address_valid("192.255.15.8")
False
>>> is_ip_v4_address_valid("172.100.0.8")
True
>>> is_ip_v4_address_valid("254.255.0.255")
False
>>> is_ip_v4_address_valid("1.2.33333333.4")
False
>>> is_ip_v4_address_valid("1.2.-3.4")
False
>>> is_ip_v4_address_valid("1.2.3")
False
>>> is_ip_v4_address_valid("1.2.3.4.5")
False
>>> is_ip_v4_address_valid("1.2.A.4")
False
>>> is_ip_v4_address_valid("0.0.0.0")
True
>>> is_ip_v4_address_valid("1.2.3.")
False
"""
octets = [int(i) for i in ip_v4_address.split(".") if i.isdigit()]
return len(octets) == 4 and all(0 <= int(octet) <= 254 for octet in octets)
if __name__ == "__main__":
ip = input().strip()
valid_or_invalid = "valid" if is_ip_v4_address_valid(ip) else "invalid"
print(f"{ip} is a {valid_or_invalid} IP v4 address.")
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Implemented an algorithm using opencv to convert a colored image into its negative
"""
from cv2 import destroyAllWindows, imread, imshow, waitKey
def convert_to_negative(img):
# getting number of pixels in the image
pixel_h, pixel_v = img.shape[0], img.shape[1]
# converting each pixel's color to its negative
for i in range(pixel_h):
for j in range(pixel_v):
img[i][j] = [255, 255, 255] - img[i][j]
return img
if __name__ == "__main__":
# read original image
img = imread("image_data/lena.jpg", 1)
# convert to its negative
neg = convert_to_negative(img)
# show result image
imshow("negative of original image", img)
waitKey(0)
destroyAllWindows()
| """
Implemented an algorithm using opencv to convert a colored image into its negative
"""
from cv2 import destroyAllWindows, imread, imshow, waitKey
def convert_to_negative(img):
# getting number of pixels in the image
pixel_h, pixel_v = img.shape[0], img.shape[1]
# converting each pixel's color to its negative
for i in range(pixel_h):
for j in range(pixel_v):
img[i][j] = [255, 255, 255] - img[i][j]
return img
if __name__ == "__main__":
# read original image
img = imread("image_data/lena.jpg", 1)
# convert to its negative
neg = convert_to_negative(img)
# show result image
imshow("negative of original image", img)
waitKey(0)
destroyAllWindows()
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
This algorithm was created for sdbm (a public-domain reimplementation of ndbm)
database library.
It was found to do well in scrambling bits, causing better distribution of the keys
and fewer splits.
It also happens to be a good general hashing function with good distribution.
The actual function (pseudo code) is:
for i in i..len(str):
hash(i) = hash(i - 1) * 65599 + str[i];
What is included below is the faster version used in gawk. [there is even a faster,
duff-device version]
The magic constant 65599 was picked out of thin air while experimenting with
different constants.
It turns out to be a prime.
This is one of the algorithms used in berkeley db (see sleepycat) and elsewhere.
source: http://www.cse.yorku.ca/~oz/hash.html
"""
def sdbm(plain_text: str) -> int:
"""
Function implements sdbm hash, easy to use, great for bits scrambling.
iterates over each character in the given string and applies function to each of
them.
>>> sdbm('Algorithms')
1462174910723540325254304520539387479031000036
>>> sdbm('scramble bits')
730247649148944819640658295400555317318720608290373040936089
"""
hash = 0
for plain_chr in plain_text:
hash = ord(plain_chr) + (hash << 6) + (hash << 16) - hash
return hash
| """
This algorithm was created for sdbm (a public-domain reimplementation of ndbm)
database library.
It was found to do well in scrambling bits, causing better distribution of the keys
and fewer splits.
It also happens to be a good general hashing function with good distribution.
The actual function (pseudo code) is:
for i in i..len(str):
hash(i) = hash(i - 1) * 65599 + str[i];
What is included below is the faster version used in gawk. [there is even a faster,
duff-device version]
The magic constant 65599 was picked out of thin air while experimenting with
different constants.
It turns out to be a prime.
This is one of the algorithms used in berkeley db (see sleepycat) and elsewhere.
source: http://www.cse.yorku.ca/~oz/hash.html
"""
def sdbm(plain_text: str) -> int:
"""
Function implements sdbm hash, easy to use, great for bits scrambling.
iterates over each character in the given string and applies function to each of
them.
>>> sdbm('Algorithms')
1462174910723540325254304520539387479031000036
>>> sdbm('scramble bits')
730247649148944819640658295400555317318720608290373040936089
"""
hash = 0
for plain_chr in plain_text:
hash = ord(plain_chr) + (hash << 6) + (hash << 16) - hash
return hash
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| def binary_search(lst, item, start, end):
if start == end:
return start if lst[start] > item else start + 1
if start > end:
return start
mid = (start + end) // 2
if lst[mid] < item:
return binary_search(lst, item, mid + 1, end)
elif lst[mid] > item:
return binary_search(lst, item, start, mid - 1)
else:
return mid
def insertion_sort(lst):
length = len(lst)
for index in range(1, length):
value = lst[index]
pos = binary_search(lst, value, 0, index - 1)
lst = lst[:pos] + [value] + lst[pos:index] + lst[index + 1 :]
return lst
def merge(left, right):
if not left:
return right
if not right:
return left
if left[0] < right[0]:
return [left[0]] + merge(left[1:], right)
return [right[0]] + merge(left, right[1:])
def tim_sort(lst):
"""
>>> tim_sort("Python")
['P', 'h', 'n', 'o', 't', 'y']
>>> tim_sort((1.1, 1, 0, -1, -1.1))
[-1.1, -1, 0, 1, 1.1]
>>> tim_sort(list(reversed(list(range(7)))))
[0, 1, 2, 3, 4, 5, 6]
>>> tim_sort([3, 2, 1]) == insertion_sort([3, 2, 1])
True
>>> tim_sort([3, 2, 1]) == sorted([3, 2, 1])
True
"""
length = len(lst)
runs, sorted_runs = [], []
new_run = [lst[0]]
sorted_array = []
i = 1
while i < length:
if lst[i] < lst[i - 1]:
runs.append(new_run)
new_run = [lst[i]]
else:
new_run.append(lst[i])
i += 1
runs.append(new_run)
for run in runs:
sorted_runs.append(insertion_sort(run))
for run in sorted_runs:
sorted_array = merge(sorted_array, run)
return sorted_array
def main():
lst = [5, 9, 10, 3, -4, 5, 178, 92, 46, -18, 0, 7]
sorted_lst = tim_sort(lst)
print(sorted_lst)
if __name__ == "__main__":
main()
| def binary_search(lst, item, start, end):
if start == end:
return start if lst[start] > item else start + 1
if start > end:
return start
mid = (start + end) // 2
if lst[mid] < item:
return binary_search(lst, item, mid + 1, end)
elif lst[mid] > item:
return binary_search(lst, item, start, mid - 1)
else:
return mid
def insertion_sort(lst):
length = len(lst)
for index in range(1, length):
value = lst[index]
pos = binary_search(lst, value, 0, index - 1)
lst = lst[:pos] + [value] + lst[pos:index] + lst[index + 1 :]
return lst
def merge(left, right):
if not left:
return right
if not right:
return left
if left[0] < right[0]:
return [left[0]] + merge(left[1:], right)
return [right[0]] + merge(left, right[1:])
def tim_sort(lst):
"""
>>> tim_sort("Python")
['P', 'h', 'n', 'o', 't', 'y']
>>> tim_sort((1.1, 1, 0, -1, -1.1))
[-1.1, -1, 0, 1, 1.1]
>>> tim_sort(list(reversed(list(range(7)))))
[0, 1, 2, 3, 4, 5, 6]
>>> tim_sort([3, 2, 1]) == insertion_sort([3, 2, 1])
True
>>> tim_sort([3, 2, 1]) == sorted([3, 2, 1])
True
"""
length = len(lst)
runs, sorted_runs = [], []
new_run = [lst[0]]
sorted_array = []
i = 1
while i < length:
if lst[i] < lst[i - 1]:
runs.append(new_run)
new_run = [lst[i]]
else:
new_run.append(lst[i])
i += 1
runs.append(new_run)
for run in runs:
sorted_runs.append(insertion_sort(run))
for run in sorted_runs:
sorted_array = merge(sorted_array, run)
return sorted_array
def main():
lst = [5, 9, 10, 3, -4, 5, 178, 92, 46, -18, 0, 7]
sorted_lst = tim_sort(lst)
print(sorted_lst)
if __name__ == "__main__":
main()
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
The sum-of-subsetsproblem states that a set of non-negative integers, and a
value M, determine all possible subsets of the given set whose summation sum
equal to given M.
Summation of the chosen numbers must be equal to given number M and one number
can be used only once.
"""
from __future__ import annotations
def generate_sum_of_subsets_soln(nums: list[int], max_sum: int) -> list[list[int]]:
result: list[list[int]] = []
path: list[int] = []
num_index = 0
remaining_nums_sum = sum(nums)
create_state_space_tree(nums, max_sum, num_index, path, result, remaining_nums_sum)
return result
def create_state_space_tree(
nums: list[int],
max_sum: int,
num_index: int,
path: list[int],
result: list[list[int]],
remaining_nums_sum: int,
) -> None:
"""
Creates a state space tree to iterate through each branch using DFS.
It terminates the branching of a node when any of the two conditions
given below satisfy.
This algorithm follows depth-fist-search and backtracks when the node is not
branchable.
"""
if sum(path) > max_sum or (remaining_nums_sum + sum(path)) < max_sum:
return
if sum(path) == max_sum:
result.append(path)
return
for num_index in range(num_index, len(nums)):
create_state_space_tree(
nums,
max_sum,
num_index + 1,
path + [nums[num_index]],
result,
remaining_nums_sum - nums[num_index],
)
"""
remove the comment to take an input from the user
print("Enter the elements")
nums = list(map(int, input().split()))
print("Enter max_sum sum")
max_sum = int(input())
"""
nums = [3, 34, 4, 12, 5, 2]
max_sum = 9
result = generate_sum_of_subsets_soln(nums, max_sum)
print(*result)
| """
The sum-of-subsetsproblem states that a set of non-negative integers, and a
value M, determine all possible subsets of the given set whose summation sum
equal to given M.
Summation of the chosen numbers must be equal to given number M and one number
can be used only once.
"""
from __future__ import annotations
def generate_sum_of_subsets_soln(nums: list[int], max_sum: int) -> list[list[int]]:
result: list[list[int]] = []
path: list[int] = []
num_index = 0
remaining_nums_sum = sum(nums)
create_state_space_tree(nums, max_sum, num_index, path, result, remaining_nums_sum)
return result
def create_state_space_tree(
nums: list[int],
max_sum: int,
num_index: int,
path: list[int],
result: list[list[int]],
remaining_nums_sum: int,
) -> None:
"""
Creates a state space tree to iterate through each branch using DFS.
It terminates the branching of a node when any of the two conditions
given below satisfy.
This algorithm follows depth-fist-search and backtracks when the node is not
branchable.
"""
if sum(path) > max_sum or (remaining_nums_sum + sum(path)) < max_sum:
return
if sum(path) == max_sum:
result.append(path)
return
for num_index in range(num_index, len(nums)):
create_state_space_tree(
nums,
max_sum,
num_index + 1,
path + [nums[num_index]],
result,
remaining_nums_sum - nums[num_index],
)
"""
remove the comment to take an input from the user
print("Enter the elements")
nums = list(map(int, input().split()))
print("Enter max_sum sum")
max_sum = int(input())
"""
nums = [3, 34, 4, 12, 5, 2]
max_sum = 9
result = generate_sum_of_subsets_soln(nums, max_sum)
print(*result)
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
YouTube Explanation: https://www.youtube.com/watch?v=f2xi3c1S95M
Given an integer n, return the minimum steps to 1
AVAILABLE STEPS:
* Decrement by 1
* if n is divisible by 2, divide by 2
* if n is divisible by 3, divide by 3
Example 1: n = 10
10 -> 9 -> 3 -> 1
Result: 3 steps
Example 2: n = 15
15 -> 5 -> 4 -> 2 -> 1
Result: 4 steps
Example 3: n = 6
6 -> 2 -> 1
Result: 2 step
"""
from __future__ import annotations
__author__ = "Alexander Joslin"
def min_steps_to_one(number: int) -> int:
"""
Minimum steps to 1 implemented using tabulation.
>>> min_steps_to_one(10)
3
>>> min_steps_to_one(15)
4
>>> min_steps_to_one(6)
2
:param number:
:return int:
"""
if number <= 0:
raise ValueError(f"n must be greater than 0. Got n = {number}")
table = [number + 1] * (number + 1)
# starting position
table[1] = 0
for i in range(1, number):
table[i + 1] = min(table[i + 1], table[i] + 1)
# check if out of bounds
if i * 2 <= number:
table[i * 2] = min(table[i * 2], table[i] + 1)
# check if out of bounds
if i * 3 <= number:
table[i * 3] = min(table[i * 3], table[i] + 1)
return table[number]
if __name__ == "__main__":
import doctest
doctest.testmod()
| """
YouTube Explanation: https://www.youtube.com/watch?v=f2xi3c1S95M
Given an integer n, return the minimum steps to 1
AVAILABLE STEPS:
* Decrement by 1
* if n is divisible by 2, divide by 2
* if n is divisible by 3, divide by 3
Example 1: n = 10
10 -> 9 -> 3 -> 1
Result: 3 steps
Example 2: n = 15
15 -> 5 -> 4 -> 2 -> 1
Result: 4 steps
Example 3: n = 6
6 -> 2 -> 1
Result: 2 step
"""
from __future__ import annotations
__author__ = "Alexander Joslin"
def min_steps_to_one(number: int) -> int:
"""
Minimum steps to 1 implemented using tabulation.
>>> min_steps_to_one(10)
3
>>> min_steps_to_one(15)
4
>>> min_steps_to_one(6)
2
:param number:
:return int:
"""
if number <= 0:
raise ValueError(f"n must be greater than 0. Got n = {number}")
table = [number + 1] * (number + 1)
# starting position
table[1] = 0
for i in range(1, number):
table[i + 1] = min(table[i + 1], table[i] + 1)
# check if out of bounds
if i * 2 <= number:
table[i * 2] = min(table[i * 2], table[i] + 1)
# check if out of bounds
if i * 3 <= number:
table[i * 3] = min(table[i * 3], table[i] + 1)
return table[number]
if __name__ == "__main__":
import doctest
doctest.testmod()
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """ A Stack using a linked list like structure """
from __future__ import annotations
from typing import Any
class Node:
def __init__(self, data):
self.data = data
self.next = None
def __str__(self):
return f"{self.data}"
class LinkedStack:
"""
Linked List Stack implementing push (to top),
pop (from top) and is_empty
>>> stack = LinkedStack()
>>> stack.is_empty()
True
>>> stack.push(5)
>>> stack.push(9)
>>> stack.push('python')
>>> stack.is_empty()
False
>>> stack.pop()
'python'
>>> stack.push('algorithms')
>>> stack.pop()
'algorithms'
>>> stack.pop()
9
>>> stack.pop()
5
>>> stack.is_empty()
True
>>> stack.pop()
Traceback (most recent call last):
...
IndexError: pop from empty stack
"""
def __init__(self) -> None:
self.top: Node | None = None
def __iter__(self):
node = self.top
while node:
yield node.data
node = node.next
def __str__(self):
"""
>>> stack = LinkedStack()
>>> stack.push("c")
>>> stack.push("b")
>>> stack.push("a")
>>> str(stack)
'a->b->c'
"""
return "->".join([str(item) for item in self])
def __len__(self):
"""
>>> stack = LinkedStack()
>>> len(stack) == 0
True
>>> stack.push("c")
>>> stack.push("b")
>>> stack.push("a")
>>> len(stack) == 3
True
"""
return len(tuple(iter(self)))
def is_empty(self) -> bool:
"""
>>> stack = LinkedStack()
>>> stack.is_empty()
True
>>> stack.push(1)
>>> stack.is_empty()
False
"""
return self.top is None
def push(self, item: Any) -> None:
"""
>>> stack = LinkedStack()
>>> stack.push("Python")
>>> stack.push("Java")
>>> stack.push("C")
>>> str(stack)
'C->Java->Python'
"""
node = Node(item)
if not self.is_empty():
node.next = self.top
self.top = node
def pop(self) -> Any:
"""
>>> stack = LinkedStack()
>>> stack.pop()
Traceback (most recent call last):
...
IndexError: pop from empty stack
>>> stack.push("c")
>>> stack.push("b")
>>> stack.push("a")
>>> stack.pop() == 'a'
True
>>> stack.pop() == 'b'
True
>>> stack.pop() == 'c'
True
"""
if self.is_empty():
raise IndexError("pop from empty stack")
assert isinstance(self.top, Node)
pop_node = self.top
self.top = self.top.next
return pop_node.data
def peek(self) -> Any:
"""
>>> stack = LinkedStack()
>>> stack.push("Java")
>>> stack.push("C")
>>> stack.push("Python")
>>> stack.peek()
'Python'
"""
if self.is_empty():
raise IndexError("peek from empty stack")
assert self.top is not None
return self.top.data
def clear(self) -> None:
"""
>>> stack = LinkedStack()
>>> stack.push("Java")
>>> stack.push("C")
>>> stack.push("Python")
>>> str(stack)
'Python->C->Java'
>>> stack.clear()
>>> len(stack) == 0
True
"""
self.top = None
if __name__ == "__main__":
from doctest import testmod
testmod()
| """ A Stack using a linked list like structure """
from __future__ import annotations
from typing import Any
class Node:
def __init__(self, data):
self.data = data
self.next = None
def __str__(self):
return f"{self.data}"
class LinkedStack:
"""
Linked List Stack implementing push (to top),
pop (from top) and is_empty
>>> stack = LinkedStack()
>>> stack.is_empty()
True
>>> stack.push(5)
>>> stack.push(9)
>>> stack.push('python')
>>> stack.is_empty()
False
>>> stack.pop()
'python'
>>> stack.push('algorithms')
>>> stack.pop()
'algorithms'
>>> stack.pop()
9
>>> stack.pop()
5
>>> stack.is_empty()
True
>>> stack.pop()
Traceback (most recent call last):
...
IndexError: pop from empty stack
"""
def __init__(self) -> None:
self.top: Node | None = None
def __iter__(self):
node = self.top
while node:
yield node.data
node = node.next
def __str__(self):
"""
>>> stack = LinkedStack()
>>> stack.push("c")
>>> stack.push("b")
>>> stack.push("a")
>>> str(stack)
'a->b->c'
"""
return "->".join([str(item) for item in self])
def __len__(self):
"""
>>> stack = LinkedStack()
>>> len(stack) == 0
True
>>> stack.push("c")
>>> stack.push("b")
>>> stack.push("a")
>>> len(stack) == 3
True
"""
return len(tuple(iter(self)))
def is_empty(self) -> bool:
"""
>>> stack = LinkedStack()
>>> stack.is_empty()
True
>>> stack.push(1)
>>> stack.is_empty()
False
"""
return self.top is None
def push(self, item: Any) -> None:
"""
>>> stack = LinkedStack()
>>> stack.push("Python")
>>> stack.push("Java")
>>> stack.push("C")
>>> str(stack)
'C->Java->Python'
"""
node = Node(item)
if not self.is_empty():
node.next = self.top
self.top = node
def pop(self) -> Any:
"""
>>> stack = LinkedStack()
>>> stack.pop()
Traceback (most recent call last):
...
IndexError: pop from empty stack
>>> stack.push("c")
>>> stack.push("b")
>>> stack.push("a")
>>> stack.pop() == 'a'
True
>>> stack.pop() == 'b'
True
>>> stack.pop() == 'c'
True
"""
if self.is_empty():
raise IndexError("pop from empty stack")
assert isinstance(self.top, Node)
pop_node = self.top
self.top = self.top.next
return pop_node.data
def peek(self) -> Any:
"""
>>> stack = LinkedStack()
>>> stack.push("Java")
>>> stack.push("C")
>>> stack.push("Python")
>>> stack.peek()
'Python'
"""
if self.is_empty():
raise IndexError("peek from empty stack")
assert self.top is not None
return self.top.data
def clear(self) -> None:
"""
>>> stack = LinkedStack()
>>> stack.push("Java")
>>> stack.push("C")
>>> stack.push("Python")
>>> str(stack)
'Python->C->Java'
>>> stack.clear()
>>> len(stack) == 0
True
"""
self.top = None
if __name__ == "__main__":
from doctest import testmod
testmod()
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| from PIL import Image
"""
Mean thresholding algorithm for image processing
https://en.wikipedia.org/wiki/Thresholding_(image_processing)
"""
def mean_threshold(image: Image) -> Image:
"""
image: is a grayscale PIL image object
"""
height, width = image.size
mean = 0
pixels = image.load()
for i in range(width):
for j in range(height):
pixel = pixels[j, i]
mean += pixel
mean //= width * height
for j in range(width):
for i in range(height):
pixels[i, j] = 255 if pixels[i, j] > mean else 0
return image
if __name__ == "__main__":
image = mean_threshold(Image.open("path_to_image").convert("L"))
image.save("output_image_path")
| from PIL import Image
"""
Mean thresholding algorithm for image processing
https://en.wikipedia.org/wiki/Thresholding_(image_processing)
"""
def mean_threshold(image: Image) -> Image:
"""
image: is a grayscale PIL image object
"""
height, width = image.size
mean = 0
pixels = image.load()
for i in range(width):
for j in range(height):
pixel = pixels[j, i]
mean += pixel
mean //= width * height
for j in range(width):
for i in range(height):
pixels[i, j] = 255 if pixels[i, j] > mean else 0
return image
if __name__ == "__main__":
image = mean_threshold(Image.open("path_to_image").convert("L"))
image.save("output_image_path")
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| from typing import Sequence
def evaluate_poly(poly: Sequence[float], x: float) -> float:
"""Evaluate a polynomial f(x) at specified point x and return the value.
Arguments:
poly -- the coefficients of a polynomial as an iterable in order of
ascending degree
x -- the point at which to evaluate the polynomial
>>> evaluate_poly((0.0, 0.0, 5.0, 9.3, 7.0), 10.0)
79800.0
"""
return sum(c * (x ** i) for i, c in enumerate(poly))
def horner(poly: Sequence[float], x: float) -> float:
"""Evaluate a polynomial at specified point using Horner's method.
In terms of computational complexity, Horner's method is an efficient method
of evaluating a polynomial. It avoids the use of expensive exponentiation,
and instead uses only multiplication and addition to evaluate the polynomial
in O(n), where n is the degree of the polynomial.
https://en.wikipedia.org/wiki/Horner's_method
Arguments:
poly -- the coefficients of a polynomial as an iterable in order of
ascending degree
x -- the point at which to evaluate the polynomial
>>> horner((0.0, 0.0, 5.0, 9.3, 7.0), 10.0)
79800.0
"""
result = 0.0
for coeff in reversed(poly):
result = result * x + coeff
return result
if __name__ == "__main__":
"""
Example:
>>> poly = (0.0, 0.0, 5.0, 9.3, 7.0) # f(x) = 7.0x^4 + 9.3x^3 + 5.0x^2
>>> x = -13.0
>>> # f(-13) = 7.0(-13)^4 + 9.3(-13)^3 + 5.0(-13)^2 = 180339.9
>>> print(evaluate_poly(poly, x))
180339.9
"""
poly = (0.0, 0.0, 5.0, 9.3, 7.0)
x = 10.0
print(evaluate_poly(poly, x))
print(horner(poly, x))
| from typing import Sequence
def evaluate_poly(poly: Sequence[float], x: float) -> float:
"""Evaluate a polynomial f(x) at specified point x and return the value.
Arguments:
poly -- the coefficients of a polynomial as an iterable in order of
ascending degree
x -- the point at which to evaluate the polynomial
>>> evaluate_poly((0.0, 0.0, 5.0, 9.3, 7.0), 10.0)
79800.0
"""
return sum(c * (x ** i) for i, c in enumerate(poly))
def horner(poly: Sequence[float], x: float) -> float:
"""Evaluate a polynomial at specified point using Horner's method.
In terms of computational complexity, Horner's method is an efficient method
of evaluating a polynomial. It avoids the use of expensive exponentiation,
and instead uses only multiplication and addition to evaluate the polynomial
in O(n), where n is the degree of the polynomial.
https://en.wikipedia.org/wiki/Horner's_method
Arguments:
poly -- the coefficients of a polynomial as an iterable in order of
ascending degree
x -- the point at which to evaluate the polynomial
>>> horner((0.0, 0.0, 5.0, 9.3, 7.0), 10.0)
79800.0
"""
result = 0.0
for coeff in reversed(poly):
result = result * x + coeff
return result
if __name__ == "__main__":
"""
Example:
>>> poly = (0.0, 0.0, 5.0, 9.3, 7.0) # f(x) = 7.0x^4 + 9.3x^3 + 5.0x^2
>>> x = -13.0
>>> # f(-13) = 7.0(-13)^4 + 9.3(-13)^3 + 5.0(-13)^2 = 180339.9
>>> print(evaluate_poly(poly, x))
180339.9
"""
poly = (0.0, 0.0, 5.0, 9.3, 7.0)
x = 10.0
print(evaluate_poly(poly, x))
print(horner(poly, x))
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| # Check whether Graph is Bipartite or Not using BFS
# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.
def checkBipartite(graph):
queue = []
visited = [False] * len(graph)
color = [-1] * len(graph)
def bfs():
while queue:
u = queue.pop(0)
visited[u] = True
for neighbour in graph[u]:
if neighbour == u:
return False
if color[neighbour] == -1:
color[neighbour] = 1 - color[u]
queue.append(neighbour)
elif color[neighbour] == color[u]:
return False
return True
for i in range(len(graph)):
if not visited[i]:
queue.append(i)
color[i] = 0
if bfs() is False:
return False
return True
if __name__ == "__main__":
# Adjacency List of graph
print(checkBipartite({0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2]}))
| # Check whether Graph is Bipartite or Not using BFS
# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.
def checkBipartite(graph):
queue = []
visited = [False] * len(graph)
color = [-1] * len(graph)
def bfs():
while queue:
u = queue.pop(0)
visited[u] = True
for neighbour in graph[u]:
if neighbour == u:
return False
if color[neighbour] == -1:
color[neighbour] = 1 - color[u]
queue.append(neighbour)
elif color[neighbour] == color[u]:
return False
return True
for i in range(len(graph)):
if not visited[i]:
queue.append(i)
color[i] = 0
if bfs() is False:
return False
return True
if __name__ == "__main__":
# Adjacency List of graph
print(checkBipartite({0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2]}))
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Each character on a computer is assigned a unique code and the preferred standard is
ASCII (American Standard Code for Information Interchange).
For example, uppercase A = 65, asterisk (*) = 42, and lowercase k = 107.
A modern encryption method is to take a text file, convert the bytes to ASCII, then
XOR each byte with a given value, taken from a secret key. The advantage with the
XOR function is that using the same encryption key on the cipher text, restores
the plain text; for example, 65 XOR 42 = 107, then 107 XOR 42 = 65.
For unbreakable encryption, the key is the same length as the plain text message, and
the key is made up of random bytes. The user would keep the encrypted message and the
encryption key in different locations, and without both "halves", it is impossible to
decrypt the message.
Unfortunately, this method is impractical for most users, so the modified method is
to use a password as a key. If the password is shorter than the message, which is
likely, the key is repeated cyclically throughout the message. The balance for this
method is using a sufficiently long password key for security, but short enough to
be memorable.
Your task has been made easy, as the encryption key consists of three lower case
characters. Using p059_cipher.txt (right click and 'Save Link/Target As...'), a
file containing the encrypted ASCII codes, and the knowledge that the plain text
must contain common English words, decrypt the message and find the sum of the ASCII
values in the original text.
"""
from __future__ import annotations
import string
from itertools import cycle, product
from pathlib import Path
VALID_CHARS: str = (
string.ascii_letters + string.digits + string.punctuation + string.whitespace
)
LOWERCASE_INTS: list[int] = [ord(letter) for letter in string.ascii_lowercase]
VALID_INTS: set[int] = {ord(char) for char in VALID_CHARS}
COMMON_WORDS: list[str] = ["the", "be", "to", "of", "and", "in", "that", "have"]
def try_key(ciphertext: list[int], key: tuple[int, ...]) -> str | None:
"""
Given an encrypted message and a possible 3-character key, decrypt the message.
If the decrypted message contains a invalid character, i.e. not an ASCII letter,
a digit, punctuation or whitespace, then we know the key is incorrect, so return
None.
>>> try_key([0, 17, 20, 4, 27], (104, 116, 120))
'hello'
>>> try_key([68, 10, 300, 4, 27], (104, 116, 120)) is None
True
"""
decoded: str = ""
keychar: int
cipherchar: int
decodedchar: int
for keychar, cipherchar in zip(cycle(key), ciphertext):
decodedchar = cipherchar ^ keychar
if decodedchar not in VALID_INTS:
return None
decoded += chr(decodedchar)
return decoded
def filter_valid_chars(ciphertext: list[int]) -> list[str]:
"""
Given an encrypted message, test all 3-character strings to try and find the
key. Return a list of the possible decrypted messages.
>>> from itertools import cycle
>>> text = "The enemy's gate is down"
>>> key = "end"
>>> encoded = [ord(k) ^ ord(c) for k,c in zip(cycle(key), text)]
>>> text in filter_valid_chars(encoded)
True
"""
possibles: list[str] = []
for key in product(LOWERCASE_INTS, repeat=3):
encoded = try_key(ciphertext, key)
if encoded is not None:
possibles.append(encoded)
return possibles
def filter_common_word(possibles: list[str], common_word: str) -> list[str]:
"""
Given a list of possible decoded messages, narrow down the possibilities
for checking for the presence of a specified common word. Only decoded messages
containing common_word will be returned.
>>> filter_common_word(['asfla adf', 'I am here', ' !?! #a'], 'am')
['I am here']
>>> filter_common_word(['athla amf', 'I am here', ' !?! #a'], 'am')
['athla amf', 'I am here']
"""
return [possible for possible in possibles if common_word in possible.lower()]
def solution(filename: str = "p059_cipher.txt") -> int:
"""
Test the ciphertext against all possible 3-character keys, then narrow down the
possibilities by filtering using common words until there's only one possible
decoded message.
>>> solution("test_cipher.txt")
3000
"""
ciphertext: list[int]
possibles: list[str]
common_word: str
decoded_text: str
data: str = Path(__file__).parent.joinpath(filename).read_text(encoding="utf-8")
ciphertext = [int(number) for number in data.strip().split(",")]
possibles = filter_valid_chars(ciphertext)
for common_word in COMMON_WORDS:
possibles = filter_common_word(possibles, common_word)
if len(possibles) == 1:
break
decoded_text = possibles[0]
return sum(ord(char) for char in decoded_text)
if __name__ == "__main__":
print(f"{solution() = }")
| """
Each character on a computer is assigned a unique code and the preferred standard is
ASCII (American Standard Code for Information Interchange).
For example, uppercase A = 65, asterisk (*) = 42, and lowercase k = 107.
A modern encryption method is to take a text file, convert the bytes to ASCII, then
XOR each byte with a given value, taken from a secret key. The advantage with the
XOR function is that using the same encryption key on the cipher text, restores
the plain text; for example, 65 XOR 42 = 107, then 107 XOR 42 = 65.
For unbreakable encryption, the key is the same length as the plain text message, and
the key is made up of random bytes. The user would keep the encrypted message and the
encryption key in different locations, and without both "halves", it is impossible to
decrypt the message.
Unfortunately, this method is impractical for most users, so the modified method is
to use a password as a key. If the password is shorter than the message, which is
likely, the key is repeated cyclically throughout the message. The balance for this
method is using a sufficiently long password key for security, but short enough to
be memorable.
Your task has been made easy, as the encryption key consists of three lower case
characters. Using p059_cipher.txt (right click and 'Save Link/Target As...'), a
file containing the encrypted ASCII codes, and the knowledge that the plain text
must contain common English words, decrypt the message and find the sum of the ASCII
values in the original text.
"""
from __future__ import annotations
import string
from itertools import cycle, product
from pathlib import Path
VALID_CHARS: str = (
string.ascii_letters + string.digits + string.punctuation + string.whitespace
)
LOWERCASE_INTS: list[int] = [ord(letter) for letter in string.ascii_lowercase]
VALID_INTS: set[int] = {ord(char) for char in VALID_CHARS}
COMMON_WORDS: list[str] = ["the", "be", "to", "of", "and", "in", "that", "have"]
def try_key(ciphertext: list[int], key: tuple[int, ...]) -> str | None:
"""
Given an encrypted message and a possible 3-character key, decrypt the message.
If the decrypted message contains a invalid character, i.e. not an ASCII letter,
a digit, punctuation or whitespace, then we know the key is incorrect, so return
None.
>>> try_key([0, 17, 20, 4, 27], (104, 116, 120))
'hello'
>>> try_key([68, 10, 300, 4, 27], (104, 116, 120)) is None
True
"""
decoded: str = ""
keychar: int
cipherchar: int
decodedchar: int
for keychar, cipherchar in zip(cycle(key), ciphertext):
decodedchar = cipherchar ^ keychar
if decodedchar not in VALID_INTS:
return None
decoded += chr(decodedchar)
return decoded
def filter_valid_chars(ciphertext: list[int]) -> list[str]:
"""
Given an encrypted message, test all 3-character strings to try and find the
key. Return a list of the possible decrypted messages.
>>> from itertools import cycle
>>> text = "The enemy's gate is down"
>>> key = "end"
>>> encoded = [ord(k) ^ ord(c) for k,c in zip(cycle(key), text)]
>>> text in filter_valid_chars(encoded)
True
"""
possibles: list[str] = []
for key in product(LOWERCASE_INTS, repeat=3):
encoded = try_key(ciphertext, key)
if encoded is not None:
possibles.append(encoded)
return possibles
def filter_common_word(possibles: list[str], common_word: str) -> list[str]:
"""
Given a list of possible decoded messages, narrow down the possibilities
for checking for the presence of a specified common word. Only decoded messages
containing common_word will be returned.
>>> filter_common_word(['asfla adf', 'I am here', ' !?! #a'], 'am')
['I am here']
>>> filter_common_word(['athla amf', 'I am here', ' !?! #a'], 'am')
['athla amf', 'I am here']
"""
return [possible for possible in possibles if common_word in possible.lower()]
def solution(filename: str = "p059_cipher.txt") -> int:
"""
Test the ciphertext against all possible 3-character keys, then narrow down the
possibilities by filtering using common words until there's only one possible
decoded message.
>>> solution("test_cipher.txt")
3000
"""
ciphertext: list[int]
possibles: list[str]
common_word: str
decoded_text: str
data: str = Path(__file__).parent.joinpath(filename).read_text(encoding="utf-8")
ciphertext = [int(number) for number in data.strip().split(",")]
possibles = filter_valid_chars(ciphertext)
for common_word in COMMON_WORDS:
possibles = filter_common_word(possibles, common_word)
if len(possibles) == 1:
break
decoded_text = possibles[0]
return sum(ord(char) for char in decoded_text)
if __name__ == "__main__":
print(f"{solution() = }")
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
The Fibonacci sequence is defined by the recurrence relation:
Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.
Hence the first 12 terms will be:
F1 = 1
F2 = 1
F3 = 2
F4 = 3
F5 = 5
F6 = 8
F7 = 13
F8 = 21
F9 = 34
F10 = 55
F11 = 89
F12 = 144
The 12th term, F12, is the first term to contain three digits.
What is the index of the first term in the Fibonacci sequence to contain 1000
digits?
"""
def solution(n: int = 1000) -> int:
"""Returns the index of the first term in the Fibonacci sequence to contain
n digits.
>>> solution(1000)
4782
>>> solution(100)
476
>>> solution(50)
237
>>> solution(3)
12
"""
f1, f2 = 1, 1
index = 2
while True:
i = 0
f = f1 + f2
f1, f2 = f2, f
index += 1
for j in str(f):
i += 1
if i == n:
break
return index
if __name__ == "__main__":
print(solution(int(str(input()).strip())))
| """
The Fibonacci sequence is defined by the recurrence relation:
Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.
Hence the first 12 terms will be:
F1 = 1
F2 = 1
F3 = 2
F4 = 3
F5 = 5
F6 = 8
F7 = 13
F8 = 21
F9 = 34
F10 = 55
F11 = 89
F12 = 144
The 12th term, F12, is the first term to contain three digits.
What is the index of the first term in the Fibonacci sequence to contain 1000
digits?
"""
def solution(n: int = 1000) -> int:
"""Returns the index of the first term in the Fibonacci sequence to contain
n digits.
>>> solution(1000)
4782
>>> solution(100)
476
>>> solution(50)
237
>>> solution(3)
12
"""
f1, f2 = 1, 1
index = 2
while True:
i = 0
f = f1 + f2
f1, f2 = f2, f
index += 1
for j in str(f):
i += 1
if i == n:
break
return index
if __name__ == "__main__":
print(solution(int(str(input()).strip())))
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| def sum_of_geometric_progression(
first_term: int, common_ratio: int, num_of_terms: int
) -> float:
""" "
Return the sum of n terms in a geometric progression.
>>> sum_of_geometric_progression(1, 2, 10)
1023.0
>>> sum_of_geometric_progression(1, 10, 5)
11111.0
>>> sum_of_geometric_progression(0, 2, 10)
0.0
>>> sum_of_geometric_progression(1, 0, 10)
1.0
>>> sum_of_geometric_progression(1, 2, 0)
-0.0
>>> sum_of_geometric_progression(-1, 2, 10)
-1023.0
>>> sum_of_geometric_progression(1, -2, 10)
-341.0
>>> sum_of_geometric_progression(1, 2, -10)
-0.9990234375
"""
if common_ratio == 1:
# Formula for sum if common ratio is 1
return num_of_terms * first_term
# Formula for finding sum of n terms of a GeometricProgression
return (first_term / (1 - common_ratio)) * (1 - common_ratio ** num_of_terms)
| def sum_of_geometric_progression(
first_term: int, common_ratio: int, num_of_terms: int
) -> float:
""" "
Return the sum of n terms in a geometric progression.
>>> sum_of_geometric_progression(1, 2, 10)
1023.0
>>> sum_of_geometric_progression(1, 10, 5)
11111.0
>>> sum_of_geometric_progression(0, 2, 10)
0.0
>>> sum_of_geometric_progression(1, 0, 10)
1.0
>>> sum_of_geometric_progression(1, 2, 0)
-0.0
>>> sum_of_geometric_progression(-1, 2, 10)
-1023.0
>>> sum_of_geometric_progression(1, -2, 10)
-341.0
>>> sum_of_geometric_progression(1, 2, -10)
-0.9990234375
"""
if common_ratio == 1:
# Formula for sum if common ratio is 1
return num_of_terms * first_term
# Formula for finding sum of n terms of a GeometricProgression
return (first_term / (1 - common_ratio)) * (1 - common_ratio ** num_of_terms)
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| #!/usr/bin/env python3
# This Python program implements an optimal binary search tree (abbreviated BST)
# building dynamic programming algorithm that delivers O(n^2) performance.
#
# The goal of the optimal BST problem is to build a low-cost BST for a
# given set of nodes, each with its own key and frequency. The frequency
# of the node is defined as how many time the node is being searched.
# The search cost of binary search tree is given by this formula:
#
# cost(1, n) = sum{i = 1 to n}((depth(node_i) + 1) * node_i_freq)
#
# where n is number of nodes in the BST. The characteristic of low-cost
# BSTs is having a faster overall search time than other implementations.
# The reason for their fast search time is that the nodes with high
# frequencies will be placed near the root of the tree while the nodes
# with low frequencies will be placed near the leaves of the tree thus
# reducing search time in the most frequent instances.
import sys
from random import randint
class Node:
"""Binary Search Tree Node"""
def __init__(self, key, freq):
self.key = key
self.freq = freq
def __str__(self):
"""
>>> str(Node(1, 2))
'Node(key=1, freq=2)'
"""
return f"Node(key={self.key}, freq={self.freq})"
def print_binary_search_tree(root, key, i, j, parent, is_left):
"""
Recursive function to print a BST from a root table.
>>> key = [3, 8, 9, 10, 17, 21]
>>> root = [[0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 1, 3], [0, 0, 2, 3, 3, 3], \
[0, 0, 0, 3, 3, 3], [0, 0, 0, 0, 4, 5], [0, 0, 0, 0, 0, 5]]
>>> print_binary_search_tree(root, key, 0, 5, -1, False)
8 is the root of the binary search tree.
3 is the left child of key 8.
10 is the right child of key 8.
9 is the left child of key 10.
21 is the right child of key 10.
17 is the left child of key 21.
"""
if i > j or i < 0 or j > len(root) - 1:
return
node = root[i][j]
if parent == -1: # root does not have a parent
print(f"{key[node]} is the root of the binary search tree.")
elif is_left:
print(f"{key[node]} is the left child of key {parent}.")
else:
print(f"{key[node]} is the right child of key {parent}.")
print_binary_search_tree(root, key, i, node - 1, key[node], True)
print_binary_search_tree(root, key, node + 1, j, key[node], False)
def find_optimal_binary_search_tree(nodes):
"""
This function calculates and prints the optimal binary search tree.
The dynamic programming algorithm below runs in O(n^2) time.
Implemented from CLRS (Introduction to Algorithms) book.
https://en.wikipedia.org/wiki/Introduction_to_Algorithms
>>> find_optimal_binary_search_tree([Node(12, 8), Node(10, 34), Node(20, 50), \
Node(42, 3), Node(25, 40), Node(37, 30)])
Binary search tree nodes:
Node(key=10, freq=34)
Node(key=12, freq=8)
Node(key=20, freq=50)
Node(key=25, freq=40)
Node(key=37, freq=30)
Node(key=42, freq=3)
<BLANKLINE>
The cost of optimal BST for given tree nodes is 324.
20 is the root of the binary search tree.
10 is the left child of key 20.
12 is the right child of key 10.
25 is the right child of key 20.
37 is the right child of key 25.
42 is the right child of key 37.
"""
# Tree nodes must be sorted first, the code below sorts the keys in
# increasing order and rearrange its frequencies accordingly.
nodes.sort(key=lambda node: node.key)
n = len(nodes)
keys = [nodes[i].key for i in range(n)]
freqs = [nodes[i].freq for i in range(n)]
# This 2D array stores the overall tree cost (which's as minimized as possible);
# for a single key, cost is equal to frequency of the key.
dp = [[freqs[i] if i == j else 0 for j in range(n)] for i in range(n)]
# sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
# array
sum = [[freqs[i] if i == j else 0 for j in range(n)] for i in range(n)]
# stores tree roots that will be used later for constructing binary search tree
root = [[i if i == j else 0 for j in range(n)] for i in range(n)]
for interval_length in range(2, n + 1):
for i in range(n - interval_length + 1):
j = i + interval_length - 1
dp[i][j] = sys.maxsize # set the value to "infinity"
sum[i][j] = sum[i][j - 1] + freqs[j]
# Apply Knuth's optimization
# Loop without optimization: for r in range(i, j + 1):
for r in range(root[i][j - 1], root[i + 1][j] + 1): # r is a temporal root
left = dp[i][r - 1] if r != i else 0 # optimal cost for left subtree
right = dp[r + 1][j] if r != j else 0 # optimal cost for right subtree
cost = left + sum[i][j] + right
if dp[i][j] > cost:
dp[i][j] = cost
root[i][j] = r
print("Binary search tree nodes:")
for node in nodes:
print(node)
print(f"\nThe cost of optimal BST for given tree nodes is {dp[0][n - 1]}.")
print_binary_search_tree(root, keys, 0, n - 1, -1, False)
def main():
# A sample binary search tree
nodes = [Node(i, randint(1, 50)) for i in range(10, 0, -1)]
find_optimal_binary_search_tree(nodes)
if __name__ == "__main__":
main()
| #!/usr/bin/env python3
# This Python program implements an optimal binary search tree (abbreviated BST)
# building dynamic programming algorithm that delivers O(n^2) performance.
#
# The goal of the optimal BST problem is to build a low-cost BST for a
# given set of nodes, each with its own key and frequency. The frequency
# of the node is defined as how many time the node is being searched.
# The search cost of binary search tree is given by this formula:
#
# cost(1, n) = sum{i = 1 to n}((depth(node_i) + 1) * node_i_freq)
#
# where n is number of nodes in the BST. The characteristic of low-cost
# BSTs is having a faster overall search time than other implementations.
# The reason for their fast search time is that the nodes with high
# frequencies will be placed near the root of the tree while the nodes
# with low frequencies will be placed near the leaves of the tree thus
# reducing search time in the most frequent instances.
import sys
from random import randint
class Node:
"""Binary Search Tree Node"""
def __init__(self, key, freq):
self.key = key
self.freq = freq
def __str__(self):
"""
>>> str(Node(1, 2))
'Node(key=1, freq=2)'
"""
return f"Node(key={self.key}, freq={self.freq})"
def print_binary_search_tree(root, key, i, j, parent, is_left):
"""
Recursive function to print a BST from a root table.
>>> key = [3, 8, 9, 10, 17, 21]
>>> root = [[0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 1, 3], [0, 0, 2, 3, 3, 3], \
[0, 0, 0, 3, 3, 3], [0, 0, 0, 0, 4, 5], [0, 0, 0, 0, 0, 5]]
>>> print_binary_search_tree(root, key, 0, 5, -1, False)
8 is the root of the binary search tree.
3 is the left child of key 8.
10 is the right child of key 8.
9 is the left child of key 10.
21 is the right child of key 10.
17 is the left child of key 21.
"""
if i > j or i < 0 or j > len(root) - 1:
return
node = root[i][j]
if parent == -1: # root does not have a parent
print(f"{key[node]} is the root of the binary search tree.")
elif is_left:
print(f"{key[node]} is the left child of key {parent}.")
else:
print(f"{key[node]} is the right child of key {parent}.")
print_binary_search_tree(root, key, i, node - 1, key[node], True)
print_binary_search_tree(root, key, node + 1, j, key[node], False)
def find_optimal_binary_search_tree(nodes):
"""
This function calculates and prints the optimal binary search tree.
The dynamic programming algorithm below runs in O(n^2) time.
Implemented from CLRS (Introduction to Algorithms) book.
https://en.wikipedia.org/wiki/Introduction_to_Algorithms
>>> find_optimal_binary_search_tree([Node(12, 8), Node(10, 34), Node(20, 50), \
Node(42, 3), Node(25, 40), Node(37, 30)])
Binary search tree nodes:
Node(key=10, freq=34)
Node(key=12, freq=8)
Node(key=20, freq=50)
Node(key=25, freq=40)
Node(key=37, freq=30)
Node(key=42, freq=3)
<BLANKLINE>
The cost of optimal BST for given tree nodes is 324.
20 is the root of the binary search tree.
10 is the left child of key 20.
12 is the right child of key 10.
25 is the right child of key 20.
37 is the right child of key 25.
42 is the right child of key 37.
"""
# Tree nodes must be sorted first, the code below sorts the keys in
# increasing order and rearrange its frequencies accordingly.
nodes.sort(key=lambda node: node.key)
n = len(nodes)
keys = [nodes[i].key for i in range(n)]
freqs = [nodes[i].freq for i in range(n)]
# This 2D array stores the overall tree cost (which's as minimized as possible);
# for a single key, cost is equal to frequency of the key.
dp = [[freqs[i] if i == j else 0 for j in range(n)] for i in range(n)]
# sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
# array
sum = [[freqs[i] if i == j else 0 for j in range(n)] for i in range(n)]
# stores tree roots that will be used later for constructing binary search tree
root = [[i if i == j else 0 for j in range(n)] for i in range(n)]
for interval_length in range(2, n + 1):
for i in range(n - interval_length + 1):
j = i + interval_length - 1
dp[i][j] = sys.maxsize # set the value to "infinity"
sum[i][j] = sum[i][j - 1] + freqs[j]
# Apply Knuth's optimization
# Loop without optimization: for r in range(i, j + 1):
for r in range(root[i][j - 1], root[i + 1][j] + 1): # r is a temporal root
left = dp[i][r - 1] if r != i else 0 # optimal cost for left subtree
right = dp[r + 1][j] if r != j else 0 # optimal cost for right subtree
cost = left + sum[i][j] + right
if dp[i][j] > cost:
dp[i][j] = cost
root[i][j] = r
print("Binary search tree nodes:")
for node in nodes:
print(node)
print(f"\nThe cost of optimal BST for given tree nodes is {dp[0][n - 1]}.")
print_binary_search_tree(root, keys, 0, n - 1, -1, False)
def main():
# A sample binary search tree
nodes = [Node(i, randint(1, 50)) for i in range(10, 0, -1)]
find_optimal_binary_search_tree(nodes)
if __name__ == "__main__":
main()
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| # flake8: noqa
"""
Binomial Heap
Reference: Advanced Data Structures, Peter Brass
"""
class Node:
"""
Node in a doubly-linked binomial tree, containing:
- value
- size of left subtree
- link to left, right and parent nodes
"""
def __init__(self, val):
self.val = val
# Number of nodes in left subtree
self.left_tree_size = 0
self.left = None
self.right = None
self.parent = None
def mergeTrees(self, other):
"""
In-place merge of two binomial trees of equal size.
Returns the root of the resulting tree
"""
assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"
if self.val < other.val:
other.left = self.right
other.parent = None
if self.right:
self.right.parent = other
self.right = other
self.left_tree_size = self.left_tree_size * 2 + 1
return self
else:
self.left = other.right
self.parent = None
if other.right:
other.right.parent = self
other.right = self
other.left_tree_size = other.left_tree_size * 2 + 1
return other
class BinomialHeap:
r"""
Min-oriented priority queue implemented with the Binomial Heap data
structure implemented with the BinomialHeap class. It supports:
- Insert element in a heap with n elements: Guaranteed logn, amoratized 1
- Merge (meld) heaps of size m and n: O(logn + logm)
- Delete Min: O(logn)
- Peek (return min without deleting it): O(1)
Example:
Create a random permutation of 30 integers to be inserted and 19 of them deleted
>>> import numpy as np
>>> permutation = np.random.permutation(list(range(30)))
Create a Heap and insert the 30 integers
__init__() test
>>> first_heap = BinomialHeap()
30 inserts - insert() test
>>> for number in permutation:
... first_heap.insert(number)
Size test
>>> print(first_heap.size)
30
Deleting - delete() test
>>> for i in range(25):
... print(first_heap.deleteMin(), end=" ")
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Create a new Heap
>>> second_heap = BinomialHeap()
>>> vals = [17, 20, 31, 34]
>>> for value in vals:
... second_heap.insert(value)
The heap should have the following structure:
17
/ \
# 31
/ \
20 34
/ \ / \
# # # #
preOrder() test
>>> print(second_heap.preOrder())
[(17, 0), ('#', 1), (31, 1), (20, 2), ('#', 3), ('#', 3), (34, 2), ('#', 3), ('#', 3)]
printing Heap - __str__() test
>>> print(second_heap)
17
-#
-31
--20
---#
---#
--34
---#
---#
mergeHeaps() test
>>> merged = second_heap.mergeHeaps(first_heap)
>>> merged.peek()
17
values in merged heap; (merge is inplace)
>>> while not first_heap.isEmpty():
... print(first_heap.deleteMin(), end=" ")
17 20 25 26 27 28 29 31 34
"""
def __init__(self, bottom_root=None, min_node=None, heap_size=0):
self.size = heap_size
self.bottom_root = bottom_root
self.min_node = min_node
def mergeHeaps(self, other):
"""
In-place merge of two binomial heaps.
Both of them become the resulting merged heap
"""
# Empty heaps corner cases
if other.size == 0:
return
if self.size == 0:
self.size = other.size
self.bottom_root = other.bottom_root
self.min_node = other.min_node
return
# Update size
self.size = self.size + other.size
# Update min.node
if self.min_node.val > other.min_node.val:
self.min_node = other.min_node
# Merge
# Order roots by left_subtree_size
combined_roots_list = []
i, j = self.bottom_root, other.bottom_root
while i or j:
if i and ((not j) or i.left_tree_size < j.left_tree_size):
combined_roots_list.append((i, True))
i = i.parent
else:
combined_roots_list.append((j, False))
j = j.parent
# Insert links between them
for i in range(len(combined_roots_list) - 1):
if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
combined_roots_list[i][0].parent = combined_roots_list[i + 1][0]
combined_roots_list[i + 1][0].left = combined_roots_list[i][0]
# Consecutively merge roots with same left_tree_size
i = combined_roots_list[0][0]
while i.parent:
if (
(i.left_tree_size == i.parent.left_tree_size) and (not i.parent.parent)
) or (
i.left_tree_size == i.parent.left_tree_size
and i.left_tree_size != i.parent.parent.left_tree_size
):
# Neighbouring Nodes
previous_node = i.left
next_node = i.parent.parent
# Merging trees
i = i.mergeTrees(i.parent)
# Updating links
i.left = previous_node
i.parent = next_node
if previous_node:
previous_node.parent = i
if next_node:
next_node.left = i
else:
i = i.parent
# Updating self.bottom_root
while i.left:
i = i.left
self.bottom_root = i
# Update other
other.size = self.size
other.bottom_root = self.bottom_root
other.min_node = self.min_node
# Return the merged heap
return self
def insert(self, val):
"""
insert a value in the heap
"""
if self.size == 0:
self.bottom_root = Node(val)
self.size = 1
self.min_node = self.bottom_root
else:
# Create new node
new_node = Node(val)
# Update size
self.size += 1
# update min_node
if val < self.min_node.val:
self.min_node = new_node
# Put new_node as a bottom_root in heap
self.bottom_root.left = new_node
new_node.parent = self.bottom_root
self.bottom_root = new_node
# Consecutively merge roots with same left_tree_size
while (
self.bottom_root.parent
and self.bottom_root.left_tree_size
== self.bottom_root.parent.left_tree_size
):
# Next node
next_node = self.bottom_root.parent.parent
# Merge
self.bottom_root = self.bottom_root.mergeTrees(self.bottom_root.parent)
# Update Links
self.bottom_root.parent = next_node
self.bottom_root.left = None
if next_node:
next_node.left = self.bottom_root
def peek(self):
"""
return min element without deleting it
"""
return self.min_node.val
def isEmpty(self):
return self.size == 0
def deleteMin(self):
"""
delete min element and return it
"""
# assert not self.isEmpty(), "Empty Heap"
# Save minimal value
min_value = self.min_node.val
# Last element in heap corner case
if self.size == 1:
# Update size
self.size = 0
# Update bottom root
self.bottom_root = None
# Update min_node
self.min_node = None
return min_value
# No right subtree corner case
# The structure of the tree implies that this should be the bottom root
# and there is at least one other root
if self.min_node.right is None:
# Update size
self.size -= 1
# Update bottom root
self.bottom_root = self.bottom_root.parent
self.bottom_root.left = None
# Update min_node
self.min_node = self.bottom_root
i = self.bottom_root.parent
while i:
if i.val < self.min_node.val:
self.min_node = i
i = i.parent
return min_value
# General case
# Find the BinomialHeap of the right subtree of min_node
bottom_of_new = self.min_node.right
bottom_of_new.parent = None
min_of_new = bottom_of_new
size_of_new = 1
# Size, min_node and bottom_root
while bottom_of_new.left:
size_of_new = size_of_new * 2 + 1
bottom_of_new = bottom_of_new.left
if bottom_of_new.val < min_of_new.val:
min_of_new = bottom_of_new
# Corner case of single root on top left path
if (not self.min_node.left) and (not self.min_node.parent):
self.size = size_of_new
self.bottom_root = bottom_of_new
self.min_node = min_of_new
# print("Single root, multiple nodes case")
return min_value
# Remaining cases
# Construct heap of right subtree
newHeap = BinomialHeap(
bottom_root=bottom_of_new, min_node=min_of_new, heap_size=size_of_new
)
# Update size
self.size = self.size - 1 - size_of_new
# Neighbour nodes
previous_node = self.min_node.left
next_node = self.min_node.parent
# Initialize new bottom_root and min_node
self.min_node = previous_node or next_node
self.bottom_root = next_node
# Update links of previous_node and search below for new min_node and
# bottom_root
if previous_node:
previous_node.parent = next_node
# Update bottom_root and search for min_node below
self.bottom_root = previous_node
self.min_node = previous_node
while self.bottom_root.left:
self.bottom_root = self.bottom_root.left
if self.bottom_root.val < self.min_node.val:
self.min_node = self.bottom_root
if next_node:
next_node.left = previous_node
# Search for new min_node above min_node
i = next_node
while i:
if i.val < self.min_node.val:
self.min_node = i
i = i.parent
# Merge heaps
self.mergeHeaps(newHeap)
return min_value
def preOrder(self):
"""
Returns the Pre-order representation of the heap including
values of nodes plus their level distance from the root;
Empty nodes appear as #
"""
# Find top root
top_root = self.bottom_root
while top_root.parent:
top_root = top_root.parent
# preorder
heap_preOrder = []
self.__traversal(top_root, heap_preOrder)
return heap_preOrder
def __traversal(self, curr_node, preorder, level=0):
"""
Pre-order traversal of nodes
"""
if curr_node:
preorder.append((curr_node.val, level))
self.__traversal(curr_node.left, preorder, level + 1)
self.__traversal(curr_node.right, preorder, level + 1)
else:
preorder.append(("#", level))
def __str__(self):
"""
Overwriting str for a pre-order print of nodes in heap;
Performance is poor, so use only for small examples
"""
if self.isEmpty():
return ""
preorder_heap = self.preOrder()
return "\n".join(("-" * level + str(value)) for value, level in preorder_heap)
# Unit Tests
if __name__ == "__main__":
import doctest
doctest.testmod()
| # flake8: noqa
"""
Binomial Heap
Reference: Advanced Data Structures, Peter Brass
"""
class Node:
"""
Node in a doubly-linked binomial tree, containing:
- value
- size of left subtree
- link to left, right and parent nodes
"""
def __init__(self, val):
self.val = val
# Number of nodes in left subtree
self.left_tree_size = 0
self.left = None
self.right = None
self.parent = None
def mergeTrees(self, other):
"""
In-place merge of two binomial trees of equal size.
Returns the root of the resulting tree
"""
assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"
if self.val < other.val:
other.left = self.right
other.parent = None
if self.right:
self.right.parent = other
self.right = other
self.left_tree_size = self.left_tree_size * 2 + 1
return self
else:
self.left = other.right
self.parent = None
if other.right:
other.right.parent = self
other.right = self
other.left_tree_size = other.left_tree_size * 2 + 1
return other
class BinomialHeap:
r"""
Min-oriented priority queue implemented with the Binomial Heap data
structure implemented with the BinomialHeap class. It supports:
- Insert element in a heap with n elements: Guaranteed logn, amoratized 1
- Merge (meld) heaps of size m and n: O(logn + logm)
- Delete Min: O(logn)
- Peek (return min without deleting it): O(1)
Example:
Create a random permutation of 30 integers to be inserted and 19 of them deleted
>>> import numpy as np
>>> permutation = np.random.permutation(list(range(30)))
Create a Heap and insert the 30 integers
__init__() test
>>> first_heap = BinomialHeap()
30 inserts - insert() test
>>> for number in permutation:
... first_heap.insert(number)
Size test
>>> print(first_heap.size)
30
Deleting - delete() test
>>> for i in range(25):
... print(first_heap.deleteMin(), end=" ")
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Create a new Heap
>>> second_heap = BinomialHeap()
>>> vals = [17, 20, 31, 34]
>>> for value in vals:
... second_heap.insert(value)
The heap should have the following structure:
17
/ \
# 31
/ \
20 34
/ \ / \
# # # #
preOrder() test
>>> print(second_heap.preOrder())
[(17, 0), ('#', 1), (31, 1), (20, 2), ('#', 3), ('#', 3), (34, 2), ('#', 3), ('#', 3)]
printing Heap - __str__() test
>>> print(second_heap)
17
-#
-31
--20
---#
---#
--34
---#
---#
mergeHeaps() test
>>> merged = second_heap.mergeHeaps(first_heap)
>>> merged.peek()
17
values in merged heap; (merge is inplace)
>>> while not first_heap.isEmpty():
... print(first_heap.deleteMin(), end=" ")
17 20 25 26 27 28 29 31 34
"""
def __init__(self, bottom_root=None, min_node=None, heap_size=0):
self.size = heap_size
self.bottom_root = bottom_root
self.min_node = min_node
def mergeHeaps(self, other):
"""
In-place merge of two binomial heaps.
Both of them become the resulting merged heap
"""
# Empty heaps corner cases
if other.size == 0:
return
if self.size == 0:
self.size = other.size
self.bottom_root = other.bottom_root
self.min_node = other.min_node
return
# Update size
self.size = self.size + other.size
# Update min.node
if self.min_node.val > other.min_node.val:
self.min_node = other.min_node
# Merge
# Order roots by left_subtree_size
combined_roots_list = []
i, j = self.bottom_root, other.bottom_root
while i or j:
if i and ((not j) or i.left_tree_size < j.left_tree_size):
combined_roots_list.append((i, True))
i = i.parent
else:
combined_roots_list.append((j, False))
j = j.parent
# Insert links between them
for i in range(len(combined_roots_list) - 1):
if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
combined_roots_list[i][0].parent = combined_roots_list[i + 1][0]
combined_roots_list[i + 1][0].left = combined_roots_list[i][0]
# Consecutively merge roots with same left_tree_size
i = combined_roots_list[0][0]
while i.parent:
if (
(i.left_tree_size == i.parent.left_tree_size) and (not i.parent.parent)
) or (
i.left_tree_size == i.parent.left_tree_size
and i.left_tree_size != i.parent.parent.left_tree_size
):
# Neighbouring Nodes
previous_node = i.left
next_node = i.parent.parent
# Merging trees
i = i.mergeTrees(i.parent)
# Updating links
i.left = previous_node
i.parent = next_node
if previous_node:
previous_node.parent = i
if next_node:
next_node.left = i
else:
i = i.parent
# Updating self.bottom_root
while i.left:
i = i.left
self.bottom_root = i
# Update other
other.size = self.size
other.bottom_root = self.bottom_root
other.min_node = self.min_node
# Return the merged heap
return self
def insert(self, val):
"""
insert a value in the heap
"""
if self.size == 0:
self.bottom_root = Node(val)
self.size = 1
self.min_node = self.bottom_root
else:
# Create new node
new_node = Node(val)
# Update size
self.size += 1
# update min_node
if val < self.min_node.val:
self.min_node = new_node
# Put new_node as a bottom_root in heap
self.bottom_root.left = new_node
new_node.parent = self.bottom_root
self.bottom_root = new_node
# Consecutively merge roots with same left_tree_size
while (
self.bottom_root.parent
and self.bottom_root.left_tree_size
== self.bottom_root.parent.left_tree_size
):
# Next node
next_node = self.bottom_root.parent.parent
# Merge
self.bottom_root = self.bottom_root.mergeTrees(self.bottom_root.parent)
# Update Links
self.bottom_root.parent = next_node
self.bottom_root.left = None
if next_node:
next_node.left = self.bottom_root
def peek(self):
"""
return min element without deleting it
"""
return self.min_node.val
def isEmpty(self):
return self.size == 0
def deleteMin(self):
"""
delete min element and return it
"""
# assert not self.isEmpty(), "Empty Heap"
# Save minimal value
min_value = self.min_node.val
# Last element in heap corner case
if self.size == 1:
# Update size
self.size = 0
# Update bottom root
self.bottom_root = None
# Update min_node
self.min_node = None
return min_value
# No right subtree corner case
# The structure of the tree implies that this should be the bottom root
# and there is at least one other root
if self.min_node.right is None:
# Update size
self.size -= 1
# Update bottom root
self.bottom_root = self.bottom_root.parent
self.bottom_root.left = None
# Update min_node
self.min_node = self.bottom_root
i = self.bottom_root.parent
while i:
if i.val < self.min_node.val:
self.min_node = i
i = i.parent
return min_value
# General case
# Find the BinomialHeap of the right subtree of min_node
bottom_of_new = self.min_node.right
bottom_of_new.parent = None
min_of_new = bottom_of_new
size_of_new = 1
# Size, min_node and bottom_root
while bottom_of_new.left:
size_of_new = size_of_new * 2 + 1
bottom_of_new = bottom_of_new.left
if bottom_of_new.val < min_of_new.val:
min_of_new = bottom_of_new
# Corner case of single root on top left path
if (not self.min_node.left) and (not self.min_node.parent):
self.size = size_of_new
self.bottom_root = bottom_of_new
self.min_node = min_of_new
# print("Single root, multiple nodes case")
return min_value
# Remaining cases
# Construct heap of right subtree
newHeap = BinomialHeap(
bottom_root=bottom_of_new, min_node=min_of_new, heap_size=size_of_new
)
# Update size
self.size = self.size - 1 - size_of_new
# Neighbour nodes
previous_node = self.min_node.left
next_node = self.min_node.parent
# Initialize new bottom_root and min_node
self.min_node = previous_node or next_node
self.bottom_root = next_node
# Update links of previous_node and search below for new min_node and
# bottom_root
if previous_node:
previous_node.parent = next_node
# Update bottom_root and search for min_node below
self.bottom_root = previous_node
self.min_node = previous_node
while self.bottom_root.left:
self.bottom_root = self.bottom_root.left
if self.bottom_root.val < self.min_node.val:
self.min_node = self.bottom_root
if next_node:
next_node.left = previous_node
# Search for new min_node above min_node
i = next_node
while i:
if i.val < self.min_node.val:
self.min_node = i
i = i.parent
# Merge heaps
self.mergeHeaps(newHeap)
return min_value
def preOrder(self):
"""
Returns the Pre-order representation of the heap including
values of nodes plus their level distance from the root;
Empty nodes appear as #
"""
# Find top root
top_root = self.bottom_root
while top_root.parent:
top_root = top_root.parent
# preorder
heap_preOrder = []
self.__traversal(top_root, heap_preOrder)
return heap_preOrder
def __traversal(self, curr_node, preorder, level=0):
"""
Pre-order traversal of nodes
"""
if curr_node:
preorder.append((curr_node.val, level))
self.__traversal(curr_node.left, preorder, level + 1)
self.__traversal(curr_node.right, preorder, level + 1)
else:
preorder.append(("#", level))
def __str__(self):
"""
Overwriting str for a pre-order print of nodes in heap;
Performance is poor, so use only for small examples
"""
if self.isEmpty():
return ""
preorder_heap = self.preOrder()
return "\n".join(("-" * level + str(value)) for value, level in preorder_heap)
# Unit Tests
if __name__ == "__main__":
import doctest
doctest.testmod()
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Project Euler Problem 27
https://projecteuler.net/problem=27
Problem Statement:
Euler discovered the remarkable quadratic formula:
n2 + n + 41
It turns out that the formula will produce 40 primes for the consecutive values
n = 0 to 39. However, when n = 40, 402 + 40 + 41 = 40(40 + 1) + 41 is divisible
by 41, and certainly when n = 41, 412 + 41 + 41 is clearly divisible by 41.
The incredible formula n2 − 79n + 1601 was discovered, which produces 80 primes
for the consecutive values n = 0 to 79. The product of the coefficients, −79 and
1601, is −126479.
Considering quadratics of the form:
n² + an + b, where |a| < 1000 and |b| < 1000
where |n| is the modulus/absolute value of ne.g. |11| = 11 and |−4| = 4
Find the product of the coefficients, a and b, for the quadratic expression that
produces the maximum number of primes for consecutive values of n, starting with
n = 0.
"""
import math
def is_prime(k: int) -> bool:
"""
Determine if a number is prime
>>> is_prime(10)
False
>>> is_prime(11)
True
"""
if k < 2 or k % 2 == 0:
return False
elif k == 2:
return True
else:
for x in range(3, int(math.sqrt(k) + 1), 2):
if k % x == 0:
return False
return True
def solution(a_limit: int = 1000, b_limit: int = 1000) -> int:
"""
>>> solution(1000, 1000)
-59231
>>> solution(200, 1000)
-59231
>>> solution(200, 200)
-4925
>>> solution(-1000, 1000)
0
>>> solution(-1000, -1000)
0
"""
longest = [0, 0, 0] # length, a, b
for a in range((a_limit * -1) + 1, a_limit):
for b in range(2, b_limit):
if is_prime(b):
count = 0
n = 0
while is_prime((n ** 2) + (a * n) + b):
count += 1
n += 1
if count > longest[0]:
longest = [count, a, b]
ans = longest[1] * longest[2]
return ans
if __name__ == "__main__":
print(solution(1000, 1000))
| """
Project Euler Problem 27
https://projecteuler.net/problem=27
Problem Statement:
Euler discovered the remarkable quadratic formula:
n2 + n + 41
It turns out that the formula will produce 40 primes for the consecutive values
n = 0 to 39. However, when n = 40, 402 + 40 + 41 = 40(40 + 1) + 41 is divisible
by 41, and certainly when n = 41, 412 + 41 + 41 is clearly divisible by 41.
The incredible formula n2 − 79n + 1601 was discovered, which produces 80 primes
for the consecutive values n = 0 to 79. The product of the coefficients, −79 and
1601, is −126479.
Considering quadratics of the form:
n² + an + b, where |a| < 1000 and |b| < 1000
where |n| is the modulus/absolute value of ne.g. |11| = 11 and |−4| = 4
Find the product of the coefficients, a and b, for the quadratic expression that
produces the maximum number of primes for consecutive values of n, starting with
n = 0.
"""
import math
def is_prime(k: int) -> bool:
"""
Determine if a number is prime
>>> is_prime(10)
False
>>> is_prime(11)
True
"""
if k < 2 or k % 2 == 0:
return False
elif k == 2:
return True
else:
for x in range(3, int(math.sqrt(k) + 1), 2):
if k % x == 0:
return False
return True
def solution(a_limit: int = 1000, b_limit: int = 1000) -> int:
"""
>>> solution(1000, 1000)
-59231
>>> solution(200, 1000)
-59231
>>> solution(200, 200)
-4925
>>> solution(-1000, 1000)
0
>>> solution(-1000, -1000)
0
"""
longest = [0, 0, 0] # length, a, b
for a in range((a_limit * -1) + 1, a_limit):
for b in range(2, b_limit):
if is_prime(b):
count = 0
n = 0
while is_prime((n ** 2) + (a * n) + b):
count += 1
n += 1
if count > longest[0]:
longest = [count, a, b]
ans = longest[1] * longest[2]
return ans
if __name__ == "__main__":
print(solution(1000, 1000))
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| -1 |
||
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| from __future__ import annotations
import math
from typing import Callable
def line_length(
fnc: Callable[[int | float], int | float],
x_start: int | float,
x_end: int | float,
steps: int = 100,
) -> float:
"""
Approximates the arc length of a line segment by treating the curve as a
sequence of linear lines and summing their lengths
:param fnc: a function which defines a curve
:param x_start: left end point to indicate the start of line segment
:param x_end: right end point to indicate end of line segment
:param steps: an accuracy gauge; more steps increases accuracy
:return: a float representing the length of the curve
>>> def f(x):
... return x
>>> f"{line_length(f, 0, 1, 10):.6f}"
'1.414214'
>>> def f(x):
... return 1
>>> f"{line_length(f, -5.5, 4.5):.6f}"
'10.000000'
>>> def f(x):
... return math.sin(5 * x) + math.cos(10 * x) + x * x/10
>>> f"{line_length(f, 0.0, 10.0, 10000):.6f}"
'69.534930'
"""
x1 = x_start
fx1 = fnc(x_start)
length = 0.0
for i in range(steps):
# Approximates curve as a sequence of linear lines and sums their length
x2 = (x_end - x_start) / steps + x1
fx2 = fnc(x2)
length += math.hypot(x2 - x1, fx2 - fx1)
# Increment step
x1 = x2
fx1 = fx2
return length
if __name__ == "__main__":
def f(x):
return math.sin(10 * x)
print("f(x) = sin(10 * x)")
print("The length of the curve from x = -10 to x = 10 is:")
i = 10
while i <= 100000:
print(f"With {i} steps: {line_length(f, -10, 10, i)}")
i *= 10
| from __future__ import annotations
import math
from typing import Callable
def line_length(
fnc: Callable[[int | float], int | float],
x_start: int | float,
x_end: int | float,
steps: int = 100,
) -> float:
"""
Approximates the arc length of a line segment by treating the curve as a
sequence of linear lines and summing their lengths
:param fnc: a function which defines a curve
:param x_start: left end point to indicate the start of line segment
:param x_end: right end point to indicate end of line segment
:param steps: an accuracy gauge; more steps increases accuracy
:return: a float representing the length of the curve
>>> def f(x):
... return x
>>> f"{line_length(f, 0, 1, 10):.6f}"
'1.414214'
>>> def f(x):
... return 1
>>> f"{line_length(f, -5.5, 4.5):.6f}"
'10.000000'
>>> def f(x):
... return math.sin(5 * x) + math.cos(10 * x) + x * x/10
>>> f"{line_length(f, 0.0, 10.0, 10000):.6f}"
'69.534930'
"""
x1 = x_start
fx1 = fnc(x_start)
length = 0.0
for i in range(steps):
# Approximates curve as a sequence of linear lines and sums their length
x2 = (x_end - x_start) / steps + x1
fx2 = fnc(x2)
length += math.hypot(x2 - x1, fx2 - fx1)
# Increment step
x1 = x2
fx1 = fx2
return length
if __name__ == "__main__":
def f(x):
return math.sin(10 * x)
print("f(x) = sin(10 * x)")
print("The length of the curve from x = -10 to x = 10 is:")
i = 10
while i <= 100000:
print(f"With {i} steps: {line_length(f, -10, 10, i)}")
i *= 10
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| from __future__ import annotations
def compare_string(string1: str, string2: str) -> str:
"""
>>> compare_string('0010','0110')
'0_10'
>>> compare_string('0110','1101')
'X'
"""
l1 = list(string1)
l2 = list(string2)
count = 0
for i in range(len(l1)):
if l1[i] != l2[i]:
count += 1
l1[i] = "_"
if count > 1:
return "X"
else:
return "".join(l1)
def check(binary: list[str]) -> list[str]:
"""
>>> check(['0.00.01.5'])
['0.00.01.5']
"""
pi = []
while 1:
check1 = ["$"] * len(binary)
temp = []
for i in range(len(binary)):
for j in range(i + 1, len(binary)):
k = compare_string(binary[i], binary[j])
if k != "X":
check1[i] = "*"
check1[j] = "*"
temp.append(k)
for i in range(len(binary)):
if check1[i] == "$":
pi.append(binary[i])
if len(temp) == 0:
return pi
binary = list(set(temp))
def decimal_to_binary(no_of_variable: int, minterms: list[float]) -> list[str]:
"""
>>> decimal_to_binary(3,[1.5])
['0.00.01.5']
"""
temp = []
s = ""
for m in minterms:
for i in range(no_of_variable):
s = str(m % 2) + s
m //= 2
temp.append(s)
s = ""
return temp
def is_for_table(string1: str, string2: str, count: int) -> bool:
"""
>>> is_for_table('__1','011',2)
True
>>> is_for_table('01_','001',1)
False
"""
l1 = list(string1)
l2 = list(string2)
count_n = 0
for i in range(len(l1)):
if l1[i] != l2[i]:
count_n += 1
if count_n == count:
return True
else:
return False
def selection(chart: list[list[int]], prime_implicants: list[str]) -> list[str]:
"""
>>> selection([[1]],['0.00.01.5'])
['0.00.01.5']
>>> selection([[1]],['0.00.01.5'])
['0.00.01.5']
"""
temp = []
select = [0] * len(chart)
for i in range(len(chart[0])):
count = 0
rem = -1
for j in range(len(chart)):
if chart[j][i] == 1:
count += 1
rem = j
if count == 1:
select[rem] = 1
for i in range(len(select)):
if select[i] == 1:
for j in range(len(chart[0])):
if chart[i][j] == 1:
for k in range(len(chart)):
chart[k][j] = 0
temp.append(prime_implicants[i])
while 1:
max_n = 0
rem = -1
count_n = 0
for i in range(len(chart)):
count_n = chart[i].count(1)
if count_n > max_n:
max_n = count_n
rem = i
if max_n == 0:
return temp
temp.append(prime_implicants[rem])
for i in range(len(chart[0])):
if chart[rem][i] == 1:
for j in range(len(chart)):
chart[j][i] = 0
def prime_implicant_chart(
prime_implicants: list[str], binary: list[str]
) -> list[list[int]]:
"""
>>> prime_implicant_chart(['0.00.01.5'],['0.00.01.5'])
[[1]]
"""
chart = [[0 for x in range(len(binary))] for x in range(len(prime_implicants))]
for i in range(len(prime_implicants)):
count = prime_implicants[i].count("_")
for j in range(len(binary)):
if is_for_table(prime_implicants[i], binary[j], count):
chart[i][j] = 1
return chart
def main():
no_of_variable = int(input("Enter the no. of variables\n"))
minterms = [
int(x)
for x in input(
"Enter the decimal representation of Minterms 'Spaces Separated'\n"
).split()
]
binary = decimal_to_binary(no_of_variable, minterms)
prime_implicants = check(binary)
print("Prime Implicants are:")
print(prime_implicants)
chart = prime_implicant_chart(prime_implicants, binary)
essential_prime_implicants = selection(chart, prime_implicants)
print("Essential Prime Implicants are:")
print(essential_prime_implicants)
if __name__ == "__main__":
import doctest
doctest.testmod()
main()
| from __future__ import annotations
def compare_string(string1: str, string2: str) -> str:
"""
>>> compare_string('0010','0110')
'0_10'
>>> compare_string('0110','1101')
'X'
"""
l1 = list(string1)
l2 = list(string2)
count = 0
for i in range(len(l1)):
if l1[i] != l2[i]:
count += 1
l1[i] = "_"
if count > 1:
return "X"
else:
return "".join(l1)
def check(binary: list[str]) -> list[str]:
"""
>>> check(['0.00.01.5'])
['0.00.01.5']
"""
pi = []
while 1:
check1 = ["$"] * len(binary)
temp = []
for i in range(len(binary)):
for j in range(i + 1, len(binary)):
k = compare_string(binary[i], binary[j])
if k != "X":
check1[i] = "*"
check1[j] = "*"
temp.append(k)
for i in range(len(binary)):
if check1[i] == "$":
pi.append(binary[i])
if len(temp) == 0:
return pi
binary = list(set(temp))
def decimal_to_binary(no_of_variable: int, minterms: list[float]) -> list[str]:
"""
>>> decimal_to_binary(3,[1.5])
['0.00.01.5']
"""
temp = []
s = ""
for m in minterms:
for i in range(no_of_variable):
s = str(m % 2) + s
m //= 2
temp.append(s)
s = ""
return temp
def is_for_table(string1: str, string2: str, count: int) -> bool:
"""
>>> is_for_table('__1','011',2)
True
>>> is_for_table('01_','001',1)
False
"""
l1 = list(string1)
l2 = list(string2)
count_n = 0
for i in range(len(l1)):
if l1[i] != l2[i]:
count_n += 1
if count_n == count:
return True
else:
return False
def selection(chart: list[list[int]], prime_implicants: list[str]) -> list[str]:
"""
>>> selection([[1]],['0.00.01.5'])
['0.00.01.5']
>>> selection([[1]],['0.00.01.5'])
['0.00.01.5']
"""
temp = []
select = [0] * len(chart)
for i in range(len(chart[0])):
count = 0
rem = -1
for j in range(len(chart)):
if chart[j][i] == 1:
count += 1
rem = j
if count == 1:
select[rem] = 1
for i in range(len(select)):
if select[i] == 1:
for j in range(len(chart[0])):
if chart[i][j] == 1:
for k in range(len(chart)):
chart[k][j] = 0
temp.append(prime_implicants[i])
while 1:
max_n = 0
rem = -1
count_n = 0
for i in range(len(chart)):
count_n = chart[i].count(1)
if count_n > max_n:
max_n = count_n
rem = i
if max_n == 0:
return temp
temp.append(prime_implicants[rem])
for i in range(len(chart[0])):
if chart[rem][i] == 1:
for j in range(len(chart)):
chart[j][i] = 0
def prime_implicant_chart(
prime_implicants: list[str], binary: list[str]
) -> list[list[int]]:
"""
>>> prime_implicant_chart(['0.00.01.5'],['0.00.01.5'])
[[1]]
"""
chart = [[0 for x in range(len(binary))] for x in range(len(prime_implicants))]
for i in range(len(prime_implicants)):
count = prime_implicants[i].count("_")
for j in range(len(binary)):
if is_for_table(prime_implicants[i], binary[j], count):
chart[i][j] = 1
return chart
def main():
no_of_variable = int(input("Enter the no. of variables\n"))
minterms = [
int(x)
for x in input(
"Enter the decimal representation of Minterms 'Spaces Separated'\n"
).split()
]
binary = decimal_to_binary(no_of_variable, minterms)
prime_implicants = check(binary)
print("Prime Implicants are:")
print(prime_implicants)
chart = prime_implicant_chart(prime_implicants, binary)
essential_prime_implicants = selection(chart, prime_implicants)
print("Essential Prime Implicants are:")
print(essential_prime_implicants)
if __name__ == "__main__":
import doctest
doctest.testmod()
main()
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
A bag contains one red disc and one blue disc. In a game of chance a player takes a
disc at random and its colour is noted. After each turn the disc is returned to the
bag, an extra red disc is added, and another disc is taken at random.
The player pays £1 to play and wins if they have taken more blue discs than red
discs at the end of the game.
If the game is played for four turns, the probability of a player winning is exactly
11/120, and so the maximum prize fund the banker should allocate for winning in this
game would be £10 before they would expect to incur a loss. Note that any payout will
be a whole number of pounds and also includes the original £1 paid to play the game,
so in the example given the player actually wins £9.
Find the maximum prize fund that should be allocated to a single game in which
fifteen turns are played.
Solution:
For each 15-disc sequence of red and blue for which there are more red than blue,
we calculate the probability of that sequence and add it to the total probability
of the player winning. The inverse of this probability gives an upper bound for
the prize if the banker wants to avoid an expected loss.
"""
from itertools import product
def solution(num_turns: int = 15) -> int:
"""
Find the maximum prize fund that should be allocated to a single game in which
fifteen turns are played.
>>> solution(4)
10
>>> solution(10)
225
"""
total_prob: float = 0.0
prob: float
num_blue: int
num_red: int
ind: int
col: int
series: tuple[int, ...]
for series in product(range(2), repeat=num_turns):
num_blue = series.count(1)
num_red = num_turns - num_blue
if num_red >= num_blue:
continue
prob = 1.0
for ind, col in enumerate(series, 2):
if col == 0:
prob *= (ind - 1) / ind
else:
prob *= 1 / ind
total_prob += prob
return int(1 / total_prob)
if __name__ == "__main__":
print(f"{solution() = }")
| """
A bag contains one red disc and one blue disc. In a game of chance a player takes a
disc at random and its colour is noted. After each turn the disc is returned to the
bag, an extra red disc is added, and another disc is taken at random.
The player pays £1 to play and wins if they have taken more blue discs than red
discs at the end of the game.
If the game is played for four turns, the probability of a player winning is exactly
11/120, and so the maximum prize fund the banker should allocate for winning in this
game would be £10 before they would expect to incur a loss. Note that any payout will
be a whole number of pounds and also includes the original £1 paid to play the game,
so in the example given the player actually wins £9.
Find the maximum prize fund that should be allocated to a single game in which
fifteen turns are played.
Solution:
For each 15-disc sequence of red and blue for which there are more red than blue,
we calculate the probability of that sequence and add it to the total probability
of the player winning. The inverse of this probability gives an upper bound for
the prize if the banker wants to avoid an expected loss.
"""
from itertools import product
def solution(num_turns: int = 15) -> int:
"""
Find the maximum prize fund that should be allocated to a single game in which
fifteen turns are played.
>>> solution(4)
10
>>> solution(10)
225
"""
total_prob: float = 0.0
prob: float
num_blue: int
num_red: int
ind: int
col: int
series: tuple[int, ...]
for series in product(range(2), repeat=num_turns):
num_blue = series.count(1)
num_red = num_turns - num_blue
if num_red >= num_blue:
continue
prob = 1.0
for ind, col in enumerate(series, 2):
if col == 0:
prob *= (ind - 1) / ind
else:
prob *= 1 / ind
total_prob += prob
return int(1 / total_prob)
if __name__ == "__main__":
print(f"{solution() = }")
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| -1 |
||
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Project Euler Problem 2: https://projecteuler.net/problem=2
Even Fibonacci Numbers
Each new term in the Fibonacci sequence is generated by adding the previous
two terms. By starting with 1 and 2, the first 10 terms will be:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
By considering the terms in the Fibonacci sequence whose values do not exceed
four million, find the sum of the even-valued terms.
References:
- https://en.wikipedia.org/wiki/Fibonacci_number
"""
def solution(n: int = 4000000) -> int:
"""
Returns the sum of all even fibonacci sequence elements that are lower
or equal to n.
>>> solution(10)
10
>>> solution(15)
10
>>> solution(2)
2
>>> solution(1)
0
>>> solution(34)
44
"""
i = 1
j = 2
total = 0
while j <= n:
if j % 2 == 0:
total += j
i, j = j, i + j
return total
if __name__ == "__main__":
print(f"{solution() = }")
| """
Project Euler Problem 2: https://projecteuler.net/problem=2
Even Fibonacci Numbers
Each new term in the Fibonacci sequence is generated by adding the previous
two terms. By starting with 1 and 2, the first 10 terms will be:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
By considering the terms in the Fibonacci sequence whose values do not exceed
four million, find the sum of the even-valued terms.
References:
- https://en.wikipedia.org/wiki/Fibonacci_number
"""
def solution(n: int = 4000000) -> int:
"""
Returns the sum of all even fibonacci sequence elements that are lower
or equal to n.
>>> solution(10)
10
>>> solution(15)
10
>>> solution(2)
2
>>> solution(1)
0
>>> solution(34)
44
"""
i = 1
j = 2
total = 0
while j <= n:
if j % 2 == 0:
total += j
i, j = j, i + j
return total
if __name__ == "__main__":
print(f"{solution() = }")
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Output:
Enter an Infix Equation = a + b ^c
Symbol | Stack | Postfix
----------------------------
c | | c
^ | ^ | c
b | ^ | cb
+ | + | cb^
a | + | cb^a
| | cb^a+
a+b^c (Infix) -> +a^bc (Prefix)
"""
def infix_2_postfix(Infix):
Stack = []
Postfix = []
priority = {
"^": 3,
"*": 2,
"/": 2,
"%": 2,
"+": 1,
"-": 1,
} # Priority of each operator
print_width = len(Infix) if (len(Infix) > 7) else 7
# Print table header for output
print(
"Symbol".center(8),
"Stack".center(print_width),
"Postfix".center(print_width),
sep=" | ",
)
print("-" * (print_width * 3 + 7))
for x in Infix:
if x.isalpha() or x.isdigit():
Postfix.append(x) # if x is Alphabet / Digit, add it to Postfix
elif x == "(":
Stack.append(x) # if x is "(" push to Stack
elif x == ")": # if x is ")" pop stack until "(" is encountered
while Stack[-1] != "(":
Postfix.append(Stack.pop()) # Pop stack & add the content to Postfix
Stack.pop()
else:
if len(Stack) == 0:
Stack.append(x) # If stack is empty, push x to stack
else: # while priority of x is not > priority of element in the stack
while len(Stack) > 0 and priority[x] <= priority[Stack[-1]]:
Postfix.append(Stack.pop()) # pop stack & add to Postfix
Stack.append(x) # push x to stack
print(
x.center(8),
("".join(Stack)).ljust(print_width),
("".join(Postfix)).ljust(print_width),
sep=" | ",
) # Output in tabular format
while len(Stack) > 0: # while stack is not empty
Postfix.append(Stack.pop()) # pop stack & add to Postfix
print(
" ".center(8),
("".join(Stack)).ljust(print_width),
("".join(Postfix)).ljust(print_width),
sep=" | ",
) # Output in tabular format
return "".join(Postfix) # return Postfix as str
def infix_2_prefix(Infix):
Infix = list(Infix[::-1]) # reverse the infix equation
for i in range(len(Infix)):
if Infix[i] == "(":
Infix[i] = ")" # change "(" to ")"
elif Infix[i] == ")":
Infix[i] = "(" # change ")" to "("
return (infix_2_postfix("".join(Infix)))[
::-1
] # call infix_2_postfix on Infix, return reverse of Postfix
if __name__ == "__main__":
Infix = input("\nEnter an Infix Equation = ") # Input an Infix equation
Infix = "".join(Infix.split()) # Remove spaces from the input
print("\n\t", Infix, "(Infix) -> ", infix_2_prefix(Infix), "(Prefix)")
| """
Output:
Enter an Infix Equation = a + b ^c
Symbol | Stack | Postfix
----------------------------
c | | c
^ | ^ | c
b | ^ | cb
+ | + | cb^
a | + | cb^a
| | cb^a+
a+b^c (Infix) -> +a^bc (Prefix)
"""
def infix_2_postfix(Infix):
Stack = []
Postfix = []
priority = {
"^": 3,
"*": 2,
"/": 2,
"%": 2,
"+": 1,
"-": 1,
} # Priority of each operator
print_width = len(Infix) if (len(Infix) > 7) else 7
# Print table header for output
print(
"Symbol".center(8),
"Stack".center(print_width),
"Postfix".center(print_width),
sep=" | ",
)
print("-" * (print_width * 3 + 7))
for x in Infix:
if x.isalpha() or x.isdigit():
Postfix.append(x) # if x is Alphabet / Digit, add it to Postfix
elif x == "(":
Stack.append(x) # if x is "(" push to Stack
elif x == ")": # if x is ")" pop stack until "(" is encountered
while Stack[-1] != "(":
Postfix.append(Stack.pop()) # Pop stack & add the content to Postfix
Stack.pop()
else:
if len(Stack) == 0:
Stack.append(x) # If stack is empty, push x to stack
else: # while priority of x is not > priority of element in the stack
while len(Stack) > 0 and priority[x] <= priority[Stack[-1]]:
Postfix.append(Stack.pop()) # pop stack & add to Postfix
Stack.append(x) # push x to stack
print(
x.center(8),
("".join(Stack)).ljust(print_width),
("".join(Postfix)).ljust(print_width),
sep=" | ",
) # Output in tabular format
while len(Stack) > 0: # while stack is not empty
Postfix.append(Stack.pop()) # pop stack & add to Postfix
print(
" ".center(8),
("".join(Stack)).ljust(print_width),
("".join(Postfix)).ljust(print_width),
sep=" | ",
) # Output in tabular format
return "".join(Postfix) # return Postfix as str
def infix_2_prefix(Infix):
Infix = list(Infix[::-1]) # reverse the infix equation
for i in range(len(Infix)):
if Infix[i] == "(":
Infix[i] = ")" # change "(" to ")"
elif Infix[i] == ")":
Infix[i] = "(" # change ")" to "("
return (infix_2_postfix("".join(Infix)))[
::-1
] # call infix_2_postfix on Infix, return reverse of Postfix
if __name__ == "__main__":
Infix = input("\nEnter an Infix Equation = ") # Input an Infix equation
Infix = "".join(Infix.split()) # Remove spaces from the input
print("\n\t", Infix, "(Infix) -> ", infix_2_prefix(Infix), "(Prefix)")
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| -1 |
||
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| from math import atan, cos, radians, sin, tan
from .haversine_distance import haversine_distance
def lamberts_ellipsoidal_distance(
lat1: float, lon1: float, lat2: float, lon2: float
) -> float:
"""
Calculate the shortest distance along the surface of an ellipsoid between
two points on the surface of earth given longitudes and latitudes
https://en.wikipedia.org/wiki/Geographical_distance#Lambert's_formula_for_long_lines
NOTE: This algorithm uses geodesy/haversine_distance.py to compute central angle,
sigma
Representing the earth as an ellipsoid allows us to approximate distances between
points on the surface much better than a sphere. Ellipsoidal formulas treat the
Earth as an oblate ellipsoid which means accounting for the flattening that happens
at the North and South poles. Lambert's formulae provide accuracy on the order of
10 meteres over thousands of kilometeres. Other methods can provide
millimeter-level accuracy but this is a simpler method to calculate long range
distances without increasing computational intensity.
Args:
lat1, lon1: latitude and longitude of coordinate 1
lat2, lon2: latitude and longitude of coordinate 2
Returns:
geographical distance between two points in metres
>>> from collections import namedtuple
>>> point_2d = namedtuple("point_2d", "lat lon")
>>> SAN_FRANCISCO = point_2d(37.774856, -122.424227)
>>> YOSEMITE = point_2d(37.864742, -119.537521)
>>> NEW_YORK = point_2d(40.713019, -74.012647)
>>> VENICE = point_2d(45.443012, 12.313071)
>>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *YOSEMITE):0,.0f} meters"
'254,351 meters'
>>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *NEW_YORK):0,.0f} meters"
'4,138,992 meters'
>>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *VENICE):0,.0f} meters"
'9,737,326 meters'
"""
# CONSTANTS per WGS84 https://en.wikipedia.org/wiki/World_Geodetic_System
# Distance in metres(m)
AXIS_A = 6378137.0
AXIS_B = 6356752.314245
EQUATORIAL_RADIUS = 6378137
# Equation Parameters
# https://en.wikipedia.org/wiki/Geographical_distance#Lambert's_formula_for_long_lines
flattening = (AXIS_A - AXIS_B) / AXIS_A
# Parametric latitudes
# https://en.wikipedia.org/wiki/Latitude#Parametric_(or_reduced)_latitude
b_lat1 = atan((1 - flattening) * tan(radians(lat1)))
b_lat2 = atan((1 - flattening) * tan(radians(lat2)))
# Compute central angle between two points
# using haversine theta. sigma = haversine_distance / equatorial radius
sigma = haversine_distance(lat1, lon1, lat2, lon2) / EQUATORIAL_RADIUS
# Intermediate P and Q values
P_value = (b_lat1 + b_lat2) / 2
Q_value = (b_lat2 - b_lat1) / 2
# Intermediate X value
# X = (sigma - sin(sigma)) * sin^2Pcos^2Q / cos^2(sigma/2)
X_numerator = (sin(P_value) ** 2) * (cos(Q_value) ** 2)
X_demonimator = cos(sigma / 2) ** 2
X_value = (sigma - sin(sigma)) * (X_numerator / X_demonimator)
# Intermediate Y value
# Y = (sigma + sin(sigma)) * cos^2Psin^2Q / sin^2(sigma/2)
Y_numerator = (cos(P_value) ** 2) * (sin(Q_value) ** 2)
Y_denominator = sin(sigma / 2) ** 2
Y_value = (sigma + sin(sigma)) * (Y_numerator / Y_denominator)
return EQUATORIAL_RADIUS * (sigma - ((flattening / 2) * (X_value + Y_value)))
if __name__ == "__main__":
import doctest
doctest.testmod()
| from math import atan, cos, radians, sin, tan
from .haversine_distance import haversine_distance
def lamberts_ellipsoidal_distance(
lat1: float, lon1: float, lat2: float, lon2: float
) -> float:
"""
Calculate the shortest distance along the surface of an ellipsoid between
two points on the surface of earth given longitudes and latitudes
https://en.wikipedia.org/wiki/Geographical_distance#Lambert's_formula_for_long_lines
NOTE: This algorithm uses geodesy/haversine_distance.py to compute central angle,
sigma
Representing the earth as an ellipsoid allows us to approximate distances between
points on the surface much better than a sphere. Ellipsoidal formulas treat the
Earth as an oblate ellipsoid which means accounting for the flattening that happens
at the North and South poles. Lambert's formulae provide accuracy on the order of
10 meteres over thousands of kilometeres. Other methods can provide
millimeter-level accuracy but this is a simpler method to calculate long range
distances without increasing computational intensity.
Args:
lat1, lon1: latitude and longitude of coordinate 1
lat2, lon2: latitude and longitude of coordinate 2
Returns:
geographical distance between two points in metres
>>> from collections import namedtuple
>>> point_2d = namedtuple("point_2d", "lat lon")
>>> SAN_FRANCISCO = point_2d(37.774856, -122.424227)
>>> YOSEMITE = point_2d(37.864742, -119.537521)
>>> NEW_YORK = point_2d(40.713019, -74.012647)
>>> VENICE = point_2d(45.443012, 12.313071)
>>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *YOSEMITE):0,.0f} meters"
'254,351 meters'
>>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *NEW_YORK):0,.0f} meters"
'4,138,992 meters'
>>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *VENICE):0,.0f} meters"
'9,737,326 meters'
"""
# CONSTANTS per WGS84 https://en.wikipedia.org/wiki/World_Geodetic_System
# Distance in metres(m)
AXIS_A = 6378137.0
AXIS_B = 6356752.314245
EQUATORIAL_RADIUS = 6378137
# Equation Parameters
# https://en.wikipedia.org/wiki/Geographical_distance#Lambert's_formula_for_long_lines
flattening = (AXIS_A - AXIS_B) / AXIS_A
# Parametric latitudes
# https://en.wikipedia.org/wiki/Latitude#Parametric_(or_reduced)_latitude
b_lat1 = atan((1 - flattening) * tan(radians(lat1)))
b_lat2 = atan((1 - flattening) * tan(radians(lat2)))
# Compute central angle between two points
# using haversine theta. sigma = haversine_distance / equatorial radius
sigma = haversine_distance(lat1, lon1, lat2, lon2) / EQUATORIAL_RADIUS
# Intermediate P and Q values
P_value = (b_lat1 + b_lat2) / 2
Q_value = (b_lat2 - b_lat1) / 2
# Intermediate X value
# X = (sigma - sin(sigma)) * sin^2Pcos^2Q / cos^2(sigma/2)
X_numerator = (sin(P_value) ** 2) * (cos(Q_value) ** 2)
X_demonimator = cos(sigma / 2) ** 2
X_value = (sigma - sin(sigma)) * (X_numerator / X_demonimator)
# Intermediate Y value
# Y = (sigma + sin(sigma)) * cos^2Psin^2Q / sin^2(sigma/2)
Y_numerator = (cos(P_value) ** 2) * (sin(Q_value) ** 2)
Y_denominator = sin(sigma / 2) ** 2
Y_value = (sigma + sin(sigma)) * (Y_numerator / Y_denominator)
return EQUATORIAL_RADIUS * (sigma - ((flattening / 2) * (X_value + Y_value)))
if __name__ == "__main__":
import doctest
doctest.testmod()
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| import string
from math import log10
"""
tf-idf Wikipedia: https://en.wikipedia.org/wiki/Tf%E2%80%93idf
tf-idf and other word frequency algorithms are often used
as a weighting factor in information retrieval and text
mining. 83% of text-based recommender systems use
tf-idf for term weighting. In Layman's terms, tf-idf
is a statistic intended to reflect how important a word
is to a document in a corpus (a collection of documents)
Here I've implemented several word frequency algorithms
that are commonly used in information retrieval: Term Frequency,
Document Frequency, and TF-IDF (Term-Frequency*Inverse-Document-Frequency)
are included.
Term Frequency is a statistical function that
returns a number representing how frequently
an expression occurs in a document. This
indicates how significant a particular term is in
a given document.
Document Frequency is a statistical function that returns
an integer representing the number of documents in a
corpus that a term occurs in (where the max number returned
would be the number of documents in the corpus).
Inverse Document Frequency is mathematically written as
log10(N/df), where N is the number of documents in your
corpus and df is the Document Frequency. If df is 0, a
ZeroDivisionError will be thrown.
Term-Frequency*Inverse-Document-Frequency is a measure
of the originality of a term. It is mathematically written
as tf*log10(N/df). It compares the number of times
a term appears in a document with the number of documents
the term appears in. If df is 0, a ZeroDivisionError will be thrown.
"""
def term_frequency(term: str, document: str) -> int:
"""
Return the number of times a term occurs within
a given document.
@params: term, the term to search a document for, and document,
the document to search within
@returns: an integer representing the number of times a term is
found within the document
@examples:
>>> term_frequency("to", "To be, or not to be")
2
"""
# strip all punctuation and newlines and replace it with ''
document_without_punctuation = document.translate(
str.maketrans("", "", string.punctuation)
).replace("\n", "")
tokenize_document = document_without_punctuation.split(" ") # word tokenization
return len([word for word in tokenize_document if word.lower() == term.lower()])
def document_frequency(term: str, corpus: str) -> tuple[int, int]:
"""
Calculate the number of documents in a corpus that contain a
given term
@params : term, the term to search each document for, and corpus, a collection of
documents. Each document should be separated by a newline.
@returns : the number of documents in the corpus that contain the term you are
searching for and the number of documents in the corpus
@examples :
>>> document_frequency("first", "This is the first document in the corpus.\\nThIs\
is the second document in the corpus.\\nTHIS is \
the third document in the corpus.")
(1, 3)
"""
corpus_without_punctuation = corpus.lower().translate(
str.maketrans("", "", string.punctuation)
) # strip all punctuation and replace it with ''
docs = corpus_without_punctuation.split("\n")
term = term.lower()
return (len([doc for doc in docs if term in doc]), len(docs))
def inverse_document_frequency(df: int, N: int, smoothing=False) -> float:
"""
Return an integer denoting the importance
of a word. This measure of importance is
calculated by log10(N/df), where N is the
number of documents and df is
the Document Frequency.
@params : df, the Document Frequency, N,
the number of documents in the corpus and
smoothing, if True return the idf-smooth
@returns : log10(N/df) or 1+log10(N/1+df)
@examples :
>>> inverse_document_frequency(3, 0)
Traceback (most recent call last):
...
ValueError: log10(0) is undefined.
>>> inverse_document_frequency(1, 3)
0.477
>>> inverse_document_frequency(0, 3)
Traceback (most recent call last):
...
ZeroDivisionError: df must be > 0
>>> inverse_document_frequency(0, 3,True)
1.477
"""
if smoothing:
if N == 0:
raise ValueError("log10(0) is undefined.")
return round(1 + log10(N / (1 + df)), 3)
if df == 0:
raise ZeroDivisionError("df must be > 0")
elif N == 0:
raise ValueError("log10(0) is undefined.")
return round(log10(N / df), 3)
def tf_idf(tf: int, idf: int) -> float:
"""
Combine the term frequency
and inverse document frequency functions to
calculate the originality of a term. This
'originality' is calculated by multiplying
the term frequency and the inverse document
frequency : tf-idf = TF * IDF
@params : tf, the term frequency, and idf, the inverse document
frequency
@examples :
>>> tf_idf(2, 0.477)
0.954
"""
return round(tf * idf, 3)
| import string
from math import log10
"""
tf-idf Wikipedia: https://en.wikipedia.org/wiki/Tf%E2%80%93idf
tf-idf and other word frequency algorithms are often used
as a weighting factor in information retrieval and text
mining. 83% of text-based recommender systems use
tf-idf for term weighting. In Layman's terms, tf-idf
is a statistic intended to reflect how important a word
is to a document in a corpus (a collection of documents)
Here I've implemented several word frequency algorithms
that are commonly used in information retrieval: Term Frequency,
Document Frequency, and TF-IDF (Term-Frequency*Inverse-Document-Frequency)
are included.
Term Frequency is a statistical function that
returns a number representing how frequently
an expression occurs in a document. This
indicates how significant a particular term is in
a given document.
Document Frequency is a statistical function that returns
an integer representing the number of documents in a
corpus that a term occurs in (where the max number returned
would be the number of documents in the corpus).
Inverse Document Frequency is mathematically written as
log10(N/df), where N is the number of documents in your
corpus and df is the Document Frequency. If df is 0, a
ZeroDivisionError will be thrown.
Term-Frequency*Inverse-Document-Frequency is a measure
of the originality of a term. It is mathematically written
as tf*log10(N/df). It compares the number of times
a term appears in a document with the number of documents
the term appears in. If df is 0, a ZeroDivisionError will be thrown.
"""
def term_frequency(term: str, document: str) -> int:
"""
Return the number of times a term occurs within
a given document.
@params: term, the term to search a document for, and document,
the document to search within
@returns: an integer representing the number of times a term is
found within the document
@examples:
>>> term_frequency("to", "To be, or not to be")
2
"""
# strip all punctuation and newlines and replace it with ''
document_without_punctuation = document.translate(
str.maketrans("", "", string.punctuation)
).replace("\n", "")
tokenize_document = document_without_punctuation.split(" ") # word tokenization
return len([word for word in tokenize_document if word.lower() == term.lower()])
def document_frequency(term: str, corpus: str) -> tuple[int, int]:
"""
Calculate the number of documents in a corpus that contain a
given term
@params : term, the term to search each document for, and corpus, a collection of
documents. Each document should be separated by a newline.
@returns : the number of documents in the corpus that contain the term you are
searching for and the number of documents in the corpus
@examples :
>>> document_frequency("first", "This is the first document in the corpus.\\nThIs\
is the second document in the corpus.\\nTHIS is \
the third document in the corpus.")
(1, 3)
"""
corpus_without_punctuation = corpus.lower().translate(
str.maketrans("", "", string.punctuation)
) # strip all punctuation and replace it with ''
docs = corpus_without_punctuation.split("\n")
term = term.lower()
return (len([doc for doc in docs if term in doc]), len(docs))
def inverse_document_frequency(df: int, N: int, smoothing=False) -> float:
"""
Return an integer denoting the importance
of a word. This measure of importance is
calculated by log10(N/df), where N is the
number of documents and df is
the Document Frequency.
@params : df, the Document Frequency, N,
the number of documents in the corpus and
smoothing, if True return the idf-smooth
@returns : log10(N/df) or 1+log10(N/1+df)
@examples :
>>> inverse_document_frequency(3, 0)
Traceback (most recent call last):
...
ValueError: log10(0) is undefined.
>>> inverse_document_frequency(1, 3)
0.477
>>> inverse_document_frequency(0, 3)
Traceback (most recent call last):
...
ZeroDivisionError: df must be > 0
>>> inverse_document_frequency(0, 3,True)
1.477
"""
if smoothing:
if N == 0:
raise ValueError("log10(0) is undefined.")
return round(1 + log10(N / (1 + df)), 3)
if df == 0:
raise ZeroDivisionError("df must be > 0")
elif N == 0:
raise ValueError("log10(0) is undefined.")
return round(log10(N / df), 3)
def tf_idf(tf: int, idf: int) -> float:
"""
Combine the term frequency
and inverse document frequency functions to
calculate the originality of a term. This
'originality' is calculated by multiplying
the term frequency and the inverse document
frequency : tf-idf = TF * IDF
@params : tf, the term frequency, and idf, the inverse document
frequency
@examples :
>>> tf_idf(2, 0.477)
0.954
"""
return round(tf * idf, 3)
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Approximates the area under the curve using the trapezoidal rule
"""
from __future__ import annotations
from typing import Callable
def trapezoidal_area(
fnc: Callable[[int | float], int | float],
x_start: int | float,
x_end: int | float,
steps: int = 100,
) -> float:
"""
Treats curve as a collection of linear lines and sums the area of the
trapezium shape they form
:param fnc: a function which defines a curve
:param x_start: left end point to indicate the start of line segment
:param x_end: right end point to indicate end of line segment
:param steps: an accuracy gauge; more steps increases the accuracy
:return: a float representing the length of the curve
>>> def f(x):
... return 5
>>> '%.3f' % trapezoidal_area(f, 12.0, 14.0, 1000)
'10.000'
>>> def f(x):
... return 9*x**2
>>> '%.4f' % trapezoidal_area(f, -4.0, 0, 10000)
'192.0000'
>>> '%.4f' % trapezoidal_area(f, -4.0, 4.0, 10000)
'384.0000'
"""
x1 = x_start
fx1 = fnc(x_start)
area = 0.0
for i in range(steps):
# Approximates small segments of curve as linear and solve
# for trapezoidal area
x2 = (x_end - x_start) / steps + x1
fx2 = fnc(x2)
area += abs(fx2 + fx1) * (x2 - x1) / 2
# Increment step
x1 = x2
fx1 = fx2
return area
if __name__ == "__main__":
def f(x):
return x ** 3
print("f(x) = x^3")
print("The area between the curve, x = -10, x = 10 and the x axis is:")
i = 10
while i <= 100000:
area = trapezoidal_area(f, -5, 5, i)
print(f"with {i} steps: {area}")
i *= 10
| """
Approximates the area under the curve using the trapezoidal rule
"""
from __future__ import annotations
from typing import Callable
def trapezoidal_area(
fnc: Callable[[int | float], int | float],
x_start: int | float,
x_end: int | float,
steps: int = 100,
) -> float:
"""
Treats curve as a collection of linear lines and sums the area of the
trapezium shape they form
:param fnc: a function which defines a curve
:param x_start: left end point to indicate the start of line segment
:param x_end: right end point to indicate end of line segment
:param steps: an accuracy gauge; more steps increases the accuracy
:return: a float representing the length of the curve
>>> def f(x):
... return 5
>>> '%.3f' % trapezoidal_area(f, 12.0, 14.0, 1000)
'10.000'
>>> def f(x):
... return 9*x**2
>>> '%.4f' % trapezoidal_area(f, -4.0, 0, 10000)
'192.0000'
>>> '%.4f' % trapezoidal_area(f, -4.0, 4.0, 10000)
'384.0000'
"""
x1 = x_start
fx1 = fnc(x_start)
area = 0.0
for i in range(steps):
# Approximates small segments of curve as linear and solve
# for trapezoidal area
x2 = (x_end - x_start) / steps + x1
fx2 = fnc(x2)
area += abs(fx2 + fx1) * (x2 - x1) / 2
# Increment step
x1 = x2
fx1 = fx2
return area
if __name__ == "__main__":
def f(x):
return x ** 3
print("f(x) = x^3")
print("The area between the curve, x = -10, x = 10 and the x axis is:")
i = 10
while i <= 100000:
area = trapezoidal_area(f, -5, 5, i)
print(f"with {i} steps: {area}")
i *= 10
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Problem Statement:
By starting at the top of the triangle below and moving to adjacent numbers on
the row below, the maximum total from top to bottom is 23.
3
7 4
2 4 6
8 5 9 3
That is, 3 + 7 + 4 + 9 = 23.
Find the maximum total from top to bottom in triangle.txt (right click and
'Save Link/Target As...'), a 15K text file containing a triangle with
one-hundred rows.
"""
import os
def solution():
"""
Finds the maximum total in a triangle as described by the problem statement
above.
>>> solution()
7273
"""
script_dir = os.path.dirname(os.path.realpath(__file__))
triangle = os.path.join(script_dir, "triangle.txt")
with open(triangle) as f:
triangle = f.readlines()
a = map(lambda x: x.rstrip("\r\n").split(" "), triangle)
a = list(map(lambda x: list(map(lambda y: int(y), x)), a))
for i in range(1, len(a)):
for j in range(len(a[i])):
if j != len(a[i - 1]):
number1 = a[i - 1][j]
else:
number1 = 0
if j > 0:
number2 = a[i - 1][j - 1]
else:
number2 = 0
a[i][j] += max(number1, number2)
return max(a[-1])
if __name__ == "__main__":
print(solution())
| """
Problem Statement:
By starting at the top of the triangle below and moving to adjacent numbers on
the row below, the maximum total from top to bottom is 23.
3
7 4
2 4 6
8 5 9 3
That is, 3 + 7 + 4 + 9 = 23.
Find the maximum total from top to bottom in triangle.txt (right click and
'Save Link/Target As...'), a 15K text file containing a triangle with
one-hundred rows.
"""
import os
def solution():
"""
Finds the maximum total in a triangle as described by the problem statement
above.
>>> solution()
7273
"""
script_dir = os.path.dirname(os.path.realpath(__file__))
triangle = os.path.join(script_dir, "triangle.txt")
with open(triangle) as f:
triangle = f.readlines()
a = map(lambda x: x.rstrip("\r\n").split(" "), triangle)
a = list(map(lambda x: list(map(lambda y: int(y), x)), a))
for i in range(1, len(a)):
for j in range(len(a[i])):
if j != len(a[i - 1]):
number1 = a[i - 1][j]
else:
number1 = 0
if j > 0:
number2 = a[i - 1][j - 1]
else:
number2 = 0
a[i][j] += max(number1, number2)
return max(a[-1])
if __name__ == "__main__":
print(solution())
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| import math
from typing import Callable
def intersection(function: Callable[[float], float], x0: float, x1: float) -> float:
"""
function is the f we want to find its root
x0 and x1 are two random starting points
>>> intersection(lambda x: x ** 3 - 1, -5, 5)
0.9999999999954654
>>> intersection(lambda x: x ** 3 - 1, 5, 5)
Traceback (most recent call last):
...
ZeroDivisionError: float division by zero, could not find root
>>> intersection(lambda x: x ** 3 - 1, 100, 200)
1.0000000000003888
>>> intersection(lambda x: x ** 2 - 4 * x + 3, 0, 2)
0.9999999998088019
>>> intersection(lambda x: x ** 2 - 4 * x + 3, 2, 4)
2.9999999998088023
>>> intersection(lambda x: x ** 2 - 4 * x + 3, 4, 1000)
3.0000000001786042
>>> intersection(math.sin, -math.pi, math.pi)
0.0
>>> intersection(math.cos, -math.pi, math.pi)
Traceback (most recent call last):
...
ZeroDivisionError: float division by zero, could not find root
"""
x_n: float = x0
x_n1: float = x1
while True:
if x_n == x_n1 or function(x_n1) == function(x_n):
raise ZeroDivisionError("float division by zero, could not find root")
x_n2: float = x_n1 - (
function(x_n1) / ((function(x_n1) - function(x_n)) / (x_n1 - x_n))
)
if abs(x_n2 - x_n1) < 10 ** -5:
return x_n2
x_n = x_n1
x_n1 = x_n2
def f(x: float) -> float:
return math.pow(x, 3) - (2 * x) - 5
if __name__ == "__main__":
print(intersection(f, 3, 3.5))
| import math
from typing import Callable
def intersection(function: Callable[[float], float], x0: float, x1: float) -> float:
"""
function is the f we want to find its root
x0 and x1 are two random starting points
>>> intersection(lambda x: x ** 3 - 1, -5, 5)
0.9999999999954654
>>> intersection(lambda x: x ** 3 - 1, 5, 5)
Traceback (most recent call last):
...
ZeroDivisionError: float division by zero, could not find root
>>> intersection(lambda x: x ** 3 - 1, 100, 200)
1.0000000000003888
>>> intersection(lambda x: x ** 2 - 4 * x + 3, 0, 2)
0.9999999998088019
>>> intersection(lambda x: x ** 2 - 4 * x + 3, 2, 4)
2.9999999998088023
>>> intersection(lambda x: x ** 2 - 4 * x + 3, 4, 1000)
3.0000000001786042
>>> intersection(math.sin, -math.pi, math.pi)
0.0
>>> intersection(math.cos, -math.pi, math.pi)
Traceback (most recent call last):
...
ZeroDivisionError: float division by zero, could not find root
"""
x_n: float = x0
x_n1: float = x1
while True:
if x_n == x_n1 or function(x_n1) == function(x_n):
raise ZeroDivisionError("float division by zero, could not find root")
x_n2: float = x_n1 - (
function(x_n1) / ((function(x_n1) - function(x_n)) / (x_n1 - x_n))
)
if abs(x_n2 - x_n1) < 10 ** -5:
return x_n2
x_n = x_n1
x_n1 = x_n2
def f(x: float) -> float:
return math.pow(x, 3) - (2 * x) - 5
if __name__ == "__main__":
print(intersection(f, 3, 3.5))
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| def printDist(dist, V):
print("\nVertex Distance")
for i in range(V):
if dist[i] != float("inf"):
print(i, "\t", int(dist[i]), end="\t")
else:
print(i, "\t", "INF", end="\t")
print()
def minDist(mdist, vset, V):
minVal = float("inf")
minInd = -1
for i in range(V):
if (not vset[i]) and mdist[i] < minVal:
minInd = i
minVal = mdist[i]
return minInd
def Dijkstra(graph, V, src):
mdist = [float("inf") for i in range(V)]
vset = [False for i in range(V)]
mdist[src] = 0.0
for i in range(V - 1):
u = minDist(mdist, vset, V)
vset[u] = True
for v in range(V):
if (
(not vset[v])
and graph[u][v] != float("inf")
and mdist[u] + graph[u][v] < mdist[v]
):
mdist[v] = mdist[u] + graph[u][v]
printDist(mdist, V)
if __name__ == "__main__":
V = int(input("Enter number of vertices: ").strip())
E = int(input("Enter number of edges: ").strip())
graph = [[float("inf") for i in range(V)] for j in range(V)]
for i in range(V):
graph[i][i] = 0.0
for i in range(E):
print("\nEdge ", i + 1)
src = int(input("Enter source:").strip())
dst = int(input("Enter destination:").strip())
weight = float(input("Enter weight:").strip())
graph[src][dst] = weight
gsrc = int(input("\nEnter shortest path source:").strip())
Dijkstra(graph, V, gsrc)
| def printDist(dist, V):
print("\nVertex Distance")
for i in range(V):
if dist[i] != float("inf"):
print(i, "\t", int(dist[i]), end="\t")
else:
print(i, "\t", "INF", end="\t")
print()
def minDist(mdist, vset, V):
minVal = float("inf")
minInd = -1
for i in range(V):
if (not vset[i]) and mdist[i] < minVal:
minInd = i
minVal = mdist[i]
return minInd
def Dijkstra(graph, V, src):
mdist = [float("inf") for i in range(V)]
vset = [False for i in range(V)]
mdist[src] = 0.0
for i in range(V - 1):
u = minDist(mdist, vset, V)
vset[u] = True
for v in range(V):
if (
(not vset[v])
and graph[u][v] != float("inf")
and mdist[u] + graph[u][v] < mdist[v]
):
mdist[v] = mdist[u] + graph[u][v]
printDist(mdist, V)
if __name__ == "__main__":
V = int(input("Enter number of vertices: ").strip())
E = int(input("Enter number of edges: ").strip())
graph = [[float("inf") for i in range(V)] for j in range(V)]
for i in range(V):
graph[i][i] = 0.0
for i in range(E):
print("\nEdge ", i + 1)
src = int(input("Enter source:").strip())
dst = int(input("Enter destination:").strip())
weight = float(input("Enter weight:").strip())
graph[src][dst] = weight
gsrc = int(input("\nEnter shortest path source:").strip())
Dijkstra(graph, V, gsrc)
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| import base64
def main() -> None:
inp = input("->")
encoded = inp.encode("utf-8") # encoded the input (we need a bytes like object)
b32encoded = base64.b32encode(encoded) # b32encoded the encoded string
print(b32encoded)
print(base64.b32decode(b32encoded).decode("utf-8")) # decoded it
if __name__ == "__main__":
main()
| import base64
def main() -> None:
inp = input("->")
encoded = inp.encode("utf-8") # encoded the input (we need a bytes like object)
b32encoded = base64.b32encode(encoded) # b32encoded the encoded string
print(b32encoded)
print(base64.b32decode(b32encoded).decode("utf-8")) # decoded it
if __name__ == "__main__":
main()
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| from collections import defaultdict
from graphs.minimum_spanning_tree_prims import PrimsAlgorithm as mst
def test_prim_successful_result():
num_nodes, num_edges = 9, 14 # noqa: F841
edges = [
[0, 1, 4],
[0, 7, 8],
[1, 2, 8],
[7, 8, 7],
[7, 6, 1],
[2, 8, 2],
[8, 6, 6],
[2, 3, 7],
[2, 5, 4],
[6, 5, 2],
[3, 5, 14],
[3, 4, 9],
[5, 4, 10],
[1, 7, 11],
]
adjancency = defaultdict(list)
for node1, node2, cost in edges:
adjancency[node1].append([node2, cost])
adjancency[node2].append([node1, cost])
result = mst(adjancency)
expected = [
[7, 6, 1],
[2, 8, 2],
[6, 5, 2],
[0, 1, 4],
[2, 5, 4],
[2, 3, 7],
[0, 7, 8],
[3, 4, 9],
]
for answer in expected:
edge = tuple(answer[:2])
reverse = tuple(edge[::-1])
assert edge in result or reverse in result
| from collections import defaultdict
from graphs.minimum_spanning_tree_prims import PrimsAlgorithm as mst
def test_prim_successful_result():
num_nodes, num_edges = 9, 14 # noqa: F841
edges = [
[0, 1, 4],
[0, 7, 8],
[1, 2, 8],
[7, 8, 7],
[7, 6, 1],
[2, 8, 2],
[8, 6, 6],
[2, 3, 7],
[2, 5, 4],
[6, 5, 2],
[3, 5, 14],
[3, 4, 9],
[5, 4, 10],
[1, 7, 11],
]
adjancency = defaultdict(list)
for node1, node2, cost in edges:
adjancency[node1].append([node2, cost])
adjancency[node2].append([node1, cost])
result = mst(adjancency)
expected = [
[7, 6, 1],
[2, 8, 2],
[6, 5, 2],
[0, 1, 4],
[2, 5, 4],
[2, 3, 7],
[0, 7, 8],
[3, 4, 9],
]
for answer in expected:
edge = tuple(answer[:2])
reverse = tuple(edge[::-1])
assert edge in result or reverse in result
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Given an array of integers and another integer target,
we are required to find a triplet from the array such that it's sum is equal to
the target.
"""
from __future__ import annotations
from itertools import permutations
from random import randint
from timeit import repeat
def make_dataset() -> tuple[list[int], int]:
arr = [randint(-1000, 1000) for i in range(10)]
r = randint(-5000, 5000)
return (arr, r)
dataset = make_dataset()
def triplet_sum1(arr: list[int], target: int) -> tuple[int, ...]:
"""
Returns a triplet in the array with sum equal to target,
else (0, 0, 0).
>>> triplet_sum1([13, 29, 7, 23, 5], 35)
(5, 7, 23)
>>> triplet_sum1([37, 9, 19, 50, 44], 65)
(9, 19, 37)
>>> arr = [6, 47, 27, 1, 15]
>>> target = 11
>>> triplet_sum1(arr, target)
(0, 0, 0)
"""
for triplet in permutations(arr, 3):
if sum(triplet) == target:
return tuple(sorted(triplet))
return (0, 0, 0)
def triplet_sum2(arr: list[int], target: int) -> tuple[int, int, int]:
"""
Returns a triplet in the array with sum equal to target,
else (0, 0, 0).
>>> triplet_sum2([13, 29, 7, 23, 5], 35)
(5, 7, 23)
>>> triplet_sum2([37, 9, 19, 50, 44], 65)
(9, 19, 37)
>>> arr = [6, 47, 27, 1, 15]
>>> target = 11
>>> triplet_sum2(arr, target)
(0, 0, 0)
"""
arr.sort()
n = len(arr)
for i in range(n - 1):
left, right = i + 1, n - 1
while left < right:
if arr[i] + arr[left] + arr[right] == target:
return (arr[i], arr[left], arr[right])
elif arr[i] + arr[left] + arr[right] < target:
left += 1
elif arr[i] + arr[left] + arr[right] > target:
right -= 1
return (0, 0, 0)
def solution_times() -> tuple[float, float]:
setup_code = """
from __main__ import dataset, triplet_sum1, triplet_sum2
"""
test_code1 = """
triplet_sum1(*dataset)
"""
test_code2 = """
triplet_sum2(*dataset)
"""
times1 = repeat(setup=setup_code, stmt=test_code1, repeat=5, number=10000)
times2 = repeat(setup=setup_code, stmt=test_code2, repeat=5, number=10000)
return (min(times1), min(times2))
if __name__ == "__main__":
from doctest import testmod
testmod()
times = solution_times()
print(f"The time for naive implementation is {times[0]}.")
print(f"The time for optimized implementation is {times[1]}.")
| """
Given an array of integers and another integer target,
we are required to find a triplet from the array such that it's sum is equal to
the target.
"""
from __future__ import annotations
from itertools import permutations
from random import randint
from timeit import repeat
def make_dataset() -> tuple[list[int], int]:
arr = [randint(-1000, 1000) for i in range(10)]
r = randint(-5000, 5000)
return (arr, r)
dataset = make_dataset()
def triplet_sum1(arr: list[int], target: int) -> tuple[int, ...]:
"""
Returns a triplet in the array with sum equal to target,
else (0, 0, 0).
>>> triplet_sum1([13, 29, 7, 23, 5], 35)
(5, 7, 23)
>>> triplet_sum1([37, 9, 19, 50, 44], 65)
(9, 19, 37)
>>> arr = [6, 47, 27, 1, 15]
>>> target = 11
>>> triplet_sum1(arr, target)
(0, 0, 0)
"""
for triplet in permutations(arr, 3):
if sum(triplet) == target:
return tuple(sorted(triplet))
return (0, 0, 0)
def triplet_sum2(arr: list[int], target: int) -> tuple[int, int, int]:
"""
Returns a triplet in the array with sum equal to target,
else (0, 0, 0).
>>> triplet_sum2([13, 29, 7, 23, 5], 35)
(5, 7, 23)
>>> triplet_sum2([37, 9, 19, 50, 44], 65)
(9, 19, 37)
>>> arr = [6, 47, 27, 1, 15]
>>> target = 11
>>> triplet_sum2(arr, target)
(0, 0, 0)
"""
arr.sort()
n = len(arr)
for i in range(n - 1):
left, right = i + 1, n - 1
while left < right:
if arr[i] + arr[left] + arr[right] == target:
return (arr[i], arr[left], arr[right])
elif arr[i] + arr[left] + arr[right] < target:
left += 1
elif arr[i] + arr[left] + arr[right] > target:
right -= 1
return (0, 0, 0)
def solution_times() -> tuple[float, float]:
setup_code = """
from __main__ import dataset, triplet_sum1, triplet_sum2
"""
test_code1 = """
triplet_sum1(*dataset)
"""
test_code2 = """
triplet_sum2(*dataset)
"""
times1 = repeat(setup=setup_code, stmt=test_code1, repeat=5, number=10000)
times2 = repeat(setup=setup_code, stmt=test_code2, repeat=5, number=10000)
return (min(times1), min(times2))
if __name__ == "__main__":
from doctest import testmod
testmod()
times = solution_times()
print(f"The time for naive implementation is {times[0]}.")
print(f"The time for optimized implementation is {times[1]}.")
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| -1 |
||
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| from binascii import hexlify
from hashlib import sha256
from os import urandom
# RFC 3526 - More Modular Exponential (MODP) Diffie-Hellman groups for
# Internet Key Exchange (IKE) https://tools.ietf.org/html/rfc3526
primes = {
# 1536-bit
5: {
"prime": int(
"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
+ "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
+ "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
+ "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
+ "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
+ "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
+ "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
+ "670C354E4ABC9804F1746C08CA237327FFFFFFFFFFFFFFFF",
base=16,
),
"generator": 2,
},
# 2048-bit
14: {
"prime": int(
"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
+ "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
+ "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
+ "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
+ "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
+ "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
+ "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
+ "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
+ "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
+ "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
+ "15728E5A8AACAA68FFFFFFFFFFFFFFFF",
base=16,
),
"generator": 2,
},
# 3072-bit
15: {
"prime": int(
"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
+ "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
+ "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
+ "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
+ "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
+ "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
+ "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
+ "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
+ "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
+ "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
+ "15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64"
+ "ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7"
+ "ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B"
+ "F12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
+ "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31"
+ "43DB5BFCE0FD108E4B82D120A93AD2CAFFFFFFFFFFFFFFFF",
base=16,
),
"generator": 2,
},
# 4096-bit
16: {
"prime": int(
"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
+ "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
+ "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
+ "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
+ "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
+ "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
+ "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
+ "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
+ "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
+ "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
+ "15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64"
+ "ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7"
+ "ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B"
+ "F12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
+ "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31"
+ "43DB5BFCE0FD108E4B82D120A92108011A723C12A787E6D7"
+ "88719A10BDBA5B2699C327186AF4E23C1A946834B6150BDA"
+ "2583E9CA2AD44CE8DBBBC2DB04DE8EF92E8EFC141FBECAA6"
+ "287C59474E6BC05D99B2964FA090C3A2233BA186515BE7ED"
+ "1F612970CEE2D7AFB81BDD762170481CD0069127D5B05AA9"
+ "93B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934063199"
+ "FFFFFFFFFFFFFFFF",
base=16,
),
"generator": 2,
},
# 6144-bit
17: {
"prime": int(
"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E08"
+ "8A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B"
+ "302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9"
+ "A637ED6B0BFF5CB6F406B7EDEE386BFB5A899FA5AE9F24117C4B1FE6"
+ "49286651ECE45B3DC2007CB8A163BF0598DA48361C55D39A69163FA8"
+ "FD24CF5F83655D23DCA3AD961C62F356208552BB9ED529077096966D"
+ "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3BE39E772C"
+ "180E86039B2783A2EC07A28FB5C55DF06F4C52C9DE2BCBF695581718"
+ "3995497CEA956AE515D2261898FA051015728E5A8AAAC42DAD33170D"
+ "04507A33A85521ABDF1CBA64ECFB850458DBEF0A8AEA71575D060C7D"
+ "B3970F85A6E1E4C7ABF5AE8CDB0933D71E8C94E04A25619DCEE3D226"
+ "1AD2EE6BF12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
+ "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB3143DB5BFC"
+ "E0FD108E4B82D120A92108011A723C12A787E6D788719A10BDBA5B26"
+ "99C327186AF4E23C1A946834B6150BDA2583E9CA2AD44CE8DBBBC2DB"
+ "04DE8EF92E8EFC141FBECAA6287C59474E6BC05D99B2964FA090C3A2"
+ "233BA186515BE7ED1F612970CEE2D7AFB81BDD762170481CD0069127"
+ "D5B05AA993B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934028492"
+ "36C3FAB4D27C7026C1D4DCB2602646DEC9751E763DBA37BDF8FF9406"
+ "AD9E530EE5DB382F413001AEB06A53ED9027D831179727B0865A8918"
+ "DA3EDBEBCF9B14ED44CE6CBACED4BB1BDB7F1447E6CC254B33205151"
+ "2BD7AF426FB8F401378CD2BF5983CA01C64B92ECF032EA15D1721D03"
+ "F482D7CE6E74FEF6D55E702F46980C82B5A84031900B1C9E59E7C97F"
+ "BEC7E8F323A97A7E36CC88BE0F1D45B7FF585AC54BD407B22B4154AA"
+ "CC8F6D7EBF48E1D814CC5ED20F8037E0A79715EEF29BE32806A1D58B"
+ "B7C5DA76F550AA3D8A1FBFF0EB19CCB1A313D55CDA56C9EC2EF29632"
+ "387FE8D76E3C0468043E8F663F4860EE12BF2D5B0B7474D6E694F91E"
+ "6DCC4024FFFFFFFFFFFFFFFF",
base=16,
),
"generator": 2,
},
# 8192-bit
18: {
"prime": int(
"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
+ "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
+ "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
+ "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
+ "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
+ "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
+ "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
+ "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
+ "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
+ "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
+ "15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64"
+ "ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7"
+ "ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B"
+ "F12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
+ "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31"
+ "43DB5BFCE0FD108E4B82D120A92108011A723C12A787E6D7"
+ "88719A10BDBA5B2699C327186AF4E23C1A946834B6150BDA"
+ "2583E9CA2AD44CE8DBBBC2DB04DE8EF92E8EFC141FBECAA6"
+ "287C59474E6BC05D99B2964FA090C3A2233BA186515BE7ED"
+ "1F612970CEE2D7AFB81BDD762170481CD0069127D5B05AA9"
+ "93B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934028492"
+ "36C3FAB4D27C7026C1D4DCB2602646DEC9751E763DBA37BD"
+ "F8FF9406AD9E530EE5DB382F413001AEB06A53ED9027D831"
+ "179727B0865A8918DA3EDBEBCF9B14ED44CE6CBACED4BB1B"
+ "DB7F1447E6CC254B332051512BD7AF426FB8F401378CD2BF"
+ "5983CA01C64B92ECF032EA15D1721D03F482D7CE6E74FEF6"
+ "D55E702F46980C82B5A84031900B1C9E59E7C97FBEC7E8F3"
+ "23A97A7E36CC88BE0F1D45B7FF585AC54BD407B22B4154AA"
+ "CC8F6D7EBF48E1D814CC5ED20F8037E0A79715EEF29BE328"
+ "06A1D58BB7C5DA76F550AA3D8A1FBFF0EB19CCB1A313D55C"
+ "DA56C9EC2EF29632387FE8D76E3C0468043E8F663F4860EE"
+ "12BF2D5B0B7474D6E694F91E6DBE115974A3926F12FEE5E4"
+ "38777CB6A932DF8CD8BEC4D073B931BA3BC832B68D9DD300"
+ "741FA7BF8AFC47ED2576F6936BA424663AAB639C5AE4F568"
+ "3423B4742BF1C978238F16CBE39D652DE3FDB8BEFC848AD9"
+ "22222E04A4037C0713EB57A81A23F0C73473FC646CEA306B"
+ "4BCBC8862F8385DDFA9D4B7FA2C087E879683303ED5BDD3A"
+ "062B3CF5B3A278A66D2A13F83F44F82DDF310EE074AB6A36"
+ "4597E899A0255DC164F31CC50846851DF9AB48195DED7EA1"
+ "B1D510BD7EE74D73FAF36BC31ECFA268359046F4EB879F92"
+ "4009438B481C6CD7889A002ED5EE382BC9190DA6FC026E47"
+ "9558E4475677E9AA9E3050E2765694DFC81F56E880B96E71"
+ "60C980DD98EDD3DFFFFFFFFFFFFFFFFF",
base=16,
),
"generator": 2,
},
}
class DiffieHellman:
"""
Class to represent the Diffie-Hellman key exchange protocol
>>> alice = DiffieHellman()
>>> bob = DiffieHellman()
>>> alice_private = alice.get_private_key()
>>> alice_public = alice.generate_public_key()
>>> bob_private = bob.get_private_key()
>>> bob_public = bob.generate_public_key()
>>> # generating shared key using the DH object
>>> alice_shared = alice.generate_shared_key(bob_public)
>>> bob_shared = bob.generate_shared_key(alice_public)
>>> assert alice_shared == bob_shared
>>> # generating shared key using static methods
>>> alice_shared = DiffieHellman.generate_shared_key_static(
... alice_private, bob_public
... )
>>> bob_shared = DiffieHellman.generate_shared_key_static(
... bob_private, alice_public
... )
>>> assert alice_shared == bob_shared
"""
# Current minimum recommendation is 2048 bit (group 14)
def __init__(self, group: int = 14) -> None:
if group not in primes:
raise ValueError("Unsupported Group")
self.prime = primes[group]["prime"]
self.generator = primes[group]["generator"]
self.__private_key = int(hexlify(urandom(32)), base=16)
def get_private_key(self) -> str:
return hex(self.__private_key)[2:]
def generate_public_key(self) -> str:
public_key = pow(self.generator, self.__private_key, self.prime)
return hex(public_key)[2:]
def is_valid_public_key(self, key: int) -> bool:
# check if the other public key is valid based on NIST SP800-56
if 2 <= key and key <= self.prime - 2:
if pow(key, (self.prime - 1) // 2, self.prime) == 1:
return True
return False
def generate_shared_key(self, other_key_str: str) -> str:
other_key = int(other_key_str, base=16)
if not self.is_valid_public_key(other_key):
raise ValueError("Invalid public key")
shared_key = pow(other_key, self.__private_key, self.prime)
return sha256(str(shared_key).encode()).hexdigest()
@staticmethod
def is_valid_public_key_static(remote_public_key_str: int, prime: int) -> bool:
# check if the other public key is valid based on NIST SP800-56
if 2 <= remote_public_key_str and remote_public_key_str <= prime - 2:
if pow(remote_public_key_str, (prime - 1) // 2, prime) == 1:
return True
return False
@staticmethod
def generate_shared_key_static(
local_private_key_str: str, remote_public_key_str: str, group: int = 14
) -> str:
local_private_key = int(local_private_key_str, base=16)
remote_public_key = int(remote_public_key_str, base=16)
prime = primes[group]["prime"]
if not DiffieHellman.is_valid_public_key_static(remote_public_key, prime):
raise ValueError("Invalid public key")
shared_key = pow(remote_public_key, local_private_key, prime)
return sha256(str(shared_key).encode()).hexdigest()
if __name__ == "__main__":
import doctest
doctest.testmod()
| from binascii import hexlify
from hashlib import sha256
from os import urandom
# RFC 3526 - More Modular Exponential (MODP) Diffie-Hellman groups for
# Internet Key Exchange (IKE) https://tools.ietf.org/html/rfc3526
primes = {
# 1536-bit
5: {
"prime": int(
"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
+ "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
+ "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
+ "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
+ "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
+ "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
+ "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
+ "670C354E4ABC9804F1746C08CA237327FFFFFFFFFFFFFFFF",
base=16,
),
"generator": 2,
},
# 2048-bit
14: {
"prime": int(
"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
+ "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
+ "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
+ "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
+ "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
+ "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
+ "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
+ "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
+ "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
+ "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
+ "15728E5A8AACAA68FFFFFFFFFFFFFFFF",
base=16,
),
"generator": 2,
},
# 3072-bit
15: {
"prime": int(
"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
+ "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
+ "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
+ "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
+ "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
+ "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
+ "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
+ "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
+ "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
+ "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
+ "15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64"
+ "ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7"
+ "ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B"
+ "F12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
+ "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31"
+ "43DB5BFCE0FD108E4B82D120A93AD2CAFFFFFFFFFFFFFFFF",
base=16,
),
"generator": 2,
},
# 4096-bit
16: {
"prime": int(
"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
+ "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
+ "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
+ "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
+ "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
+ "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
+ "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
+ "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
+ "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
+ "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
+ "15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64"
+ "ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7"
+ "ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B"
+ "F12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
+ "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31"
+ "43DB5BFCE0FD108E4B82D120A92108011A723C12A787E6D7"
+ "88719A10BDBA5B2699C327186AF4E23C1A946834B6150BDA"
+ "2583E9CA2AD44CE8DBBBC2DB04DE8EF92E8EFC141FBECAA6"
+ "287C59474E6BC05D99B2964FA090C3A2233BA186515BE7ED"
+ "1F612970CEE2D7AFB81BDD762170481CD0069127D5B05AA9"
+ "93B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934063199"
+ "FFFFFFFFFFFFFFFF",
base=16,
),
"generator": 2,
},
# 6144-bit
17: {
"prime": int(
"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E08"
+ "8A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B"
+ "302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9"
+ "A637ED6B0BFF5CB6F406B7EDEE386BFB5A899FA5AE9F24117C4B1FE6"
+ "49286651ECE45B3DC2007CB8A163BF0598DA48361C55D39A69163FA8"
+ "FD24CF5F83655D23DCA3AD961C62F356208552BB9ED529077096966D"
+ "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3BE39E772C"
+ "180E86039B2783A2EC07A28FB5C55DF06F4C52C9DE2BCBF695581718"
+ "3995497CEA956AE515D2261898FA051015728E5A8AAAC42DAD33170D"
+ "04507A33A85521ABDF1CBA64ECFB850458DBEF0A8AEA71575D060C7D"
+ "B3970F85A6E1E4C7ABF5AE8CDB0933D71E8C94E04A25619DCEE3D226"
+ "1AD2EE6BF12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
+ "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB3143DB5BFC"
+ "E0FD108E4B82D120A92108011A723C12A787E6D788719A10BDBA5B26"
+ "99C327186AF4E23C1A946834B6150BDA2583E9CA2AD44CE8DBBBC2DB"
+ "04DE8EF92E8EFC141FBECAA6287C59474E6BC05D99B2964FA090C3A2"
+ "233BA186515BE7ED1F612970CEE2D7AFB81BDD762170481CD0069127"
+ "D5B05AA993B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934028492"
+ "36C3FAB4D27C7026C1D4DCB2602646DEC9751E763DBA37BDF8FF9406"
+ "AD9E530EE5DB382F413001AEB06A53ED9027D831179727B0865A8918"
+ "DA3EDBEBCF9B14ED44CE6CBACED4BB1BDB7F1447E6CC254B33205151"
+ "2BD7AF426FB8F401378CD2BF5983CA01C64B92ECF032EA15D1721D03"
+ "F482D7CE6E74FEF6D55E702F46980C82B5A84031900B1C9E59E7C97F"
+ "BEC7E8F323A97A7E36CC88BE0F1D45B7FF585AC54BD407B22B4154AA"
+ "CC8F6D7EBF48E1D814CC5ED20F8037E0A79715EEF29BE32806A1D58B"
+ "B7C5DA76F550AA3D8A1FBFF0EB19CCB1A313D55CDA56C9EC2EF29632"
+ "387FE8D76E3C0468043E8F663F4860EE12BF2D5B0B7474D6E694F91E"
+ "6DCC4024FFFFFFFFFFFFFFFF",
base=16,
),
"generator": 2,
},
# 8192-bit
18: {
"prime": int(
"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
+ "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
+ "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
+ "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
+ "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
+ "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
+ "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
+ "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
+ "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
+ "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
+ "15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64"
+ "ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7"
+ "ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B"
+ "F12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
+ "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31"
+ "43DB5BFCE0FD108E4B82D120A92108011A723C12A787E6D7"
+ "88719A10BDBA5B2699C327186AF4E23C1A946834B6150BDA"
+ "2583E9CA2AD44CE8DBBBC2DB04DE8EF92E8EFC141FBECAA6"
+ "287C59474E6BC05D99B2964FA090C3A2233BA186515BE7ED"
+ "1F612970CEE2D7AFB81BDD762170481CD0069127D5B05AA9"
+ "93B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934028492"
+ "36C3FAB4D27C7026C1D4DCB2602646DEC9751E763DBA37BD"
+ "F8FF9406AD9E530EE5DB382F413001AEB06A53ED9027D831"
+ "179727B0865A8918DA3EDBEBCF9B14ED44CE6CBACED4BB1B"
+ "DB7F1447E6CC254B332051512BD7AF426FB8F401378CD2BF"
+ "5983CA01C64B92ECF032EA15D1721D03F482D7CE6E74FEF6"
+ "D55E702F46980C82B5A84031900B1C9E59E7C97FBEC7E8F3"
+ "23A97A7E36CC88BE0F1D45B7FF585AC54BD407B22B4154AA"
+ "CC8F6D7EBF48E1D814CC5ED20F8037E0A79715EEF29BE328"
+ "06A1D58BB7C5DA76F550AA3D8A1FBFF0EB19CCB1A313D55C"
+ "DA56C9EC2EF29632387FE8D76E3C0468043E8F663F4860EE"
+ "12BF2D5B0B7474D6E694F91E6DBE115974A3926F12FEE5E4"
+ "38777CB6A932DF8CD8BEC4D073B931BA3BC832B68D9DD300"
+ "741FA7BF8AFC47ED2576F6936BA424663AAB639C5AE4F568"
+ "3423B4742BF1C978238F16CBE39D652DE3FDB8BEFC848AD9"
+ "22222E04A4037C0713EB57A81A23F0C73473FC646CEA306B"
+ "4BCBC8862F8385DDFA9D4B7FA2C087E879683303ED5BDD3A"
+ "062B3CF5B3A278A66D2A13F83F44F82DDF310EE074AB6A36"
+ "4597E899A0255DC164F31CC50846851DF9AB48195DED7EA1"
+ "B1D510BD7EE74D73FAF36BC31ECFA268359046F4EB879F92"
+ "4009438B481C6CD7889A002ED5EE382BC9190DA6FC026E47"
+ "9558E4475677E9AA9E3050E2765694DFC81F56E880B96E71"
+ "60C980DD98EDD3DFFFFFFFFFFFFFFFFF",
base=16,
),
"generator": 2,
},
}
class DiffieHellman:
"""
Class to represent the Diffie-Hellman key exchange protocol
>>> alice = DiffieHellman()
>>> bob = DiffieHellman()
>>> alice_private = alice.get_private_key()
>>> alice_public = alice.generate_public_key()
>>> bob_private = bob.get_private_key()
>>> bob_public = bob.generate_public_key()
>>> # generating shared key using the DH object
>>> alice_shared = alice.generate_shared_key(bob_public)
>>> bob_shared = bob.generate_shared_key(alice_public)
>>> assert alice_shared == bob_shared
>>> # generating shared key using static methods
>>> alice_shared = DiffieHellman.generate_shared_key_static(
... alice_private, bob_public
... )
>>> bob_shared = DiffieHellman.generate_shared_key_static(
... bob_private, alice_public
... )
>>> assert alice_shared == bob_shared
"""
# Current minimum recommendation is 2048 bit (group 14)
def __init__(self, group: int = 14) -> None:
if group not in primes:
raise ValueError("Unsupported Group")
self.prime = primes[group]["prime"]
self.generator = primes[group]["generator"]
self.__private_key = int(hexlify(urandom(32)), base=16)
def get_private_key(self) -> str:
return hex(self.__private_key)[2:]
def generate_public_key(self) -> str:
public_key = pow(self.generator, self.__private_key, self.prime)
return hex(public_key)[2:]
def is_valid_public_key(self, key: int) -> bool:
# check if the other public key is valid based on NIST SP800-56
if 2 <= key and key <= self.prime - 2:
if pow(key, (self.prime - 1) // 2, self.prime) == 1:
return True
return False
def generate_shared_key(self, other_key_str: str) -> str:
other_key = int(other_key_str, base=16)
if not self.is_valid_public_key(other_key):
raise ValueError("Invalid public key")
shared_key = pow(other_key, self.__private_key, self.prime)
return sha256(str(shared_key).encode()).hexdigest()
@staticmethod
def is_valid_public_key_static(remote_public_key_str: int, prime: int) -> bool:
# check if the other public key is valid based on NIST SP800-56
if 2 <= remote_public_key_str and remote_public_key_str <= prime - 2:
if pow(remote_public_key_str, (prime - 1) // 2, prime) == 1:
return True
return False
@staticmethod
def generate_shared_key_static(
local_private_key_str: str, remote_public_key_str: str, group: int = 14
) -> str:
local_private_key = int(local_private_key_str, base=16)
remote_public_key = int(remote_public_key_str, base=16)
prime = primes[group]["prime"]
if not DiffieHellman.is_valid_public_key_static(remote_public_key, prime):
raise ValueError("Invalid public key")
shared_key = pow(remote_public_key, local_private_key, prime)
return sha256(str(shared_key).encode()).hexdigest()
if __name__ == "__main__":
import doctest
doctest.testmod()
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| import argparse
import datetime
def zeller(date_input: str) -> str:
"""
Zellers Congruence Algorithm
Find the day of the week for nearly any Gregorian or Julian calendar date
>>> zeller('01-31-2010')
'Your date 01-31-2010, is a Sunday!'
Validate out of range month
>>> zeller('13-31-2010')
Traceback (most recent call last):
...
ValueError: Month must be between 1 - 12
>>> zeller('.2-31-2010')
Traceback (most recent call last):
...
ValueError: invalid literal for int() with base 10: '.2'
Validate out of range date:
>>> zeller('01-33-2010')
Traceback (most recent call last):
...
ValueError: Date must be between 1 - 31
>>> zeller('01-.4-2010')
Traceback (most recent call last):
...
ValueError: invalid literal for int() with base 10: '.4'
Validate second separator:
>>> zeller('01-31*2010')
Traceback (most recent call last):
...
ValueError: Date separator must be '-' or '/'
Validate first separator:
>>> zeller('01^31-2010')
Traceback (most recent call last):
...
ValueError: Date separator must be '-' or '/'
Validate out of range year:
>>> zeller('01-31-8999')
Traceback (most recent call last):
...
ValueError: Year out of range. There has to be some sort of limit...right?
Test null input:
>>> zeller()
Traceback (most recent call last):
...
TypeError: zeller() missing 1 required positional argument: 'date_input'
Test length of date_input:
>>> zeller('')
Traceback (most recent call last):
...
ValueError: Must be 10 characters long
>>> zeller('01-31-19082939')
Traceback (most recent call last):
...
ValueError: Must be 10 characters long"""
# Days of the week for response
days = {
"0": "Sunday",
"1": "Monday",
"2": "Tuesday",
"3": "Wednesday",
"4": "Thursday",
"5": "Friday",
"6": "Saturday",
}
convert_datetime_days = {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 0}
# Validate
if not 0 < len(date_input) < 11:
raise ValueError("Must be 10 characters long")
# Get month
m: int = int(date_input[0] + date_input[1])
# Validate
if not 0 < m < 13:
raise ValueError("Month must be between 1 - 12")
sep_1: str = date_input[2]
# Validate
if sep_1 not in ["-", "/"]:
raise ValueError("Date separator must be '-' or '/'")
# Get day
d: int = int(date_input[3] + date_input[4])
# Validate
if not 0 < d < 32:
raise ValueError("Date must be between 1 - 31")
# Get second separator
sep_2: str = date_input[5]
# Validate
if sep_2 not in ["-", "/"]:
raise ValueError("Date separator must be '-' or '/'")
# Get year
y: int = int(date_input[6] + date_input[7] + date_input[8] + date_input[9])
# Arbitrary year range
if not 45 < y < 8500:
raise ValueError(
"Year out of range. There has to be some sort of limit...right?"
)
# Get datetime obj for validation
dt_ck = datetime.date(int(y), int(m), int(d))
# Start math
if m <= 2:
y = y - 1
m = m + 12
# maths var
c: int = int(str(y)[:2])
k: int = int(str(y)[2:])
t: int = int(2.6 * m - 5.39)
u: int = int(c / 4)
v: int = int(k / 4)
x: int = int(d + k)
z: int = int(t + u + v + x)
w: int = int(z - (2 * c))
f: int = round(w % 7)
# End math
# Validate math
if f != convert_datetime_days[dt_ck.weekday()]:
raise AssertionError("The date was evaluated incorrectly. Contact developer.")
# Response
response: str = f"Your date {date_input}, is a {days[str(f)]}!"
return response
if __name__ == "__main__":
import doctest
doctest.testmod()
parser = argparse.ArgumentParser(
description=(
"Find out what day of the week nearly any date is or was. Enter "
"date as a string in the mm-dd-yyyy or mm/dd/yyyy format"
)
)
parser.add_argument(
"date_input", type=str, help="Date as a string (mm-dd-yyyy or mm/dd/yyyy)"
)
args = parser.parse_args()
zeller(args.date_input)
| import argparse
import datetime
def zeller(date_input: str) -> str:
"""
Zellers Congruence Algorithm
Find the day of the week for nearly any Gregorian or Julian calendar date
>>> zeller('01-31-2010')
'Your date 01-31-2010, is a Sunday!'
Validate out of range month
>>> zeller('13-31-2010')
Traceback (most recent call last):
...
ValueError: Month must be between 1 - 12
>>> zeller('.2-31-2010')
Traceback (most recent call last):
...
ValueError: invalid literal for int() with base 10: '.2'
Validate out of range date:
>>> zeller('01-33-2010')
Traceback (most recent call last):
...
ValueError: Date must be between 1 - 31
>>> zeller('01-.4-2010')
Traceback (most recent call last):
...
ValueError: invalid literal for int() with base 10: '.4'
Validate second separator:
>>> zeller('01-31*2010')
Traceback (most recent call last):
...
ValueError: Date separator must be '-' or '/'
Validate first separator:
>>> zeller('01^31-2010')
Traceback (most recent call last):
...
ValueError: Date separator must be '-' or '/'
Validate out of range year:
>>> zeller('01-31-8999')
Traceback (most recent call last):
...
ValueError: Year out of range. There has to be some sort of limit...right?
Test null input:
>>> zeller()
Traceback (most recent call last):
...
TypeError: zeller() missing 1 required positional argument: 'date_input'
Test length of date_input:
>>> zeller('')
Traceback (most recent call last):
...
ValueError: Must be 10 characters long
>>> zeller('01-31-19082939')
Traceback (most recent call last):
...
ValueError: Must be 10 characters long"""
# Days of the week for response
days = {
"0": "Sunday",
"1": "Monday",
"2": "Tuesday",
"3": "Wednesday",
"4": "Thursday",
"5": "Friday",
"6": "Saturday",
}
convert_datetime_days = {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 0}
# Validate
if not 0 < len(date_input) < 11:
raise ValueError("Must be 10 characters long")
# Get month
m: int = int(date_input[0] + date_input[1])
# Validate
if not 0 < m < 13:
raise ValueError("Month must be between 1 - 12")
sep_1: str = date_input[2]
# Validate
if sep_1 not in ["-", "/"]:
raise ValueError("Date separator must be '-' or '/'")
# Get day
d: int = int(date_input[3] + date_input[4])
# Validate
if not 0 < d < 32:
raise ValueError("Date must be between 1 - 31")
# Get second separator
sep_2: str = date_input[5]
# Validate
if sep_2 not in ["-", "/"]:
raise ValueError("Date separator must be '-' or '/'")
# Get year
y: int = int(date_input[6] + date_input[7] + date_input[8] + date_input[9])
# Arbitrary year range
if not 45 < y < 8500:
raise ValueError(
"Year out of range. There has to be some sort of limit...right?"
)
# Get datetime obj for validation
dt_ck = datetime.date(int(y), int(m), int(d))
# Start math
if m <= 2:
y = y - 1
m = m + 12
# maths var
c: int = int(str(y)[:2])
k: int = int(str(y)[2:])
t: int = int(2.6 * m - 5.39)
u: int = int(c / 4)
v: int = int(k / 4)
x: int = int(d + k)
z: int = int(t + u + v + x)
w: int = int(z - (2 * c))
f: int = round(w % 7)
# End math
# Validate math
if f != convert_datetime_days[dt_ck.weekday()]:
raise AssertionError("The date was evaluated incorrectly. Contact developer.")
# Response
response: str = f"Your date {date_input}, is a {days[str(f)]}!"
return response
if __name__ == "__main__":
import doctest
doctest.testmod()
parser = argparse.ArgumentParser(
description=(
"Find out what day of the week nearly any date is or was. Enter "
"date as a string in the mm-dd-yyyy or mm/dd/yyyy format"
)
)
parser.add_argument(
"date_input", type=str, help="Date as a string (mm-dd-yyyy or mm/dd/yyyy)"
)
args = parser.parse_args()
zeller(args.date_input)
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Print all the Catalan numbers from 0 to n, n being the user input.
* The Catalan numbers are a sequence of positive integers that
* appear in many counting problems in combinatorics [1]. Such
* problems include counting [2]:
* - The number of Dyck words of length 2n
* - The number well-formed expressions with n pairs of parentheses
* (e.g., `()()` is valid but `())(` is not)
* - The number of different ways n + 1 factors can be completely
* parenthesized (e.g., for n = 2, C(n) = 2 and (ab)c and a(bc)
* are the two valid ways to parenthesize.
* - The number of full binary trees with n + 1 leaves
* A Catalan number satisfies the following recurrence relation
* which we will use in this algorithm [1].
* C(0) = C(1) = 1
* C(n) = sum(C(i).C(n-i-1)), from i = 0 to n-1
* In addition, the n-th Catalan number can be calculated using
* the closed form formula below [1]:
* C(n) = (1 / (n + 1)) * (2n choose n)
* Sources:
* [1] https://brilliant.org/wiki/catalan-numbers/
* [2] https://en.wikipedia.org/wiki/Catalan_number
"""
def catalan_numbers(upper_limit: int) -> "list[int]":
"""
Return a list of the Catalan number sequence from 0 through `upper_limit`.
>>> catalan_numbers(5)
[1, 1, 2, 5, 14, 42]
>>> catalan_numbers(2)
[1, 1, 2]
>>> catalan_numbers(-1)
Traceback (most recent call last):
ValueError: Limit for the Catalan sequence must be ≥ 0
"""
if upper_limit < 0:
raise ValueError("Limit for the Catalan sequence must be ≥ 0")
catalan_list = [0] * (upper_limit + 1)
# Base case: C(0) = C(1) = 1
catalan_list[0] = 1
if upper_limit > 0:
catalan_list[1] = 1
# Recurrence relation: C(i) = sum(C(j).C(i-j-1)), from j = 0 to i
for i in range(2, upper_limit + 1):
for j in range(i):
catalan_list[i] += catalan_list[j] * catalan_list[i - j - 1]
return catalan_list
if __name__ == "__main__":
print("\n********* Catalan Numbers Using Dynamic Programming ************\n")
print("\n*** Enter -1 at any time to quit ***")
print("\nEnter the upper limit (≥ 0) for the Catalan number sequence: ", end="")
try:
while True:
N = int(input().strip())
if N < 0:
print("\n********* Goodbye!! ************")
break
else:
print(f"The Catalan numbers from 0 through {N} are:")
print(catalan_numbers(N))
print("Try another upper limit for the sequence: ", end="")
except (NameError, ValueError):
print("\n********* Invalid input, goodbye! ************\n")
import doctest
doctest.testmod()
| """
Print all the Catalan numbers from 0 to n, n being the user input.
* The Catalan numbers are a sequence of positive integers that
* appear in many counting problems in combinatorics [1]. Such
* problems include counting [2]:
* - The number of Dyck words of length 2n
* - The number well-formed expressions with n pairs of parentheses
* (e.g., `()()` is valid but `())(` is not)
* - The number of different ways n + 1 factors can be completely
* parenthesized (e.g., for n = 2, C(n) = 2 and (ab)c and a(bc)
* are the two valid ways to parenthesize.
* - The number of full binary trees with n + 1 leaves
* A Catalan number satisfies the following recurrence relation
* which we will use in this algorithm [1].
* C(0) = C(1) = 1
* C(n) = sum(C(i).C(n-i-1)), from i = 0 to n-1
* In addition, the n-th Catalan number can be calculated using
* the closed form formula below [1]:
* C(n) = (1 / (n + 1)) * (2n choose n)
* Sources:
* [1] https://brilliant.org/wiki/catalan-numbers/
* [2] https://en.wikipedia.org/wiki/Catalan_number
"""
def catalan_numbers(upper_limit: int) -> "list[int]":
"""
Return a list of the Catalan number sequence from 0 through `upper_limit`.
>>> catalan_numbers(5)
[1, 1, 2, 5, 14, 42]
>>> catalan_numbers(2)
[1, 1, 2]
>>> catalan_numbers(-1)
Traceback (most recent call last):
ValueError: Limit for the Catalan sequence must be ≥ 0
"""
if upper_limit < 0:
raise ValueError("Limit for the Catalan sequence must be ≥ 0")
catalan_list = [0] * (upper_limit + 1)
# Base case: C(0) = C(1) = 1
catalan_list[0] = 1
if upper_limit > 0:
catalan_list[1] = 1
# Recurrence relation: C(i) = sum(C(j).C(i-j-1)), from j = 0 to i
for i in range(2, upper_limit + 1):
for j in range(i):
catalan_list[i] += catalan_list[j] * catalan_list[i - j - 1]
return catalan_list
if __name__ == "__main__":
print("\n********* Catalan Numbers Using Dynamic Programming ************\n")
print("\n*** Enter -1 at any time to quit ***")
print("\nEnter the upper limit (≥ 0) for the Catalan number sequence: ", end="")
try:
while True:
N = int(input().strip())
if N < 0:
print("\n********* Goodbye!! ************")
break
else:
print(f"The Catalan numbers from 0 through {N} are:")
print(catalan_numbers(N))
print("Try another upper limit for the sequence: ", end="")
except (NameError, ValueError):
print("\n********* Invalid input, goodbye! ************\n")
import doctest
doctest.testmod()
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
The RGB color model is an additive color model in which red, green, and blue light
are added together in various ways to reproduce a broad array of colors. The name
of the model comes from the initials of the three additive primary colors, red,
green, and blue. Meanwhile, the HSV representation models how colors appear under
light. In it, colors are represented using three components: hue, saturation and
(brightness-)value. This file provides functions for converting colors from one
representation to the other.
(description adapted from https://en.wikipedia.org/wiki/RGB_color_model and
https://en.wikipedia.org/wiki/HSL_and_HSV).
"""
def hsv_to_rgb(hue: float, saturation: float, value: float) -> list[int]:
"""
Conversion from the HSV-representation to the RGB-representation.
Expected RGB-values taken from
https://www.rapidtables.com/convert/color/hsv-to-rgb.html
>>> hsv_to_rgb(0, 0, 0)
[0, 0, 0]
>>> hsv_to_rgb(0, 0, 1)
[255, 255, 255]
>>> hsv_to_rgb(0, 1, 1)
[255, 0, 0]
>>> hsv_to_rgb(60, 1, 1)
[255, 255, 0]
>>> hsv_to_rgb(120, 1, 1)
[0, 255, 0]
>>> hsv_to_rgb(240, 1, 1)
[0, 0, 255]
>>> hsv_to_rgb(300, 1, 1)
[255, 0, 255]
>>> hsv_to_rgb(180, 0.5, 0.5)
[64, 128, 128]
>>> hsv_to_rgb(234, 0.14, 0.88)
[193, 196, 224]
>>> hsv_to_rgb(330, 0.75, 0.5)
[128, 32, 80]
"""
if hue < 0 or hue > 360:
raise Exception("hue should be between 0 and 360")
if saturation < 0 or saturation > 1:
raise Exception("saturation should be between 0 and 1")
if value < 0 or value > 1:
raise Exception("value should be between 0 and 1")
chroma = value * saturation
hue_section = hue / 60
second_largest_component = chroma * (1 - abs(hue_section % 2 - 1))
match_value = value - chroma
if hue_section >= 0 and hue_section <= 1:
red = round(255 * (chroma + match_value))
green = round(255 * (second_largest_component + match_value))
blue = round(255 * (match_value))
elif hue_section > 1 and hue_section <= 2:
red = round(255 * (second_largest_component + match_value))
green = round(255 * (chroma + match_value))
blue = round(255 * (match_value))
elif hue_section > 2 and hue_section <= 3:
red = round(255 * (match_value))
green = round(255 * (chroma + match_value))
blue = round(255 * (second_largest_component + match_value))
elif hue_section > 3 and hue_section <= 4:
red = round(255 * (match_value))
green = round(255 * (second_largest_component + match_value))
blue = round(255 * (chroma + match_value))
elif hue_section > 4 and hue_section <= 5:
red = round(255 * (second_largest_component + match_value))
green = round(255 * (match_value))
blue = round(255 * (chroma + match_value))
else:
red = round(255 * (chroma + match_value))
green = round(255 * (match_value))
blue = round(255 * (second_largest_component + match_value))
return [red, green, blue]
def rgb_to_hsv(red: int, green: int, blue: int) -> list[float]:
"""
Conversion from the RGB-representation to the HSV-representation.
The tested values are the reverse values from the hsv_to_rgb-doctests.
Function "approximately_equal_hsv" is needed because of small deviations due to
rounding for the RGB-values.
>>> approximately_equal_hsv(rgb_to_hsv(0, 0, 0), [0, 0, 0])
True
>>> approximately_equal_hsv(rgb_to_hsv(255, 255, 255), [0, 0, 1])
True
>>> approximately_equal_hsv(rgb_to_hsv(255, 0, 0), [0, 1, 1])
True
>>> approximately_equal_hsv(rgb_to_hsv(255, 255, 0), [60, 1, 1])
True
>>> approximately_equal_hsv(rgb_to_hsv(0, 255, 0), [120, 1, 1])
True
>>> approximately_equal_hsv(rgb_to_hsv(0, 0, 255), [240, 1, 1])
True
>>> approximately_equal_hsv(rgb_to_hsv(255, 0, 255), [300, 1, 1])
True
>>> approximately_equal_hsv(rgb_to_hsv(64, 128, 128), [180, 0.5, 0.5])
True
>>> approximately_equal_hsv(rgb_to_hsv(193, 196, 224), [234, 0.14, 0.88])
True
>>> approximately_equal_hsv(rgb_to_hsv(128, 32, 80), [330, 0.75, 0.5])
True
"""
if red < 0 or red > 255:
raise Exception("red should be between 0 and 255")
if green < 0 or green > 255:
raise Exception("green should be between 0 and 255")
if blue < 0 or blue > 255:
raise Exception("blue should be between 0 and 255")
float_red = red / 255
float_green = green / 255
float_blue = blue / 255
value = max(max(float_red, float_green), float_blue)
chroma = value - min(min(float_red, float_green), float_blue)
saturation = 0 if value == 0 else chroma / value
if chroma == 0:
hue = 0.0
elif value == float_red:
hue = 60 * (0 + (float_green - float_blue) / chroma)
elif value == float_green:
hue = 60 * (2 + (float_blue - float_red) / chroma)
else:
hue = 60 * (4 + (float_red - float_green) / chroma)
hue = (hue + 360) % 360
return [hue, saturation, value]
def approximately_equal_hsv(hsv_1: list[float], hsv_2: list[float]) -> bool:
"""
Utility-function to check that two hsv-colors are approximately equal
>>> approximately_equal_hsv([0, 0, 0], [0, 0, 0])
True
>>> approximately_equal_hsv([180, 0.5, 0.3], [179.9999, 0.500001, 0.30001])
True
>>> approximately_equal_hsv([0, 0, 0], [1, 0, 0])
False
>>> approximately_equal_hsv([180, 0.5, 0.3], [179.9999, 0.6, 0.30001])
False
"""
check_hue = abs(hsv_1[0] - hsv_2[0]) < 0.2
check_saturation = abs(hsv_1[1] - hsv_2[1]) < 0.002
check_value = abs(hsv_1[2] - hsv_2[2]) < 0.002
return check_hue and check_saturation and check_value
| """
The RGB color model is an additive color model in which red, green, and blue light
are added together in various ways to reproduce a broad array of colors. The name
of the model comes from the initials of the three additive primary colors, red,
green, and blue. Meanwhile, the HSV representation models how colors appear under
light. In it, colors are represented using three components: hue, saturation and
(brightness-)value. This file provides functions for converting colors from one
representation to the other.
(description adapted from https://en.wikipedia.org/wiki/RGB_color_model and
https://en.wikipedia.org/wiki/HSL_and_HSV).
"""
def hsv_to_rgb(hue: float, saturation: float, value: float) -> list[int]:
"""
Conversion from the HSV-representation to the RGB-representation.
Expected RGB-values taken from
https://www.rapidtables.com/convert/color/hsv-to-rgb.html
>>> hsv_to_rgb(0, 0, 0)
[0, 0, 0]
>>> hsv_to_rgb(0, 0, 1)
[255, 255, 255]
>>> hsv_to_rgb(0, 1, 1)
[255, 0, 0]
>>> hsv_to_rgb(60, 1, 1)
[255, 255, 0]
>>> hsv_to_rgb(120, 1, 1)
[0, 255, 0]
>>> hsv_to_rgb(240, 1, 1)
[0, 0, 255]
>>> hsv_to_rgb(300, 1, 1)
[255, 0, 255]
>>> hsv_to_rgb(180, 0.5, 0.5)
[64, 128, 128]
>>> hsv_to_rgb(234, 0.14, 0.88)
[193, 196, 224]
>>> hsv_to_rgb(330, 0.75, 0.5)
[128, 32, 80]
"""
if hue < 0 or hue > 360:
raise Exception("hue should be between 0 and 360")
if saturation < 0 or saturation > 1:
raise Exception("saturation should be between 0 and 1")
if value < 0 or value > 1:
raise Exception("value should be between 0 and 1")
chroma = value * saturation
hue_section = hue / 60
second_largest_component = chroma * (1 - abs(hue_section % 2 - 1))
match_value = value - chroma
if hue_section >= 0 and hue_section <= 1:
red = round(255 * (chroma + match_value))
green = round(255 * (second_largest_component + match_value))
blue = round(255 * (match_value))
elif hue_section > 1 and hue_section <= 2:
red = round(255 * (second_largest_component + match_value))
green = round(255 * (chroma + match_value))
blue = round(255 * (match_value))
elif hue_section > 2 and hue_section <= 3:
red = round(255 * (match_value))
green = round(255 * (chroma + match_value))
blue = round(255 * (second_largest_component + match_value))
elif hue_section > 3 and hue_section <= 4:
red = round(255 * (match_value))
green = round(255 * (second_largest_component + match_value))
blue = round(255 * (chroma + match_value))
elif hue_section > 4 and hue_section <= 5:
red = round(255 * (second_largest_component + match_value))
green = round(255 * (match_value))
blue = round(255 * (chroma + match_value))
else:
red = round(255 * (chroma + match_value))
green = round(255 * (match_value))
blue = round(255 * (second_largest_component + match_value))
return [red, green, blue]
def rgb_to_hsv(red: int, green: int, blue: int) -> list[float]:
"""
Conversion from the RGB-representation to the HSV-representation.
The tested values are the reverse values from the hsv_to_rgb-doctests.
Function "approximately_equal_hsv" is needed because of small deviations due to
rounding for the RGB-values.
>>> approximately_equal_hsv(rgb_to_hsv(0, 0, 0), [0, 0, 0])
True
>>> approximately_equal_hsv(rgb_to_hsv(255, 255, 255), [0, 0, 1])
True
>>> approximately_equal_hsv(rgb_to_hsv(255, 0, 0), [0, 1, 1])
True
>>> approximately_equal_hsv(rgb_to_hsv(255, 255, 0), [60, 1, 1])
True
>>> approximately_equal_hsv(rgb_to_hsv(0, 255, 0), [120, 1, 1])
True
>>> approximately_equal_hsv(rgb_to_hsv(0, 0, 255), [240, 1, 1])
True
>>> approximately_equal_hsv(rgb_to_hsv(255, 0, 255), [300, 1, 1])
True
>>> approximately_equal_hsv(rgb_to_hsv(64, 128, 128), [180, 0.5, 0.5])
True
>>> approximately_equal_hsv(rgb_to_hsv(193, 196, 224), [234, 0.14, 0.88])
True
>>> approximately_equal_hsv(rgb_to_hsv(128, 32, 80), [330, 0.75, 0.5])
True
"""
if red < 0 or red > 255:
raise Exception("red should be between 0 and 255")
if green < 0 or green > 255:
raise Exception("green should be between 0 and 255")
if blue < 0 or blue > 255:
raise Exception("blue should be between 0 and 255")
float_red = red / 255
float_green = green / 255
float_blue = blue / 255
value = max(max(float_red, float_green), float_blue)
chroma = value - min(min(float_red, float_green), float_blue)
saturation = 0 if value == 0 else chroma / value
if chroma == 0:
hue = 0.0
elif value == float_red:
hue = 60 * (0 + (float_green - float_blue) / chroma)
elif value == float_green:
hue = 60 * (2 + (float_blue - float_red) / chroma)
else:
hue = 60 * (4 + (float_red - float_green) / chroma)
hue = (hue + 360) % 360
return [hue, saturation, value]
def approximately_equal_hsv(hsv_1: list[float], hsv_2: list[float]) -> bool:
"""
Utility-function to check that two hsv-colors are approximately equal
>>> approximately_equal_hsv([0, 0, 0], [0, 0, 0])
True
>>> approximately_equal_hsv([180, 0.5, 0.3], [179.9999, 0.500001, 0.30001])
True
>>> approximately_equal_hsv([0, 0, 0], [1, 0, 0])
False
>>> approximately_equal_hsv([180, 0.5, 0.3], [179.9999, 0.6, 0.30001])
False
"""
check_hue = abs(hsv_1[0] - hsv_2[0]) < 0.2
check_saturation = abs(hsv_1[1] - hsv_2[1]) < 0.002
check_value = abs(hsv_1[2] - hsv_2[2]) < 0.002
return check_hue and check_saturation and check_value
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| def search(list_data: list, key: int, left: int = 0, right: int = 0) -> int:
"""
Iterate through the array to find the index of key using recursion.
:param list_data: the list to be searched
:param key: the key to be searched
:param left: the index of first element
:param right: the index of last element
:return: the index of key value if found, -1 otherwise.
>>> search(list(range(0, 11)), 5)
5
>>> search([1, 2, 4, 5, 3], 4)
2
>>> search([1, 2, 4, 5, 3], 6)
-1
>>> search([5], 5)
0
>>> search([], 1)
-1
"""
right = right or len(list_data) - 1
if left > right:
return -1
elif list_data[left] == key:
return left
elif list_data[right] == key:
return right
else:
return search(list_data, key, left + 1, right - 1)
if __name__ == "__main__":
import doctest
doctest.testmod()
| def search(list_data: list, key: int, left: int = 0, right: int = 0) -> int:
"""
Iterate through the array to find the index of key using recursion.
:param list_data: the list to be searched
:param key: the key to be searched
:param left: the index of first element
:param right: the index of last element
:return: the index of key value if found, -1 otherwise.
>>> search(list(range(0, 11)), 5)
5
>>> search([1, 2, 4, 5, 3], 4)
2
>>> search([1, 2, 4, 5, 3], 6)
-1
>>> search([5], 5)
0
>>> search([], 1)
-1
"""
right = right or len(list_data) - 1
if left > right:
return -1
elif list_data[left] == key:
return left
elif list_data[right] == key:
return right
else:
return search(list_data, key, left + 1, right - 1)
if __name__ == "__main__":
import doctest
doctest.testmod()
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
In the game of darts a player throws three darts at a target board which is
split into twenty equal sized sections numbered one to twenty.

The score of a dart is determined by the number of the region that the dart
lands in. A dart landing outside the red/green outer ring scores zero. The black
and cream regions inside this ring represent single scores. However, the red/green
outer ring and middle ring score double and treble scores respectively.
At the centre of the board are two concentric circles called the bull region, or
bulls-eye. The outer bull is worth 25 points and the inner bull is a double,
worth 50 points.
There are many variations of rules but in the most popular game the players will
begin with a score 301 or 501 and the first player to reduce their running total
to zero is a winner. However, it is normal to play a "doubles out" system, which
means that the player must land a double (including the double bulls-eye at the
centre of the board) on their final dart to win; any other dart that would reduce
their running total to one or lower means the score for that set of three darts
is "bust".
When a player is able to finish on their current score it is called a "checkout"
and the highest checkout is 170: T20 T20 D25 (two treble 20s and double bull).
There are exactly eleven distinct ways to checkout on a score of 6:
D3
D1 D2
S2 D2
D2 D1
S4 D1
S1 S1 D2
S1 T1 D1
S1 S3 D1
D1 D1 D1
D1 S2 D1
S2 S2 D1
Note that D1 D2 is considered different to D2 D1 as they finish on different
doubles. However, the combination S1 T1 D1 is considered the same as T1 S1 D1.
In addition we shall not include misses in considering combinations; for example,
D3 is the same as 0 D3 and 0 0 D3.
Incredibly there are 42336 distinct ways of checking out in total.
How many distinct ways can a player checkout with a score less than 100?
Solution:
We first construct a list of the possible dart values, separated by type.
We then iterate through the doubles, followed by the possible 2 following throws.
If the total of these three darts is less than the given limit, we increment
the counter.
"""
from itertools import combinations_with_replacement
def solution(limit: int = 100) -> int:
"""
Count the number of distinct ways a player can checkout with a score
less than limit.
>>> solution(171)
42336
>>> solution(50)
12577
"""
singles: list[int] = [x for x in range(1, 21)] + [25]
doubles: list[int] = [2 * x for x in range(1, 21)] + [50]
triples: list[int] = [3 * x for x in range(1, 21)]
all_values: list[int] = singles + doubles + triples + [0]
num_checkouts: int = 0
double: int
throw1: int
throw2: int
checkout_total: int
for double in doubles:
for throw1, throw2 in combinations_with_replacement(all_values, 2):
checkout_total = double + throw1 + throw2
if checkout_total < limit:
num_checkouts += 1
return num_checkouts
if __name__ == "__main__":
print(f"{solution() = }")
| """
In the game of darts a player throws three darts at a target board which is
split into twenty equal sized sections numbered one to twenty.

The score of a dart is determined by the number of the region that the dart
lands in. A dart landing outside the red/green outer ring scores zero. The black
and cream regions inside this ring represent single scores. However, the red/green
outer ring and middle ring score double and treble scores respectively.
At the centre of the board are two concentric circles called the bull region, or
bulls-eye. The outer bull is worth 25 points and the inner bull is a double,
worth 50 points.
There are many variations of rules but in the most popular game the players will
begin with a score 301 or 501 and the first player to reduce their running total
to zero is a winner. However, it is normal to play a "doubles out" system, which
means that the player must land a double (including the double bulls-eye at the
centre of the board) on their final dart to win; any other dart that would reduce
their running total to one or lower means the score for that set of three darts
is "bust".
When a player is able to finish on their current score it is called a "checkout"
and the highest checkout is 170: T20 T20 D25 (two treble 20s and double bull).
There are exactly eleven distinct ways to checkout on a score of 6:
D3
D1 D2
S2 D2
D2 D1
S4 D1
S1 S1 D2
S1 T1 D1
S1 S3 D1
D1 D1 D1
D1 S2 D1
S2 S2 D1
Note that D1 D2 is considered different to D2 D1 as they finish on different
doubles. However, the combination S1 T1 D1 is considered the same as T1 S1 D1.
In addition we shall not include misses in considering combinations; for example,
D3 is the same as 0 D3 and 0 0 D3.
Incredibly there are 42336 distinct ways of checking out in total.
How many distinct ways can a player checkout with a score less than 100?
Solution:
We first construct a list of the possible dart values, separated by type.
We then iterate through the doubles, followed by the possible 2 following throws.
If the total of these three darts is less than the given limit, we increment
the counter.
"""
from itertools import combinations_with_replacement
def solution(limit: int = 100) -> int:
"""
Count the number of distinct ways a player can checkout with a score
less than limit.
>>> solution(171)
42336
>>> solution(50)
12577
"""
singles: list[int] = [x for x in range(1, 21)] + [25]
doubles: list[int] = [2 * x for x in range(1, 21)] + [50]
triples: list[int] = [3 * x for x in range(1, 21)]
all_values: list[int] = singles + doubles + triples + [0]
num_checkouts: int = 0
double: int
throw1: int
throw2: int
checkout_total: int
for double in doubles:
for throw1, throw2 in combinations_with_replacement(all_values, 2):
checkout_total = double + throw1 + throw2
if checkout_total < limit:
num_checkouts += 1
return num_checkouts
if __name__ == "__main__":
print(f"{solution() = }")
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Highly divisible triangular numbers
Problem 12
The sequence of triangle numbers is generated by adding the natural numbers. So
the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten
terms would be:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
Let us list the factors of the first seven triangle numbers:
1: 1
3: 1,3
6: 1,2,3,6
10: 1,2,5,10
15: 1,3,5,15
21: 1,3,7,21
28: 1,2,4,7,14,28
We can see that 28 is the first triangle number to have over five divisors.
What is the value of the first triangle number to have over five hundred
divisors?
"""
def triangle_number_generator():
for n in range(1, 1000000):
yield n * (n + 1) // 2
def count_divisors(n):
return sum(2 for i in range(1, int(n ** 0.5) + 1) if n % i == 0 and i * i != n)
def solution():
"""Returns the value of the first triangle number to have over five hundred
divisors.
# The code below has been commented due to slow execution affecting Travis.
# >>> solution()
# 76576500
"""
return next(i for i in triangle_number_generator() if count_divisors(i) > 500)
if __name__ == "__main__":
print(solution())
| """
Highly divisible triangular numbers
Problem 12
The sequence of triangle numbers is generated by adding the natural numbers. So
the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten
terms would be:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
Let us list the factors of the first seven triangle numbers:
1: 1
3: 1,3
6: 1,2,3,6
10: 1,2,5,10
15: 1,3,5,15
21: 1,3,7,21
28: 1,2,4,7,14,28
We can see that 28 is the first triangle number to have over five divisors.
What is the value of the first triangle number to have over five hundred
divisors?
"""
def triangle_number_generator():
for n in range(1, 1000000):
yield n * (n + 1) // 2
def count_divisors(n):
return sum(2 for i in range(1, int(n ** 0.5) + 1) if n % i == 0 and i * i != n)
def solution():
"""Returns the value of the first triangle number to have over five hundred
divisors.
# The code below has been commented due to slow execution affecting Travis.
# >>> solution()
# 76576500
"""
return next(i for i in triangle_number_generator() if count_divisors(i) > 500)
if __name__ == "__main__":
print(solution())
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
A Python implementation of the quick select algorithm, which is efficient for
calculating the value that would appear in the index of a list if it would be
sorted, even if it is not already sorted
https://en.wikipedia.org/wiki/Quickselect
"""
import random
def _partition(data: list, pivot) -> tuple:
"""
Three way partition the data into smaller, equal and greater lists,
in relationship to the pivot
:param data: The data to be sorted (a list)
:param pivot: The value to partition the data on
:return: Three list: smaller, equal and greater
"""
less, equal, greater = [], [], []
for element in data:
if element < pivot:
less.append(element)
elif element > pivot:
greater.append(element)
else:
equal.append(element)
return less, equal, greater
def quick_select(items: list, index: int):
"""
>>> quick_select([2, 4, 5, 7, 899, 54, 32], 5)
54
>>> quick_select([2, 4, 5, 7, 899, 54, 32], 1)
4
>>> quick_select([5, 4, 3, 2], 2)
4
>>> quick_select([3, 5, 7, 10, 2, 12], 3)
7
"""
# index = len(items) // 2 when trying to find the median
# (value of index when items is sorted)
# invalid input
if index >= len(items) or index < 0:
return None
pivot = items[random.randint(0, len(items) - 1)]
count = 0
smaller, equal, larger = _partition(items, pivot)
count = len(equal)
m = len(smaller)
# index is the pivot
if m <= index < m + count:
return pivot
# must be in smaller
elif m > index:
return quick_select(smaller, index)
# must be in larger
else:
return quick_select(larger, index - (m + count))
| """
A Python implementation of the quick select algorithm, which is efficient for
calculating the value that would appear in the index of a list if it would be
sorted, even if it is not already sorted
https://en.wikipedia.org/wiki/Quickselect
"""
import random
def _partition(data: list, pivot) -> tuple:
"""
Three way partition the data into smaller, equal and greater lists,
in relationship to the pivot
:param data: The data to be sorted (a list)
:param pivot: The value to partition the data on
:return: Three list: smaller, equal and greater
"""
less, equal, greater = [], [], []
for element in data:
if element < pivot:
less.append(element)
elif element > pivot:
greater.append(element)
else:
equal.append(element)
return less, equal, greater
def quick_select(items: list, index: int):
"""
>>> quick_select([2, 4, 5, 7, 899, 54, 32], 5)
54
>>> quick_select([2, 4, 5, 7, 899, 54, 32], 1)
4
>>> quick_select([5, 4, 3, 2], 2)
4
>>> quick_select([3, 5, 7, 10, 2, 12], 3)
7
"""
# index = len(items) // 2 when trying to find the median
# (value of index when items is sorted)
# invalid input
if index >= len(items) or index < 0:
return None
pivot = items[random.randint(0, len(items) - 1)]
count = 0
smaller, equal, larger = _partition(items, pivot)
count = len(equal)
m = len(smaller)
# index is the pivot
if m <= index < m + count:
return pivot
# must be in smaller
elif m > index:
return quick_select(smaller, index)
# must be in larger
else:
return quick_select(larger, index - (m + count))
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| # A Python implementation of the Banker's Algorithm in Operating Systems using
# Processes and Resources
# {
# "Author: "Biney Kingsley ([email protected]), [email protected]",
# "Date": 28-10-2018
# }
"""
The Banker's algorithm is a resource allocation and deadlock avoidance algorithm
developed by Edsger Dijkstra that tests for safety by simulating the allocation of
predetermined maximum possible amounts of all resources, and then makes a "s-state"
check to test for possible deadlock conditions for all other pending activities,
before deciding whether allocation should be allowed to continue.
[Source] Wikipedia
[Credit] Rosetta Code C implementation helped very much.
(https://rosettacode.org/wiki/Banker%27s_algorithm)
"""
from __future__ import annotations
import time
import numpy as np
test_claim_vector = [8, 5, 9, 7]
test_allocated_res_table = [
[2, 0, 1, 1],
[0, 1, 2, 1],
[4, 0, 0, 3],
[0, 2, 1, 0],
[1, 0, 3, 0],
]
test_maximum_claim_table = [
[3, 2, 1, 4],
[0, 2, 5, 2],
[5, 1, 0, 5],
[1, 5, 3, 0],
[3, 0, 3, 3],
]
class BankersAlgorithm:
def __init__(
self,
claim_vector: list[int],
allocated_resources_table: list[list[int]],
maximum_claim_table: list[list[int]],
) -> None:
"""
:param claim_vector: A nxn/nxm list depicting the amount of each resources
(eg. memory, interface, semaphores, etc.) available.
:param allocated_resources_table: A nxn/nxm list depicting the amount of each
resource each process is currently holding
:param maximum_claim_table: A nxn/nxm list depicting how much of each resource
the system currently has available
"""
self.__claim_vector = claim_vector
self.__allocated_resources_table = allocated_resources_table
self.__maximum_claim_table = maximum_claim_table
def __processes_resource_summation(self) -> list[int]:
"""
Check for allocated resources in line with each resource in the claim vector
"""
return [
sum(p_item[i] for p_item in self.__allocated_resources_table)
for i in range(len(self.__allocated_resources_table[0]))
]
def __available_resources(self) -> list[int]:
"""
Check for available resources in line with each resource in the claim vector
"""
return np.array(self.__claim_vector) - np.array(
self.__processes_resource_summation()
)
def __need(self) -> list[list[int]]:
"""
Implement safety checker that calculates the needs by ensuring that
max_claim[i][j] - alloc_table[i][j] <= avail[j]
"""
return [
list(np.array(self.__maximum_claim_table[i]) - np.array(allocated_resource))
for i, allocated_resource in enumerate(self.__allocated_resources_table)
]
def __need_index_manager(self) -> dict[int, list[int]]:
"""
This function builds an index control dictionary to track original ids/indices
of processes when altered during execution of method "main"
Return: {0: [a: int, b: int], 1: [c: int, d: int]}
>>> (BankersAlgorithm(test_claim_vector, test_allocated_res_table,
... test_maximum_claim_table)._BankersAlgorithm__need_index_manager()
... ) # doctest: +NORMALIZE_WHITESPACE
{0: [1, 2, 0, 3], 1: [0, 1, 3, 1], 2: [1, 1, 0, 2], 3: [1, 3, 2, 0],
4: [2, 0, 0, 3]}
"""
return {self.__need().index(i): i for i in self.__need()}
def main(self, **kwargs) -> None:
"""
Utilize various methods in this class to simulate the Banker's algorithm
Return: None
>>> BankersAlgorithm(test_claim_vector, test_allocated_res_table,
... test_maximum_claim_table).main(describe=True)
Allocated Resource Table
P1 2 0 1 1
<BLANKLINE>
P2 0 1 2 1
<BLANKLINE>
P3 4 0 0 3
<BLANKLINE>
P4 0 2 1 0
<BLANKLINE>
P5 1 0 3 0
<BLANKLINE>
System Resource Table
P1 3 2 1 4
<BLANKLINE>
P2 0 2 5 2
<BLANKLINE>
P3 5 1 0 5
<BLANKLINE>
P4 1 5 3 0
<BLANKLINE>
P5 3 0 3 3
<BLANKLINE>
Current Usage by Active Processes: 8 5 9 7
Initial Available Resources: 1 2 2 2
__________________________________________________
<BLANKLINE>
Process 3 is executing.
Updated available resource stack for processes: 5 2 2 5
The process is in a safe state.
<BLANKLINE>
Process 1 is executing.
Updated available resource stack for processes: 7 2 3 6
The process is in a safe state.
<BLANKLINE>
Process 2 is executing.
Updated available resource stack for processes: 7 3 5 7
The process is in a safe state.
<BLANKLINE>
Process 4 is executing.
Updated available resource stack for processes: 7 5 6 7
The process is in a safe state.
<BLANKLINE>
Process 5 is executing.
Updated available resource stack for processes: 8 5 9 7
The process is in a safe state.
<BLANKLINE>
"""
need_list = self.__need()
alloc_resources_table = self.__allocated_resources_table
available_resources = self.__available_resources()
need_index_manager = self.__need_index_manager()
for kw, val in kwargs.items():
if kw and val is True:
self.__pretty_data()
print("_" * 50 + "\n")
while need_list:
safe = False
for each_need in need_list:
execution = True
for index, need in enumerate(each_need):
if need > available_resources[index]:
execution = False
break
if execution:
safe = True
# get the original index of the process from ind_ctrl db
for original_need_index, need_clone in need_index_manager.items():
if each_need == need_clone:
process_number = original_need_index
print(f"Process {process_number + 1} is executing.")
# remove the process run from stack
need_list.remove(each_need)
# update available/freed resources stack
available_resources = np.array(available_resources) + np.array(
alloc_resources_table[process_number]
)
print(
"Updated available resource stack for processes: "
+ " ".join([str(x) for x in available_resources])
)
break
if safe:
print("The process is in a safe state.\n")
else:
print("System in unsafe state. Aborting...\n")
break
def __pretty_data(self):
"""
Properly align display of the algorithm's solution
"""
print(" " * 9 + "Allocated Resource Table")
for item in self.__allocated_resources_table:
print(
f"P{self.__allocated_resources_table.index(item) + 1}"
+ " ".join(f"{it:>8}" for it in item)
+ "\n"
)
print(" " * 9 + "System Resource Table")
for item in self.__maximum_claim_table:
print(
f"P{self.__maximum_claim_table.index(item) + 1}"
+ " ".join(f"{it:>8}" for it in item)
+ "\n"
)
print(
"Current Usage by Active Processes: "
+ " ".join(str(x) for x in self.__claim_vector)
)
print(
"Initial Available Resources: "
+ " ".join(str(x) for x in self.__available_resources())
)
time.sleep(1)
if __name__ == "__main__":
import doctest
doctest.testmod()
| # A Python implementation of the Banker's Algorithm in Operating Systems using
# Processes and Resources
# {
# "Author: "Biney Kingsley ([email protected]), [email protected]",
# "Date": 28-10-2018
# }
"""
The Banker's algorithm is a resource allocation and deadlock avoidance algorithm
developed by Edsger Dijkstra that tests for safety by simulating the allocation of
predetermined maximum possible amounts of all resources, and then makes a "s-state"
check to test for possible deadlock conditions for all other pending activities,
before deciding whether allocation should be allowed to continue.
[Source] Wikipedia
[Credit] Rosetta Code C implementation helped very much.
(https://rosettacode.org/wiki/Banker%27s_algorithm)
"""
from __future__ import annotations
import time
import numpy as np
test_claim_vector = [8, 5, 9, 7]
test_allocated_res_table = [
[2, 0, 1, 1],
[0, 1, 2, 1],
[4, 0, 0, 3],
[0, 2, 1, 0],
[1, 0, 3, 0],
]
test_maximum_claim_table = [
[3, 2, 1, 4],
[0, 2, 5, 2],
[5, 1, 0, 5],
[1, 5, 3, 0],
[3, 0, 3, 3],
]
class BankersAlgorithm:
def __init__(
self,
claim_vector: list[int],
allocated_resources_table: list[list[int]],
maximum_claim_table: list[list[int]],
) -> None:
"""
:param claim_vector: A nxn/nxm list depicting the amount of each resources
(eg. memory, interface, semaphores, etc.) available.
:param allocated_resources_table: A nxn/nxm list depicting the amount of each
resource each process is currently holding
:param maximum_claim_table: A nxn/nxm list depicting how much of each resource
the system currently has available
"""
self.__claim_vector = claim_vector
self.__allocated_resources_table = allocated_resources_table
self.__maximum_claim_table = maximum_claim_table
def __processes_resource_summation(self) -> list[int]:
"""
Check for allocated resources in line with each resource in the claim vector
"""
return [
sum(p_item[i] for p_item in self.__allocated_resources_table)
for i in range(len(self.__allocated_resources_table[0]))
]
def __available_resources(self) -> list[int]:
"""
Check for available resources in line with each resource in the claim vector
"""
return np.array(self.__claim_vector) - np.array(
self.__processes_resource_summation()
)
def __need(self) -> list[list[int]]:
"""
Implement safety checker that calculates the needs by ensuring that
max_claim[i][j] - alloc_table[i][j] <= avail[j]
"""
return [
list(np.array(self.__maximum_claim_table[i]) - np.array(allocated_resource))
for i, allocated_resource in enumerate(self.__allocated_resources_table)
]
def __need_index_manager(self) -> dict[int, list[int]]:
"""
This function builds an index control dictionary to track original ids/indices
of processes when altered during execution of method "main"
Return: {0: [a: int, b: int], 1: [c: int, d: int]}
>>> (BankersAlgorithm(test_claim_vector, test_allocated_res_table,
... test_maximum_claim_table)._BankersAlgorithm__need_index_manager()
... ) # doctest: +NORMALIZE_WHITESPACE
{0: [1, 2, 0, 3], 1: [0, 1, 3, 1], 2: [1, 1, 0, 2], 3: [1, 3, 2, 0],
4: [2, 0, 0, 3]}
"""
return {self.__need().index(i): i for i in self.__need()}
def main(self, **kwargs) -> None:
"""
Utilize various methods in this class to simulate the Banker's algorithm
Return: None
>>> BankersAlgorithm(test_claim_vector, test_allocated_res_table,
... test_maximum_claim_table).main(describe=True)
Allocated Resource Table
P1 2 0 1 1
<BLANKLINE>
P2 0 1 2 1
<BLANKLINE>
P3 4 0 0 3
<BLANKLINE>
P4 0 2 1 0
<BLANKLINE>
P5 1 0 3 0
<BLANKLINE>
System Resource Table
P1 3 2 1 4
<BLANKLINE>
P2 0 2 5 2
<BLANKLINE>
P3 5 1 0 5
<BLANKLINE>
P4 1 5 3 0
<BLANKLINE>
P5 3 0 3 3
<BLANKLINE>
Current Usage by Active Processes: 8 5 9 7
Initial Available Resources: 1 2 2 2
__________________________________________________
<BLANKLINE>
Process 3 is executing.
Updated available resource stack for processes: 5 2 2 5
The process is in a safe state.
<BLANKLINE>
Process 1 is executing.
Updated available resource stack for processes: 7 2 3 6
The process is in a safe state.
<BLANKLINE>
Process 2 is executing.
Updated available resource stack for processes: 7 3 5 7
The process is in a safe state.
<BLANKLINE>
Process 4 is executing.
Updated available resource stack for processes: 7 5 6 7
The process is in a safe state.
<BLANKLINE>
Process 5 is executing.
Updated available resource stack for processes: 8 5 9 7
The process is in a safe state.
<BLANKLINE>
"""
need_list = self.__need()
alloc_resources_table = self.__allocated_resources_table
available_resources = self.__available_resources()
need_index_manager = self.__need_index_manager()
for kw, val in kwargs.items():
if kw and val is True:
self.__pretty_data()
print("_" * 50 + "\n")
while need_list:
safe = False
for each_need in need_list:
execution = True
for index, need in enumerate(each_need):
if need > available_resources[index]:
execution = False
break
if execution:
safe = True
# get the original index of the process from ind_ctrl db
for original_need_index, need_clone in need_index_manager.items():
if each_need == need_clone:
process_number = original_need_index
print(f"Process {process_number + 1} is executing.")
# remove the process run from stack
need_list.remove(each_need)
# update available/freed resources stack
available_resources = np.array(available_resources) + np.array(
alloc_resources_table[process_number]
)
print(
"Updated available resource stack for processes: "
+ " ".join([str(x) for x in available_resources])
)
break
if safe:
print("The process is in a safe state.\n")
else:
print("System in unsafe state. Aborting...\n")
break
def __pretty_data(self):
"""
Properly align display of the algorithm's solution
"""
print(" " * 9 + "Allocated Resource Table")
for item in self.__allocated_resources_table:
print(
f"P{self.__allocated_resources_table.index(item) + 1}"
+ " ".join(f"{it:>8}" for it in item)
+ "\n"
)
print(" " * 9 + "System Resource Table")
for item in self.__maximum_claim_table:
print(
f"P{self.__maximum_claim_table.index(item) + 1}"
+ " ".join(f"{it:>8}" for it in item)
+ "\n"
)
print(
"Current Usage by Active Processes: "
+ " ".join(str(x) for x in self.__claim_vector)
)
print(
"Initial Available Resources: "
+ " ".join(str(x) for x in self.__available_resources())
)
time.sleep(1)
if __name__ == "__main__":
import doctest
doctest.testmod()
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| from calendar import day_name
from datetime import datetime
def date_to_weekday(inp_date: str) -> str:
"""
It returns the day name of the given date string.
:param inp_date:
:return: String
>>> date_to_weekday("7/8/2035")
'Tuesday'
>>> date_to_weekday("7/8/2021")
'Saturday'
>>> date_to_weekday("1/1/2021")
'Friday'
"""
day, month, year = (int(x) for x in inp_date.split("/"))
if year % 100 == 0:
year = "00"
new_base_date: str = f"{day}/{month}/{year%100} 0:0:0"
date_time_obj: datetime.date = datetime.strptime(new_base_date, "%d/%m/%y %H:%M:%S")
out_put_day: int = date_time_obj.weekday()
return day_name[out_put_day]
if __name__ == "__main__":
print(date_to_weekday("1/1/2021"), end=" ")
| from calendar import day_name
from datetime import datetime
def date_to_weekday(inp_date: str) -> str:
"""
It returns the day name of the given date string.
:param inp_date:
:return: String
>>> date_to_weekday("7/8/2035")
'Tuesday'
>>> date_to_weekday("7/8/2021")
'Saturday'
>>> date_to_weekday("1/1/2021")
'Friday'
"""
day, month, year = (int(x) for x in inp_date.split("/"))
if year % 100 == 0:
year = "00"
new_base_date: str = f"{day}/{month}/{year%100} 0:0:0"
date_time_obj: datetime.date = datetime.strptime(new_base_date, "%d/%m/%y %H:%M:%S")
out_put_day: int = date_time_obj.weekday()
return day_name[out_put_day]
if __name__ == "__main__":
print(date_to_weekday("1/1/2021"), end=" ")
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| -1 |
||
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Ugly numbers are numbers whose only prime factors are 2, 3 or 5. The sequence
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, … shows the first 11 ugly numbers. By convention,
1 is included.
Given an integer n, we have to find the nth ugly number.
For more details, refer this article
https://www.geeksforgeeks.org/ugly-numbers/
"""
def ugly_numbers(n: int) -> int:
"""
Returns the nth ugly number.
>>> ugly_numbers(100)
1536
>>> ugly_numbers(0)
1
>>> ugly_numbers(20)
36
>>> ugly_numbers(-5)
1
>>> ugly_numbers(-5.5)
Traceback (most recent call last):
...
TypeError: 'float' object cannot be interpreted as an integer
"""
ugly_nums = [1]
i2, i3, i5 = 0, 0, 0
next_2 = ugly_nums[i2] * 2
next_3 = ugly_nums[i3] * 3
next_5 = ugly_nums[i5] * 5
for i in range(1, n):
next_num = min(next_2, next_3, next_5)
ugly_nums.append(next_num)
if next_num == next_2:
i2 += 1
next_2 = ugly_nums[i2] * 2
if next_num == next_3:
i3 += 1
next_3 = ugly_nums[i3] * 3
if next_num == next_5:
i5 += 1
next_5 = ugly_nums[i5] * 5
return ugly_nums[-1]
if __name__ == "__main__":
from doctest import testmod
testmod(verbose=True)
print(f"{ugly_numbers(200) = }")
| """
Ugly numbers are numbers whose only prime factors are 2, 3 or 5. The sequence
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, … shows the first 11 ugly numbers. By convention,
1 is included.
Given an integer n, we have to find the nth ugly number.
For more details, refer this article
https://www.geeksforgeeks.org/ugly-numbers/
"""
def ugly_numbers(n: int) -> int:
"""
Returns the nth ugly number.
>>> ugly_numbers(100)
1536
>>> ugly_numbers(0)
1
>>> ugly_numbers(20)
36
>>> ugly_numbers(-5)
1
>>> ugly_numbers(-5.5)
Traceback (most recent call last):
...
TypeError: 'float' object cannot be interpreted as an integer
"""
ugly_nums = [1]
i2, i3, i5 = 0, 0, 0
next_2 = ugly_nums[i2] * 2
next_3 = ugly_nums[i3] * 3
next_5 = ugly_nums[i5] * 5
for i in range(1, n):
next_num = min(next_2, next_3, next_5)
ugly_nums.append(next_num)
if next_num == next_2:
i2 += 1
next_2 = ugly_nums[i2] * 2
if next_num == next_3:
i3 += 1
next_3 = ugly_nums[i3] * 3
if next_num == next_5:
i5 += 1
next_5 = ugly_nums[i5] * 5
return ugly_nums[-1]
if __name__ == "__main__":
from doctest import testmod
testmod(verbose=True)
print(f"{ugly_numbers(200) = }")
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
https://en.wikipedia.org/wiki/Computus#Gauss'_Easter_algorithm
"""
import math
from datetime import datetime, timedelta
def gauss_easter(year: int) -> datetime:
"""
Calculation Gregorian easter date for given year
>>> gauss_easter(2007)
datetime.datetime(2007, 4, 8, 0, 0)
>>> gauss_easter(2008)
datetime.datetime(2008, 3, 23, 0, 0)
>>> gauss_easter(2020)
datetime.datetime(2020, 4, 12, 0, 0)
>>> gauss_easter(2021)
datetime.datetime(2021, 4, 4, 0, 0)
"""
metonic_cycle = year % 19
julian_leap_year = year % 4
non_leap_year = year % 7
leap_day_inhibits = math.floor(year / 100)
lunar_orbit_correction = math.floor((13 + 8 * leap_day_inhibits) / 25)
leap_day_reinstall_number = leap_day_inhibits / 4
secular_moon_shift = (
15 - lunar_orbit_correction + leap_day_inhibits - leap_day_reinstall_number
) % 30
century_starting_point = (4 + leap_day_inhibits - leap_day_reinstall_number) % 7
# days to be added to March 21
days_to_add = (19 * metonic_cycle + secular_moon_shift) % 30
# PHM -> Paschal Full Moon
days_from_phm_to_sunday = (
2 * julian_leap_year
+ 4 * non_leap_year
+ 6 * days_to_add
+ century_starting_point
) % 7
if days_to_add == 29 and days_from_phm_to_sunday == 6:
return datetime(year, 4, 19)
elif days_to_add == 28 and days_from_phm_to_sunday == 6:
return datetime(year, 4, 18)
else:
return datetime(year, 3, 22) + timedelta(
days=int(days_to_add + days_from_phm_to_sunday)
)
if __name__ == "__main__":
for year in (1994, 2000, 2010, 2021, 2023):
tense = "will be" if year > datetime.now().year else "was"
print(f"Easter in {year} {tense} {gauss_easter(year)}")
| """
https://en.wikipedia.org/wiki/Computus#Gauss'_Easter_algorithm
"""
import math
from datetime import datetime, timedelta
def gauss_easter(year: int) -> datetime:
"""
Calculation Gregorian easter date for given year
>>> gauss_easter(2007)
datetime.datetime(2007, 4, 8, 0, 0)
>>> gauss_easter(2008)
datetime.datetime(2008, 3, 23, 0, 0)
>>> gauss_easter(2020)
datetime.datetime(2020, 4, 12, 0, 0)
>>> gauss_easter(2021)
datetime.datetime(2021, 4, 4, 0, 0)
"""
metonic_cycle = year % 19
julian_leap_year = year % 4
non_leap_year = year % 7
leap_day_inhibits = math.floor(year / 100)
lunar_orbit_correction = math.floor((13 + 8 * leap_day_inhibits) / 25)
leap_day_reinstall_number = leap_day_inhibits / 4
secular_moon_shift = (
15 - lunar_orbit_correction + leap_day_inhibits - leap_day_reinstall_number
) % 30
century_starting_point = (4 + leap_day_inhibits - leap_day_reinstall_number) % 7
# days to be added to March 21
days_to_add = (19 * metonic_cycle + secular_moon_shift) % 30
# PHM -> Paschal Full Moon
days_from_phm_to_sunday = (
2 * julian_leap_year
+ 4 * non_leap_year
+ 6 * days_to_add
+ century_starting_point
) % 7
if days_to_add == 29 and days_from_phm_to_sunday == 6:
return datetime(year, 4, 19)
elif days_to_add == 28 and days_from_phm_to_sunday == 6:
return datetime(year, 4, 18)
else:
return datetime(year, 3, 22) + timedelta(
days=int(days_to_add + days_from_phm_to_sunday)
)
if __name__ == "__main__":
for year in (1994, 2000, 2010, 2021, 2023):
tense = "will be" if year > datetime.now().year else "was"
print(f"Easter in {year} {tense} {gauss_easter(year)}")
| -1 |
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| -1 |
||
TheAlgorithms/Python | 4,747 | [mypy] fix type annotations for all Project Euler problems | ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| pikulet | "2021-09-10T06:11:28Z" | "2021-10-11T16:33:45Z" | e311b02e704891b2f31a1e2c8fe2df77a032b09b | bcfca67faa120cc4cb42775af302d6d52d3a3f1e | [mypy] fix type annotations for all Project Euler problems. ### **Describe your change:**
Fixes #4052
* [ ] Add an algorithm?
* [x] Fix a bug or typo in an existing algorithm?
* [ ] Documentation change?
### **Checklist:**
* [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
* [x] This pull request is all my own work -- I have not plagiarized.
* [x] I know that pull requests will not be merged if they fail the automated tests.
* [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
* [x] All new Python files are placed inside an existing directory.
* [x] All filenames are in all lowercase characters with no spaces or dashes.
* [x] All functions and variable names follow Python naming conventions.
* [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
* [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
* [x] All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
* [x] If this pull request resolves one or more open issues then the commit message contains `Fixes: #{$ISSUE_NO}`.
| """
Project Euler Problem 6: https://projecteuler.net/problem=6
Sum square difference
The sum of the squares of the first ten natural numbers is,
1^2 + 2^2 + ... + 10^2 = 385
The square of the sum of the first ten natural numbers is,
(1 + 2 + ... + 10)^2 = 55^2 = 3025
Hence the difference between the sum of the squares of the first ten
natural numbers and the square of the sum is 3025 - 385 = 2640.
Find the difference between the sum of the squares of the first one
hundred natural numbers and the square of the sum.
"""
def solution(n: int = 100) -> int:
"""
Returns the difference between the sum of the squares of the first n
natural numbers and the square of the sum.
>>> solution(10)
2640
>>> solution(15)
13160
>>> solution(20)
41230
>>> solution(50)
1582700
"""
sum_of_squares = n * (n + 1) * (2 * n + 1) / 6
square_of_sum = (n * (n + 1) / 2) ** 2
return int(square_of_sum - sum_of_squares)
if __name__ == "__main__":
print(f"{solution() = }")
| """
Project Euler Problem 6: https://projecteuler.net/problem=6
Sum square difference
The sum of the squares of the first ten natural numbers is,
1^2 + 2^2 + ... + 10^2 = 385
The square of the sum of the first ten natural numbers is,
(1 + 2 + ... + 10)^2 = 55^2 = 3025
Hence the difference between the sum of the squares of the first ten
natural numbers and the square of the sum is 3025 - 385 = 2640.
Find the difference between the sum of the squares of the first one
hundred natural numbers and the square of the sum.
"""
def solution(n: int = 100) -> int:
"""
Returns the difference between the sum of the squares of the first n
natural numbers and the square of the sum.
>>> solution(10)
2640
>>> solution(15)
13160
>>> solution(20)
41230
>>> solution(50)
1582700
"""
sum_of_squares = n * (n + 1) * (2 * n + 1) / 6
square_of_sum = (n * (n + 1) / 2) ** 2
return int(square_of_sum - sum_of_squares)
if __name__ == "__main__":
print(f"{solution() = }")
| -1 |
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