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stringlengths 30
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14.4k
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61.9k
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|---|---|---|---|---|---|
http://rosettacode.org/wiki/Power_set
|
Power set
|
A set is a collection (container) of certain values,
without any particular order, and no repeated values.
It corresponds with a finite set in mathematics.
A set can be implemented as an associative array (partial mapping)
in which the value of each key-value pair is ignored.
Given a set S, the power set (or powerset) of S, written P(S), or 2S, is the set of all subsets of S.
Task
By using a library or built-in set type, or by defining a set type with necessary operations, write a function with a set S as input that yields the power set 2S of S.
For example, the power set of {1,2,3,4} is
{{}, {1}, {2}, {1,2}, {3}, {1,3}, {2,3}, {1,2,3}, {4}, {1,4}, {2,4}, {1,2,4}, {3,4}, {1,3,4}, {2,3,4}, {1,2,3,4}}.
For a set which contains n elements, the corresponding power set has 2n elements, including the edge cases of empty set.
The power set of the empty set is the set which contains itself (20 = 1):
P
{\displaystyle {\mathcal {P}}}
(
∅
{\displaystyle \varnothing }
) = {
∅
{\displaystyle \varnothing }
}
And the power set of the set which contains only the empty set, has two subsets, the empty set and the set which contains the empty set (21 = 2):
P
{\displaystyle {\mathcal {P}}}
({
∅
{\displaystyle \varnothing }
}) = {
∅
{\displaystyle \varnothing }
, {
∅
{\displaystyle \varnothing }
} }
Extra credit: Demonstrate that your language supports these last two powersets.
|
#AutoHotkey
|
AutoHotkey
|
a = 1,a,-- ; elements separated by commas
StringSplit a, a, `, ; a0 = #elements, a1,a2,... = elements of the set
t = {
Loop % (1<<a0) { ; generate all 0-1 sequences
x := A_Index-1
Loop % a0
t .= (x>>A_Index-1) & 1 ? a%A_Index% "," : ""
t .= "}`n{" ; new subsets in new lines
}
MsgBox % RegExReplace(SubStr(t,1,StrLen(t)-1),",}","}")
|
http://rosettacode.org/wiki/Primality_by_trial_division
|
Primality by trial division
|
Task
Write a boolean function that tells whether a given integer is prime.
Remember that 1 and all non-positive numbers are not prime.
Use trial division.
Even numbers greater than 2 may be eliminated right away.
A loop from 3 to √ n will suffice, but other loops are allowed.
Related tasks
count in factors
prime decomposition
AKS test for primes
factors of an integer
Sieve of Eratosthenes
factors of a Mersenne number
trial factoring of a Mersenne number
partition an integer X into N primes
sequence of primes by Trial Division
|
#AppleScript
|
AppleScript
|
on isPrime(n)
if (n < 3) then return (n is 2)
if (n mod 2 is 0) then return false
repeat with i from 3 to (n ^ 0.5) div 1 by 2
if (n mod i is 0) then return false
end repeat
return true
end isPrime
-- Test code:
set output to {}
repeat with n from -7 to 100
if (isPrime(n)) then set end of output to n
end repeat
return output
|
http://rosettacode.org/wiki/Price_fraction
|
Price fraction
|
A friend of mine runs a pharmacy. He has a specialized function in his Dispensary application which receives a decimal value of currency and replaces it to a standard value. This value is regulated by a government department.
Task
Given a floating point value between 0.00 and 1.00, rescale according to the following table:
>= 0.00 < 0.06 := 0.10
>= 0.06 < 0.11 := 0.18
>= 0.11 < 0.16 := 0.26
>= 0.16 < 0.21 := 0.32
>= 0.21 < 0.26 := 0.38
>= 0.26 < 0.31 := 0.44
>= 0.31 < 0.36 := 0.50
>= 0.36 < 0.41 := 0.54
>= 0.41 < 0.46 := 0.58
>= 0.46 < 0.51 := 0.62
>= 0.51 < 0.56 := 0.66
>= 0.56 < 0.61 := 0.70
>= 0.61 < 0.66 := 0.74
>= 0.66 < 0.71 := 0.78
>= 0.71 < 0.76 := 0.82
>= 0.76 < 0.81 := 0.86
>= 0.81 < 0.86 := 0.90
>= 0.86 < 0.91 := 0.94
>= 0.91 < 0.96 := 0.98
>= 0.96 < 1.01 := 1.00
|
#C.23
|
C#
|
namespace ConsoleApplication1
{
class Program
{
static void Main(string[] args)
{
for (int x = 0; x < 10; x++)
{
Console.WriteLine("In: {0:0.00}, Out: {1:0.00}", ((double)x) / 10, SpecialRound(((double)x) / 10));
}
Console.WriteLine();
for (int x = 0; x < 10; x++)
{
Console.WriteLine("In: {0:0.00}, Out: {1:0.00}", ((double)x) / 10 + 0.05, SpecialRound(((double)x) / 10 + 0.05));
}
Console.WriteLine();
Console.WriteLine("In: {0:0.00}, Out: {1:0.00}", 1.01, SpecialRound(1.01));
Console.Read();
}
private static double SpecialRound(double inValue)
{
if (inValue > 1) return 1;
double[] Splitters = new double[] {
0.00 , 0.06 , 0.11 , 0.16 , 0.21 ,
0.26 , 0.31 , 0.36 , 0.41 , 0.46 ,
0.51 , 0.56 , 0.61 , 0.66 , 0.71 ,
0.76 , 0.81 , 0.86 , 0.91 , 0.96 };
double[] replacements = new double[] {
0.10 , 0.18 , 0.26 , 0.32 , 0.38 ,
0.44 , 0.50 , 0.54 , 0.58 , 0.62 ,
0.66 , 0.70 , 0.74 , 0.78 , 0.82 ,
0.86 , 0.90 , 0.94 , 0.98 , 1.00 };
for (int x = 0; x < Splitters.Length - 1; x++)
{
if (inValue >= Splitters[x] &&
inValue < Splitters[x + 1])
{
return replacements[x];
}
}
return inValue;
}
}
}
|
http://rosettacode.org/wiki/Proper_divisors
|
Proper divisors
|
The proper divisors of a positive integer N are those numbers, other than N itself, that divide N without remainder.
For N > 1 they will always include 1, but for N == 1 there are no proper divisors.
Examples
The proper divisors of 6 are 1, 2, and 3.
The proper divisors of 100 are 1, 2, 4, 5, 10, 20, 25, and 50.
Task
Create a routine to generate all the proper divisors of a number.
use it to show the proper divisors of the numbers 1 to 10 inclusive.
Find a number in the range 1 to 20,000 with the most proper divisors. Show the number and just the count of how many proper divisors it has.
Show all output here.
Related tasks
Amicable pairs
Abundant, deficient and perfect number classifications
Aliquot sequence classifications
Factors of an integer
Prime decomposition
|
#Factor
|
Factor
|
USING: formatting io kernel math math.functions
math.primes.factors math.ranges prettyprint sequences ;
: #divisors ( m -- n )
dup sqrt >integer 1 + [1,b] [ divisor? ] with count dup +
1 - ;
10 [1,b] [ dup pprint bl divisors but-last . ] each
20000 [1,b] [ #divisors ] supremum-by dup #divisors
"%d with %d divisors.\n" printf
|
http://rosettacode.org/wiki/Probabilistic_choice
|
Probabilistic choice
|
Given a mapping between items and their required probability of occurrence, generate a million items randomly subject to the given probabilities and compare the target probability of occurrence versus the generated values.
The total of all the probabilities should equal one. (Because floating point arithmetic is involved, this is subject to rounding errors).
aleph 1/5.0
beth 1/6.0
gimel 1/7.0
daleth 1/8.0
he 1/9.0
waw 1/10.0
zayin 1/11.0
heth 1759/27720 # adjusted so that probabilities add to 1
Related task
Random number generator (device)
|
#J
|
J
|
main=: verb define
hdr=. ' target actual '
lbls=. ; ,:&.> ;:'aleph beth gimel daleth he waw zayin heth'
prtn=. +/\ pt=. (, 1-+/)1r1%5+i.7
da=. prtn I. ?y # 0
pa=. y%~ +/ da =/ i.8
hdr, lbls,. 9j6 ": |: pt,:pa
)
Note 'named abbreviations'
hdr (header)
lbls (labels)
pt (target proportions)
prtn (partitions corresponding to target proportions)
da (distribution of actual values among partitions)
pa (actual proportions)
)
|
http://rosettacode.org/wiki/Priority_queue
|
Priority queue
|
A priority queue is somewhat similar to a queue, with an important distinction: each item is added to a priority queue with a priority level, and will be later removed from the queue with the highest priority element first. That is, the items are (conceptually) stored in the queue in priority order instead of in insertion order.
Task
Create a priority queue. The queue must support at least two operations:
Insertion. An element is added to the queue with a priority (a numeric value).
Top item removal. Deletes the element or one of the elements with the current top priority and return it.
Optionally, other operations may be defined, such as peeking (find what current top priority/top element is), merging (combining two priority queues into one), etc.
To test your implementation, insert a number of elements into the queue, each with some random priority.
Then dequeue them sequentially; now the elements should be sorted by priority.
You can use the following task/priority items as input data:
Priority Task
══════════ ════════════════
3 Clear drains
4 Feed cat
5 Make tea
1 Solve RC tasks
2 Tax return
The implementation should try to be efficient. A typical implementation has O(log n) insertion and extraction time, where n is the number of items in the queue.
You may choose to impose certain limits such as small range of allowed priority levels, limited capacity, etc. If so, discuss the reasons behind it.
|
#Go
|
Go
|
package main
import (
"fmt"
"container/heap"
)
type Task struct {
priority int
name string
}
type TaskPQ []Task
func (self TaskPQ) Len() int { return len(self) }
func (self TaskPQ) Less(i, j int) bool {
return self[i].priority < self[j].priority
}
func (self TaskPQ) Swap(i, j int) { self[i], self[j] = self[j], self[i] }
func (self *TaskPQ) Push(x interface{}) { *self = append(*self, x.(Task)) }
func (self *TaskPQ) Pop() (popped interface{}) {
popped = (*self)[len(*self)-1]
*self = (*self)[:len(*self)-1]
return
}
func main() {
pq := &TaskPQ{{3, "Clear drains"},
{4, "Feed cat"},
{5, "Make tea"},
{1, "Solve RC tasks"}}
// heapify
heap.Init(pq)
// enqueue
heap.Push(pq, Task{2, "Tax return"})
for pq.Len() != 0 {
// dequeue
fmt.Println(heap.Pop(pq))
}
}
|
http://rosettacode.org/wiki/Problem_of_Apollonius
|
Problem of Apollonius
|
Task
Implement a solution to the Problem of Apollonius (description on Wikipedia) which is the problem of finding the circle that is tangent to three specified circles (colored black in the diagram below to the right).
There is an algebraic solution which is pretty straightforward.
The solutions to the example in the code are shown in the diagram (below and to the right).
The red circle is "internally tangent" to all three black circles, and the green circle is "externally tangent" to all three black circles.
|
#Python
|
Python
|
from collections import namedtuple
import math
Circle = namedtuple('Circle', 'x, y, r')
def solveApollonius(c1, c2, c3, s1, s2, s3):
'''
>>> solveApollonius((0, 0, 1), (4, 0, 1), (2, 4, 2), 1,1,1)
Circle(x=2.0, y=2.1, r=3.9)
>>> solveApollonius((0, 0, 1), (4, 0, 1), (2, 4, 2), -1,-1,-1)
Circle(x=2.0, y=0.8333333333333333, r=1.1666666666666667)
'''
x1, y1, r1 = c1
x2, y2, r2 = c2
x3, y3, r3 = c3
v11 = 2*x2 - 2*x1
v12 = 2*y2 - 2*y1
v13 = x1*x1 - x2*x2 + y1*y1 - y2*y2 - r1*r1 + r2*r2
v14 = 2*s2*r2 - 2*s1*r1
v21 = 2*x3 - 2*x2
v22 = 2*y3 - 2*y2
v23 = x2*x2 - x3*x3 + y2*y2 - y3*y3 - r2*r2 + r3*r3
v24 = 2*s3*r3 - 2*s2*r2
w12 = v12/v11
w13 = v13/v11
w14 = v14/v11
w22 = v22/v21-w12
w23 = v23/v21-w13
w24 = v24/v21-w14
P = -w23/w22
Q = w24/w22
M = -w12*P-w13
N = w14 - w12*Q
a = N*N + Q*Q - 1
b = 2*M*N - 2*N*x1 + 2*P*Q - 2*Q*y1 + 2*s1*r1
c = x1*x1 + M*M - 2*M*x1 + P*P + y1*y1 - 2*P*y1 - r1*r1
# Find a root of a quadratic equation. This requires the circle centers not to be e.g. colinear
D = b*b-4*a*c
rs = (-b-math.sqrt(D))/(2*a)
xs = M+N*rs
ys = P+Q*rs
return Circle(xs, ys, rs)
if __name__ == '__main__':
c1, c2, c3 = Circle(0, 0, 1), Circle(4, 0, 1), Circle(2, 4, 2)
print(solveApollonius(c1, c2, c3, 1, 1, 1)) #Expects "Circle[x=2.00,y=2.10,r=3.90]" (green circle in image)
print(solveApollonius(c1, c2, c3, -1, -1, -1)) #Expects "Circle[x=2.00,y=0.83,r=1.17]" (red circle in image)
|
http://rosettacode.org/wiki/Program_name
|
Program name
|
The task is to programmatically obtain the name used to invoke the program. (For example determine whether the user ran "python hello.py", or "python hellocaller.py", a program importing the code from "hello.py".)
Sometimes a multiline shebang is necessary in order to provide the script name to a language's internal ARGV.
See also Command-line arguments
Examples from GitHub.
|
#Scala
|
Scala
|
object ScriptName extends App {
println(s"Program of instantiated object: ${this.getClass.getName}")
// Not recommended, due various implementations
println(s"Program via enviroment: ${System.getProperty("sun.java.command")}")
}
|
http://rosettacode.org/wiki/Program_name
|
Program name
|
The task is to programmatically obtain the name used to invoke the program. (For example determine whether the user ran "python hello.py", or "python hellocaller.py", a program importing the code from "hello.py".)
Sometimes a multiline shebang is necessary in order to provide the script name to a language's internal ARGV.
See also Command-line arguments
Examples from GitHub.
|
#Scheme
|
Scheme
|
#!/bin/sh
#|
exec csi -ss $0 ${1+"$@"}
exit
|#
(use posix)
(require-extension srfi-1) ; lists
(require-extension srfi-13) ; strings
(define (main args)
(let ((prog (cdr (program))))
(display (format "Program: ~a\n" prog))
(exit)))
(define (program)
(if (string=? (car (argv)) "csi")
(let ((s-index (list-index (lambda (x) (string-contains x "-s")) (argv))))
(if (number? s-index)
(cons 'interpreted (list-ref (argv) (+ 1 s-index)))
(cons 'unknown "")))
(cons 'compiled (car (argv)))))
(if (equal? (car (program)) 'compiled)
(main (cdr (argv))))
|
http://rosettacode.org/wiki/Pythagorean_triples
|
Pythagorean triples
|
A Pythagorean triple is defined as three positive integers
(
a
,
b
,
c
)
{\displaystyle (a,b,c)}
where
a
<
b
<
c
{\displaystyle a<b<c}
, and
a
2
+
b
2
=
c
2
.
{\displaystyle a^{2}+b^{2}=c^{2}.}
They are called primitive triples if
a
,
b
,
c
{\displaystyle a,b,c}
are co-prime, that is, if their pairwise greatest common divisors
g
c
d
(
a
,
b
)
=
g
c
d
(
a
,
c
)
=
g
c
d
(
b
,
c
)
=
1
{\displaystyle {\rm {gcd}}(a,b)={\rm {gcd}}(a,c)={\rm {gcd}}(b,c)=1}
.
Because of their relationship through the Pythagorean theorem, a, b, and c are co-prime if a and b are co-prime (
g
c
d
(
a
,
b
)
=
1
{\displaystyle {\rm {gcd}}(a,b)=1}
).
Each triple forms the length of the sides of a right triangle, whose perimeter is
P
=
a
+
b
+
c
{\displaystyle P=a+b+c}
.
Task
The task is to determine how many Pythagorean triples there are with a perimeter no larger than 100 and the number of these that are primitive.
Extra credit
Deal with large values. Can your program handle a maximum perimeter of 1,000,000? What about 10,000,000? 100,000,000?
Note: the extra credit is not for you to demonstrate how fast your language is compared to others; you need a proper algorithm to solve them in a timely manner.
Related tasks
Euler's sum of powers conjecture
List comprehensions
Pythagorean quadruples
|
#Racket
|
Racket
|
#lang racket
#| Euclid's enumeration formula and counting is fast enough for extra credit.
For maximum perimeter P₀, the primitive triples are enumerated by n,m with:
1 ≤ n < m
perimeter P(n, m) ≤ P₀ where P(n, m) = (m² - n²) + 2mn + (m² + n²) = 2m(m+n)
m and n of different parity and coprime.
Since n < m, a simple close non-tight bound on n is P(n, n) < P₀.
For each of these the exact set of m's can be enumerated.
Each primitive triple with perimeter p represents one triple for each kp ≤ P₀,
of which there are floor(P₀/p) k's. |#
(define (P n m) (* 2 m (+ m n)))
(define (number-of-triples P₀)
(for/fold ([primitive 0] [all 0])
([n (in-naturals 1)]
#:break (>= (P n n) P₀))
(for*/fold ([primitive′ primitive] [all′ all])
([m (in-naturals (+ n 1))]
#:break (> (P n m) P₀)
#:when (and (odd? (- m n)) (coprime? m n)))
(values (+ primitive′ 1)
(+ all′ (quotient P₀ (P n m)))))))
(define (print-results P₀)
(define-values (primitive all) (number-of-triples P₀))
(printf "~a ~a:\n ~a, ~a.\n"
"Number of Pythagorean triples and primitive triples with perimeter ≤"
P₀
all primitive))
(print-results 100)
(time (print-results (* 100 1000 1000)))
#|
Number of Pythagorean triples and primitive triples with perimeter ≤ 100:
17, 7.
Number of Pythagorean triples and primitive triples with perimeter ≤ 100000000:
113236940, 7023027.
cpu time: 11976 real time: 12215 gc time: 2381
|#
|
http://rosettacode.org/wiki/Program_termination
|
Program termination
|
Task
Show the syntax for a complete stoppage of a program inside a conditional.
This includes all threads/processes which are part of your program.
Explain the cleanup (or lack thereof) caused by the termination (allocated memory, database connections, open files, object finalizers/destructors, run-on-exit hooks, etc.).
Unless otherwise described, no special cleanup outside that provided by the operating system is provided.
|
#PowerShell
|
PowerShell
|
if (somecondition) {
exit
}
|
http://rosettacode.org/wiki/Program_termination
|
Program termination
|
Task
Show the syntax for a complete stoppage of a program inside a conditional.
This includes all threads/processes which are part of your program.
Explain the cleanup (or lack thereof) caused by the termination (allocated memory, database connections, open files, object finalizers/destructors, run-on-exit hooks, etc.).
Unless otherwise described, no special cleanup outside that provided by the operating system is provided.
|
#Prolog
|
Prolog
|
halt.
|
http://rosettacode.org/wiki/Primality_by_Wilson%27s_theorem
|
Primality by Wilson's theorem
|
Task
Write a boolean function that tells whether a given integer is prime using Wilson's theorem.
By Wilson's theorem, a number p is prime if and only if p divides (p - 1)! + 1.
Remember that 1 and all non-positive integers are not prime.
See also
Cut-the-knot: Wilson's theorem.
Wikipedia: Wilson's theorem
|
#Nim
|
Nim
|
import strutils, sugar
proc facmod(n, m: int): int =
## Compute (n - 1)! mod m.
result = 1
for k in 2..n:
result = (result * k) mod m
func isPrime(n: int): bool = (facmod(n - 1, n) + 1) mod n == 0
let primes = collect(newSeq):
for n in 2..100:
if n.isPrime: n
echo "Prime numbers between 2 and 100:"
echo primes.join(" ")
|
http://rosettacode.org/wiki/Primality_by_Wilson%27s_theorem
|
Primality by Wilson's theorem
|
Task
Write a boolean function that tells whether a given integer is prime using Wilson's theorem.
By Wilson's theorem, a number p is prime if and only if p divides (p - 1)! + 1.
Remember that 1 and all non-positive integers are not prime.
See also
Cut-the-knot: Wilson's theorem.
Wikipedia: Wilson's theorem
|
#PARI.2FGP
|
PARI/GP
|
Wilson(n) = prod(i=1,n-1,Mod(i,n))==-1
|
http://rosettacode.org/wiki/Prime_conspiracy
|
Prime conspiracy
|
A recent discovery, quoted from Quantamagazine (March 13, 2016):
Two mathematicians have uncovered a simple, previously unnoticed property of
prime numbers — those numbers that are divisible only by 1 and themselves.
Prime numbers, it seems, have decided preferences about the final digits of
the primes that immediately follow them.
and
This conspiracy among prime numbers seems, at first glance, to violate a
longstanding assumption in number theory: that prime numbers behave much
like random numbers.
─── (original authors from Stanford University):
─── Kannan Soundararajan and Robert Lemke Oliver
The task is to check this assertion, modulo 10.
Lets call i -> j a transition if i is the last decimal digit of a prime, and j the last decimal digit of the following prime.
Task
Considering the first one million primes. Count, for any pair of successive primes, the number of transitions i -> j and print them along with their relative frequency, sorted by i .
You can see that, for a given i , frequencies are not evenly distributed.
Observation
(Modulo 10), primes whose last digit is 9 "prefer" the digit 1 to the digit 9, as its following prime.
Extra credit
Do the same for one hundred million primes.
Example for 10,000 primes
10000 first primes. Transitions prime % 10 → next-prime % 10.
1 → 1 count: 365 frequency: 3.65 %
1 → 3 count: 833 frequency: 8.33 %
1 → 7 count: 889 frequency: 8.89 %
1 → 9 count: 397 frequency: 3.97 %
2 → 3 count: 1 frequency: 0.01 %
3 → 1 count: 529 frequency: 5.29 %
3 → 3 count: 324 frequency: 3.24 %
3 → 5 count: 1 frequency: 0.01 %
3 → 7 count: 754 frequency: 7.54 %
3 → 9 count: 907 frequency: 9.07 %
5 → 7 count: 1 frequency: 0.01 %
7 → 1 count: 655 frequency: 6.55 %
7 → 3 count: 722 frequency: 7.22 %
7 → 7 count: 323 frequency: 3.23 %
7 → 9 count: 808 frequency: 8.08 %
9 → 1 count: 935 frequency: 9.35 %
9 → 3 count: 635 frequency: 6.35 %
9 → 7 count: 541 frequency: 5.41 %
9 → 9 count: 379 frequency: 3.79 %
|
#Prolog
|
Prolog
|
% table of nth prime values (up to 100,000)
nthprime( 10, 29).
nthprime( 100, 541).
nthprime( 1000, 7919).
nthprime( 10000, 104729).
nthprime(100000, 1299709).
conspiracy(M) :-
N is 10**M,
nthprime(N, P),
sieve(P, Ps),
tally(Ps, Counts),
sort(Counts, Sorted),
show(Sorted).
show(Results) :-
forall(
member(tr(D1, D2, Count), Results),
format("~d -> ~d: ~d~n", [D1, D2, Count])).
% count results
tally(L, R) :- tally(L, [], R).
tally([_], T, T) :- !.
tally([A|As], T0, R) :-
[B|_] = As,
Da is A mod 10, Db is B mod 10,
count(Da, Db, T0, T1),
tally(As, T1, R).
count(D1, D2, [], [tr(D1, D2, 1)]) :- !.
count(D1, D2, [tr(D1, D2, N)|Ts], [tr(D1, D2, Sn)|Ts]) :- succ(N, Sn), !.
count(D1, D2, [T|Ts], [T|Us]) :- count(D1, D2, Ts, Us).
% implement a prime sieve
sieve(Limit, Ps) :-
numlist(2, Limit, Ns),
sieve(Limit, Ns, Ps).
sieve(Limit, W, W) :- W = [P|_], P*P > Limit, !.
sieve(Limit, [P|Xs], [P|Ys]) :-
Q is P*P,
remove_multiples(P, Q, Xs, R),
sieve(Limit, R, Ys).
remove_multiples(_, _, [], []) :- !.
remove_multiples(N, M, [A|As], R) :-
A =:= M, !,
remove_multiples(N, M, As, R).
remove_multiples(N, M, [A|As], [A|R]) :-
A < M, !,
remove_multiples(N, M, As, R).
remove_multiples(N, M, L, R) :-
plus(M, N, M2),
remove_multiples(N, M2, L, R).
|
http://rosettacode.org/wiki/Prime_decomposition
|
Prime decomposition
|
The prime decomposition of a number is defined as a list of prime numbers
which when all multiplied together, are equal to that number.
Example
12 = 2 × 2 × 3, so its prime decomposition is {2, 2, 3}
Task
Write a function which returns an array or collection which contains the prime decomposition of a given number
n
{\displaystyle n}
greater than 1.
If your language does not have an isPrime-like function available,
you may assume that you have a function which determines
whether a number is prime (note its name before your code).
If you would like to test code from this task, you may use code from trial division or the Sieve of Eratosthenes.
Note: The program must not be limited by the word size of your computer or some other artificial limit; it should work for any number regardless of size (ignoring the physical limits of RAM etc).
Related tasks
count in factors
factors of an integer
Sieve of Eratosthenes
primality by trial division
factors of a Mersenne number
trial factoring of a Mersenne number
partition an integer X into N primes
sequence of primes by Trial Division
|
#C
|
C
|
#include <inttypes.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
typedef uint32_t pint;
typedef uint64_t xint;
typedef unsigned int uint;
#define PRIuPINT PRIu32 /* printf macro for pint */
#define PRIuXINT PRIu64 /* printf macro for xint */
#define MAX_FACTORS 63 /* because 2^64 is too large for xint */
uint8_t *pbits;
#define MAX_PRIME (~(pint)0)
#define MAX_PRIME_SQ 65535U
#define PBITS (MAX_PRIME / 30 + 1)
pint next_prime(pint);
int is_prime(xint);
void sieve(pint);
uint8_t bit_pos[30] = {
0, 1<<0, 0, 0, 0, 0,
0, 1<<1, 0, 0, 0, 1<<2,
0, 1<<3, 0, 0, 0, 1<<4,
0, 1<<5, 0, 0, 0, 1<<6,
0, 0, 0, 0, 0, 1<<7,
};
uint8_t rem_num[] = { 1, 7, 11, 13, 17, 19, 23, 29 };
void init_primes()
{
FILE *fp;
pint s, tgt = 4;
if (!(pbits = malloc(PBITS))) {
perror("malloc");
exit(1);
}
if ((fp = fopen("primebits", "r"))) {
fread(pbits, 1, PBITS, fp);
fclose(fp);
return;
}
memset(pbits, 255, PBITS);
for (s = 7; s <= MAX_PRIME_SQ; s = next_prime(s)) {
if (s > tgt) {
tgt *= 2;
fprintf(stderr, "sieve %"PRIuPINT"\n", s);
}
sieve(s);
}
fp = fopen("primebits", "w");
fwrite(pbits, 1, PBITS, fp);
fclose(fp);
}
int is_prime(xint x)
{
pint p;
if (x > 5) {
if (x < MAX_PRIME)
return pbits[x/30] & bit_pos[x % 30];
for (p = 2; p && (xint)p * p <= x; p = next_prime(p))
if (x % p == 0) return 0;
return 1;
}
return x == 2 || x == 3 || x == 5;
}
void sieve(pint p)
{
unsigned char b[8];
off_t ofs[8];
int i, q;
for (i = 0; i < 8; i++) {
q = rem_num[i] * p;
b[i] = ~bit_pos[q % 30];
ofs[i] = q / 30;
}
for (q = ofs[1], i = 7; i; i--)
ofs[i] -= ofs[i-1];
for (ofs[0] = p, i = 1; i < 8; i++)
ofs[0] -= ofs[i];
for (i = 1; q < PBITS; q += ofs[i = (i + 1) & 7])
pbits[q] &= b[i];
}
pint next_prime(pint p)
{
off_t addr;
uint8_t bits, rem;
if (p > 5) {
addr = p / 30;
bits = bit_pos[ p % 30 ] << 1;
for (rem = 0; (1 << rem) < bits; rem++);
while (pbits[addr] < bits || !bits) {
if (++addr >= PBITS) return 0;
bits = 1;
rem = 0;
}
if (addr >= PBITS) return 0;
while (!(pbits[addr] & bits)) {
rem++;
bits <<= 1;
}
return p = addr * 30 + rem_num[rem];
}
switch(p) {
case 2: return 3;
case 3: return 5;
case 5: return 7;
}
return 2;
}
int decompose(xint n, xint *f)
{
pint p = 0;
int i = 0;
/* check small primes: not strictly necessary */
if (n <= MAX_PRIME && is_prime(n)) {
f[0] = n;
return 1;
}
while (n >= (xint)p * p) {
if (!(p = next_prime(p))) break;
while (n % p == 0) {
n /= p;
f[i++] = p;
}
}
if (n > 1) f[i++] = n;
return i;
}
int main()
{
int i, len;
pint p = 0;
xint f[MAX_FACTORS], po;
init_primes();
for (p = 1; p < 64; p++) {
po = (1LLU << p) - 1;
printf("2^%"PRIuPINT" - 1 = %"PRIuXINT, p, po);
fflush(stdout);
if ((len = decompose(po, f)) > 1)
for (i = 0; i < len; i++)
printf(" %c %"PRIuXINT, i?'x':'=', f[i]);
putchar('\n');
}
return 0;
}
|
http://rosettacode.org/wiki/Pointers_and_references
|
Pointers and references
|
Basic Data Operation
This is a basic data operation. It represents a fundamental action on a basic data type.
You may see other such operations in the Basic Data Operations category, or:
Integer Operations
Arithmetic |
Comparison
Boolean Operations
Bitwise |
Logical
String Operations
Concatenation |
Interpolation |
Comparison |
Matching
Memory Operations
Pointers & references |
Addresses
In this task, the goal is to demonstrate common operations on pointers and references. These examples show pointer operations on the stack, which can be dangerous and is rarely done. Pointers and references are commonly used along with Memory allocation on the heap.
|
#ALGOL_68
|
ALGOL 68
|
INT var := 3;
REF INT pointer := var;
|
http://rosettacode.org/wiki/Pointers_and_references
|
Pointers and references
|
Basic Data Operation
This is a basic data operation. It represents a fundamental action on a basic data type.
You may see other such operations in the Basic Data Operations category, or:
Integer Operations
Arithmetic |
Comparison
Boolean Operations
Bitwise |
Logical
String Operations
Concatenation |
Interpolation |
Comparison |
Matching
Memory Operations
Pointers & references |
Addresses
In this task, the goal is to demonstrate common operations on pointers and references. These examples show pointer operations on the stack, which can be dangerous and is rarely done. Pointers and references are commonly used along with Memory allocation on the heap.
|
#ARM_Assembly
|
ARM Assembly
|
;this example uses VASM syntax, your assembler may not use the # before constants or the semicolon for comments
MOV R1,#0x04000000
MOV R0,#0x403
STR R0,[R1] ;store 0x403 into memory address 0x04000000.
|
http://rosettacode.org/wiki/Polymorphism
|
Polymorphism
|
Task
Create two classes Point(x,y) and Circle(x,y,r) with a polymorphic function print, accessors for (x,y,r), copy constructor, assignment and destructor and every possible default constructors
|
#Ada
|
Ada
|
package Shapes is
type Point is tagged private;
procedure Print(Item : in Point);
function Setx(Item : in Point; Val : Integer) return Point;
function Sety(Item : in Point; Val : Integer) return Point;
function Getx(Item : in Point) return Integer;
function Gety(Item : in Point) return Integer;
function Create return Point;
function Create(X : Integer) return Point;
function Create(X, Y : Integer) return Point;
private
type Point is tagged record
X : Integer := 0;
Y : Integer := 0;
end record;
end Shapes;
|
http://rosettacode.org/wiki/Polymorphism
|
Polymorphism
|
Task
Create two classes Point(x,y) and Circle(x,y,r) with a polymorphic function print, accessors for (x,y,r), copy constructor, assignment and destructor and every possible default constructors
|
#Aikido
|
Aikido
|
class Point (protected x=0.0, protected y=0.0) {
public function print {
println ("Point")
}
public function getX { return x }
public function getY { return y }
public function setX(nx) { x = nx }
public function setY(ny) { y = ny }
}
class Circle (x=0.0, y=0.0, r=0.0) extends Point (x, y) {
public function print {
println ("Circle")
}
public function getR { return r }
public function setR(nr) { r = nr }
}
var p = new Point (1, 2)
var c = new Circle (1, 2, 3)
p.print()
c.print()
|
http://rosettacode.org/wiki/Poker_hand_analyser
|
Poker hand analyser
|
Task
Create a program to parse a single five card poker hand and rank it according to this list of poker hands.
A poker hand is specified as a space separated list of five playing cards.
Each input card has two characters indicating face and suit.
Example
2d (two of diamonds).
Faces are: a, 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k
Suits are: h (hearts), d (diamonds), c (clubs), and s (spades), or
alternatively, the unicode card-suit characters: ♥ ♦ ♣ ♠
Duplicate cards are illegal.
The program should analyze a single hand and produce one of the following outputs:
straight-flush
four-of-a-kind
full-house
flush
straight
three-of-a-kind
two-pair
one-pair
high-card
invalid
Examples
2♥ 2♦ 2♣ k♣ q♦: three-of-a-kind
2♥ 5♥ 7♦ 8♣ 9♠: high-card
a♥ 2♦ 3♣ 4♣ 5♦: straight
2♥ 3♥ 2♦ 3♣ 3♦: full-house
2♥ 7♥ 2♦ 3♣ 3♦: two-pair
2♥ 7♥ 7♦ 7♣ 7♠: four-of-a-kind
10♥ j♥ q♥ k♥ a♥: straight-flush
4♥ 4♠ k♠ 5♦ 10♠: one-pair
q♣ 10♣ 7♣ 6♣ q♣: invalid
The programs output for the above examples should be displayed here on this page.
Extra credit
use the playing card characters introduced with Unicode 6.0 (U+1F0A1 - U+1F0DE).
allow two jokers
use the symbol joker
duplicates would be allowed (for jokers only)
five-of-a-kind would then be the highest hand
More extra credit examples
joker 2♦ 2♠ k♠ q♦: three-of-a-kind
joker 5♥ 7♦ 8♠ 9♦: straight
joker 2♦ 3♠ 4♠ 5♠: straight
joker 3♥ 2♦ 3♠ 3♦: four-of-a-kind
joker 7♥ 2♦ 3♠ 3♦: three-of-a-kind
joker 7♥ 7♦ 7♠ 7♣: five-of-a-kind
joker j♥ q♥ k♥ A♥: straight-flush
joker 4♣ k♣ 5♦ 10♠: one-pair
joker k♣ 7♣ 6♣ 4♣: flush
joker 2♦ joker 4♠ 5♠: straight
joker Q♦ joker A♠ 10♠: straight
joker Q♦ joker A♦ 10♦: straight-flush
joker 2♦ 2♠ joker q♦: four-of-a-kind
Related tasks
Playing cards
Card shuffles
Deal cards_for_FreeCell
War Card_Game
Go Fish
|
#11l
|
11l
|
F analyzeHandHelper(faceCount, suitCount)
V
p1 = 0B
p2 = 0B
t = 0B
f = 0B
fl = 0B
st = 0B
L(fc) faceCount
S fc
2 {I p1 {p2 = 1B} E p1 = 1B}
3 {t = 1B}
4 {f = 1B}
L(sc) suitCount
I sc == 5
fl = 1B
I !p1 & !p2 & !t & !f
V s = 0
L(fc) faceCount
I fc != 0
s++
E
s = 0
I s == 5
L.break
st = (s == 5) | (s == 4 & faceCount[0] != 0 & faceCount[1] == 0)
I st & fl {R ‘straight-flush’}
E I f {R ‘four-of-a-kind’}
E I p1 & t {R ‘full-house’}
E I fl {R ‘flush’}
E I st {R ‘straight’}
E I t {R ‘three-of-a-kind’}
E I p1 & p2 {R ‘two-pair’}
E I p1 {R ‘one-pair’}
E {R ‘high-card’}
F analyzeHand(inHand)
V handLen = 5
V face = ‘A23456789TJQK’
V suit = ‘SHCD’
V errorMessage = ‘invalid hand.’
V hand = sorted(inHand.split(‘ ’))
I hand.len != handLen
R errorMessage
I Set(hand).len != handLen
R errorMessage‘ Duplicated cards.’
V faceCount = [0] * face.len
V suitCount = [0] * suit.len
L(card) hand
I card.len != 2
R errorMessage
V? n = face.find(card[0])
V? l = suit.find(card[1])
I n == N | l == N
R errorMessage
faceCount[n]++
suitCount[l]++
R analyzeHandHelper(faceCount, suitCount)
L(hand) [‘2H 2D 2S KS QD’,
‘2H 5H 7D 8S 9D’,
‘AH 2D 3S 4S 5S’,
‘2H 3H 2D 3S 3D’,
‘2H 7H 2D 3S 3D’,
‘2H 7H 7D 7S 7C’,
‘TH JH QH KH AH’,
‘4H 4C KC 5D TC’,
‘QC TC 7C 6C 4C’]
print(hand‘: ’analyzeHand(hand))
|
http://rosettacode.org/wiki/Population_count
|
Population count
|
Population count
You are encouraged to solve this task according to the task description, using any language you may know.
The population count is the number of 1s (ones) in the binary representation of a non-negative integer.
Population count is also known as:
pop count
popcount
sideways sum
bit summation
Hamming weight
For example, 5 (which is 101 in binary) has a population count of 2.
Evil numbers are non-negative integers that have an even population count.
Odious numbers are positive integers that have an odd population count.
Task
write a function (or routine) to return the population count of a non-negative integer.
all computation of the lists below should start with 0 (zero indexed).
display the pop count of the 1st thirty powers of 3 (30, 31, 32, 33, 34, ∙∙∙ 329).
display the 1st thirty evil numbers.
display the 1st thirty odious numbers.
display each list of integers on one line (which may or may not include a title), each set of integers being shown should be properly identified.
See also
The On-Line Encyclopedia of Integer Sequences: A000120 population count.
The On-Line Encyclopedia of Integer Sequences: A000069 odious numbers.
The On-Line Encyclopedia of Integer Sequences: A001969 evil numbers.
|
#ALGOL_68
|
ALGOL 68
|
# returns the population count (number of bits on) of the non-negative #
# integer n #
PROC population count = ( LONG INT n )INT:
BEGIN
LONG INT number := n;
INT result := 0;
WHILE number > 0 DO
IF ODD number THEN result +:= 1 FI;
number OVERAB 2
OD;
result
END # population # ;
# population count of 3^0, 3^1, 3*2, ..., 3^29 #
LONG INT power of three := 1;
print( ( "3^x pop counts:" ) );
FOR power FROM 0 TO 29 DO
print( ( " ", whole( population count( power of three ), 0 ) ) );
power of three *:= 3
OD;
print( ( newline ) );
# print the first thirty evil numbers (even population count) #
INT evil count := 0;
print( ( "evil numbers :" ) );
FOR n FROM 0 WHILE evil count < 30 DO
IF NOT ODD population count( n ) THEN
print( ( " ", whole( n, 0 ) ) );
evil count +:= 1
FI
OD;
print( ( newline ) );
# print the first thirty odious numbers (odd population count) #
INT odious count := 0;
print( ( "odious numbers:" ) );
FOR n WHILE odious count < 30 DO
IF ODD population count( n ) THEN
print( ( " ", whole( n, 0 ) ) );
odious count +:= 1
FI
OD;
print( ( newline ) )
|
http://rosettacode.org/wiki/Polynomial_long_division
|
Polynomial long division
|
This page uses content from Wikipedia. The original article was at Polynomial long division. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree.
Let us suppose a polynomial is represented by a vector,
x
{\displaystyle x}
(i.e., an ordered collection of coefficients) so that the
i
{\displaystyle i}
th element keeps the coefficient of
x
i
{\displaystyle x^{i}}
, and the multiplication by a monomial is a shift of the vector's elements "towards right" (injecting ones from left) followed by a multiplication of each element by the coefficient of the monomial.
Then a pseudocode for the polynomial long division using the conventions described above could be:
degree(P):
return the index of the last non-zero element of P;
if all elements are 0, return -∞
polynomial_long_division(N, D) returns (q, r):
// N, D, q, r are vectors
if degree(D) < 0 then error
q ← 0
while degree(N) ≥ degree(D)
d ← D shifted right by (degree(N) - degree(D))
q(degree(N) - degree(D)) ← N(degree(N)) / d(degree(d))
// by construction, degree(d) = degree(N) of course
d ← d * q(degree(N) - degree(D))
N ← N - d
endwhile
r ← N
return (q, r)
Note: vector * scalar multiplies each element of the vector by the scalar; vectorA - vectorB subtracts each element of the vectorB from the element of the vectorA with "the same index". The vectors in the pseudocode are zero-based.
Error handling (for allocations or for wrong inputs) is not mandatory.
Conventions can be different; in particular, note that if the first coefficient in the vector is the highest power of x for the polynomial represented by the vector, then the algorithm becomes simpler.
Example for clarification
This example is from Wikipedia, but changed to show how the given pseudocode works.
0 1 2 3
----------------------
N: -42 0 -12 1 degree = 3
D: -3 1 0 0 degree = 1
d(N) - d(D) = 2, so let's shift D towards right by 2:
N: -42 0 -12 1
d: 0 0 -3 1
N(3)/d(3) = 1, so d is unchanged. Now remember that "shifting by 2"
is like multiplying by x2, and the final multiplication
(here by 1) is the coefficient of this monomial. Let's store this
into q:
0 1 2
---------------
q: 0 0 1
now compute N - d, and let it be the "new" N, and let's loop
N: -42 0 -9 0 degree = 2
D: -3 1 0 0 degree = 1
d(N) - d(D) = 1, right shift D by 1 and let it be d
N: -42 0 -9 0
d: 0 -3 1 0 * -9/1 = -9
q: 0 -9 1
d: 0 27 -9 0
N ← N - d
N: -42 -27 0 0 degree = 1
D: -3 1 0 0 degree = 1
looping again... d(N)-d(D)=0, so no shift is needed; we
multiply D by -27 (= -27/1) storing the result in d, then
q: -27 -9 1
and
N: -42 -27 0 0 -
d: 81 -27 0 0 =
N: -123 0 0 0 (last N)
d(N) < d(D), so now r ← N, and the result is:
0 1 2
-------------
q: -27 -9 1 → x2 - 9x - 27
r: -123 0 0 → -123
Related task
Polynomial derivative
|
#C.23
|
C#
|
using System;
namespace PolynomialLongDivision {
class Solution {
public Solution(double[] q, double[] r) {
Quotient = q;
Remainder = r;
}
public double[] Quotient { get; }
public double[] Remainder { get; }
}
class Program {
static int PolyDegree(double[] p) {
for (int i = p.Length - 1; i >= 0; --i) {
if (p[i] != 0.0) return i;
}
return int.MinValue;
}
static double[] PolyShiftRight(double[] p, int places) {
if (places <= 0) return p;
int pd = PolyDegree(p);
if (pd + places >= p.Length) {
throw new ArgumentOutOfRangeException("The number of places to be shifted is too large");
}
double[] d = new double[p.Length];
p.CopyTo(d, 0);
for (int i = pd; i >= 0; --i) {
d[i + places] = d[i];
d[i] = 0.0;
}
return d;
}
static void PolyMultiply(double[] p, double m) {
for (int i = 0; i < p.Length; ++i) {
p[i] *= m;
}
}
static void PolySubtract(double[] p, double[] s) {
for (int i = 0; i < p.Length; ++i) {
p[i] -= s[i];
}
}
static Solution PolyLongDiv(double[] n, double[] d) {
if (n.Length != d.Length) {
throw new ArgumentException("Numerator and denominator vectors must have the same size");
}
int nd = PolyDegree(n);
int dd = PolyDegree(d);
if (dd < 0) {
throw new ArgumentException("Divisor must have at least one one-zero coefficient");
}
if (nd < dd) {
throw new ArgumentException("The degree of the divisor cannot exceed that of the numerator");
}
double[] n2 = new double[n.Length];
n.CopyTo(n2, 0);
double[] q = new double[n.Length];
while (nd >= dd) {
double[] d2 = PolyShiftRight(d, nd - dd);
q[nd - dd] = n2[nd] / d2[nd];
PolyMultiply(d2, q[nd - dd]);
PolySubtract(n2, d2);
nd = PolyDegree(n2);
}
return new Solution(q, n2);
}
static void PolyShow(double[] p) {
int pd = PolyDegree(p);
for (int i = pd; i >= 0; --i) {
double coeff = p[i];
if (coeff == 0.0) continue;
if (coeff == 1.0) {
if (i < pd) {
Console.Write(" + ");
}
} else if (coeff == -1.0) {
if (i < pd) {
Console.Write(" - ");
} else {
Console.Write("-");
}
} else if (coeff < 0.0) {
if (i < pd) {
Console.Write(" - {0:F1}", -coeff);
} else {
Console.Write("{0:F1}", coeff);
}
} else {
if (i < pd) {
Console.Write(" + {0:F1}", coeff);
} else {
Console.Write("{0:F1}", coeff);
}
}
if (i > 1) Console.Write("x^{0}", i);
else if (i == 1) Console.Write("x");
}
Console.WriteLine();
}
static void Main(string[] args) {
double[] n = { -42.0, 0.0, -12.0, 1.0 };
double[] d = { -3.0, 1.0, 0.0, 0.0 };
Console.Write("Numerator : ");
PolyShow(n);
Console.Write("Denominator : ");
PolyShow(d);
Console.WriteLine("-------------------------------------");
Solution sol = PolyLongDiv(n, d);
Console.Write("Quotient : ");
PolyShow(sol.Quotient);
Console.Write("Remainder : ");
PolyShow(sol.Remainder);
}
}
}
|
http://rosettacode.org/wiki/Polymorphic_copy
|
Polymorphic copy
|
An object is polymorphic when its specific type may vary.
The types a specific value may take, is called class.
It is trivial to copy an object if its type is known:
int x;
int y = x;
Here x is not polymorphic, so y is declared of same type (int) as x.
But if the specific type of x were unknown, then y could not be declared of any specific type.
The task: let a polymorphic object contain an instance of some specific type S derived from a type T.
The type T is known.
The type S is possibly unknown until run time.
The objective is to create an exact copy of such polymorphic object (not to create a reference, nor a pointer to).
Let further the type T have a method overridden by S.
This method is to be called on the copy to demonstrate that the specific type of the copy is indeed S.
|
#Common_Lisp
|
Common Lisp
|
(defstruct super foo)
(defstruct (sub (:include super)) bar)
(defgeneric frob (thing))
(defmethod frob ((super super))
(format t "~&Super has foo = ~w." (super-foo super)))
(defmethod frob ((sub sub))
(format t "~&Sub has foo = ~w, bar = ~w."
(sub-foo sub) (sub-bar sub)))
|
http://rosettacode.org/wiki/Polymorphic_copy
|
Polymorphic copy
|
An object is polymorphic when its specific type may vary.
The types a specific value may take, is called class.
It is trivial to copy an object if its type is known:
int x;
int y = x;
Here x is not polymorphic, so y is declared of same type (int) as x.
But if the specific type of x were unknown, then y could not be declared of any specific type.
The task: let a polymorphic object contain an instance of some specific type S derived from a type T.
The type T is known.
The type S is possibly unknown until run time.
The objective is to create an exact copy of such polymorphic object (not to create a reference, nor a pointer to).
Let further the type T have a method overridden by S.
This method is to be called on the copy to demonstrate that the specific type of the copy is indeed S.
|
#D
|
D
|
class T {
override string toString() { return "I'm the instance of T"; }
T duplicate() { return new T; }
}
class S : T {
override string toString() { return "I'm the instance of S"; }
override T duplicate() { return new S; }
}
void main () {
import std.stdio;
T orig = new S;
T copy = orig.duplicate();
writeln(orig);
writeln(copy);
}
|
http://rosettacode.org/wiki/Polyspiral
|
Polyspiral
|
A Polyspiral is a spiral made of multiple line segments, whereby each segment is larger (or smaller) than the previous one by a given amount. Each segment also changes direction at a given angle.
Task
Animate a series of polyspirals, by drawing a complete spiral then incrementing the angle, and (after clearing the background) drawing the next, and so on. Every spiral will be a frame of the animation. The animation may stop as it goes full circle or continue indefinitely. The given input values may be varied.
If animation is not practical in your programming environment, you may show a single frame instead.
Pseudo code
set incr to 0.0
// animation loop
WHILE true
incr = (incr + 0.05) MOD 360
x = width / 2
y = height / 2
length = 5
angle = incr
// spiral loop
FOR 1 TO 150
drawline
change direction by angle
length = length + 3
angle = (angle + incr) MOD 360
ENDFOR
|
#JavaScript
|
JavaScript
|
<!-- Polyspiral.html -->
<html>
<head><title>Polyspiral Generator</title></head>
<script>
// Basic function for family of Polyspirals
// Where: rng - range (prime parameter), w2 - half of canvas width,
// d - direction (1 - clockwise, -1 - counter clockwise).
function ppsp(ctx, rng, w2, d) {
// Note: coefficients c, it, sc, sc2, sc3 are selected to fit canvas.
var c=Math.PI*rng, it=c/w2, sc=2, sc2=50, sc3=0.1, t, x, y;
console.log("Polyspiral PARs rng,w2,d:", rng, "/", w2, "/", d);
if (rng>1000) {sc=sc3}
ctx.beginPath();
for(var i=0; i<sc2*c; i++) {
t=it*i;
x = sc*t*Math.cos(d*t)+w2; y = sc*t*Math.sin(d*t)+w2;
ctx.lineTo(x, y);
}//fend i
ctx.stroke();
}
// ******************************************
// pspiral() - Generating and plotting Polyspirals
function pspiral() {
// Setting basic vars for canvas and inpu parameters
var cvs = document.getElementById('cvsId');
var ctx = cvs.getContext("2d");
var w = cvs.width, h = cvs.height;
var w2=w/2;
var clr = document.getElementById("color").value; // color
var d = document.getElementById("dir").value; // direction
var rng = document.getElementById("rng").value; // range
rng=Number(rng);
ctx.fillStyle="white"; ctx.fillRect(0,0,w,h);
ctx.strokeStyle=clr;
// Plotting spiral.
ppsp(ctx, rng, w2, d)
}//func end
</script></head>
<body style="font-family: arial, helvatica, sans-serif;">
<b>Color: </b>
<select id="color">
<option value="red">red</option>
<option value="darkred" selected>darkred</option>
<option value="green">green</option>
<option value="darkgreen">darkgreen</option>
<option value="blue">blue</option>
<option value="navy">navy</option>
<option value="brown">brown</option>
<option value="maroon">maroon</option>
<option value="black">black</option>
</select>
<b>Direction: </b>
<input id="dir" value="1" type="number" min="-1" max="1" size="1">
<b>Range: </b>
<input id="rng" value="10" type="number" min="10" max="4000" step="10" size="4">
<input type="button" value="Plot it!" onclick="pspiral();"> <br>
<h3> Polyspiral</h3>
<canvas id="cvsId" width="640" height="640" style="border: 2px inset;"></canvas>
</body>
</html>
|
http://rosettacode.org/wiki/Polyspiral
|
Polyspiral
|
A Polyspiral is a spiral made of multiple line segments, whereby each segment is larger (or smaller) than the previous one by a given amount. Each segment also changes direction at a given angle.
Task
Animate a series of polyspirals, by drawing a complete spiral then incrementing the angle, and (after clearing the background) drawing the next, and so on. Every spiral will be a frame of the animation. The animation may stop as it goes full circle or continue indefinitely. The given input values may be varied.
If animation is not practical in your programming environment, you may show a single frame instead.
Pseudo code
set incr to 0.0
// animation loop
WHILE true
incr = (incr + 0.05) MOD 360
x = width / 2
y = height / 2
length = 5
angle = incr
// spiral loop
FOR 1 TO 150
drawline
change direction by angle
length = length + 3
angle = (angle + incr) MOD 360
ENDFOR
|
#Julia
|
Julia
|
using Gtk, Graphics, Colors
const can = @GtkCanvas()
const win = GtkWindow(can, "Polyspiral", 360, 360)
const drawiters = 72
const colorseq = [colorant"blue", colorant"red", colorant"green", colorant"black", colorant"gold"]
const angleiters = [0, 0, 0]
const angles = [75, 100, 135, 160]
Base.length(v::Vec2) = sqrt(v.x * v.x + v.y * v.y)
function drawline(ctx, p1, p2, color, width=1)
move_to(ctx, p1.x, p1.y)
set_source(ctx, color)
line_to(ctx, p2.x, p2.y)
set_line_width(ctx, width)
stroke(ctx)
end
@guarded draw(can) do widget
δ(r, θ) = Vec2(r * cospi(θ/180), r * sinpi(θ/180))
nextpoint(p, r, θ) = (dp = δ(r, θ); Point(p.x + dp.x, p.y + dp.y))
colorindex = (angleiters[1] % 5) + 1
colr = colorseq[colorindex]
ctx = getgc(can)
h = height(can)
w = width(can)
x = 0.5 * w
y = 0.5 * h
θ = angleiters[2] * rand() * 3
δθ = angleiters[2]
r = 5
δr = 3
p1 = Point(x, y)
for i in 1:drawiters
if angleiters[3] == 0
set_source(ctx, colorant"gray90")
rectangle(ctx, 0, 0, w, h)
fill(ctx)
continue
end
p2 = nextpoint(p1, r, θ)
drawline(ctx, p1, p2, colr, 2)
θ = θ + δθ
r = r + δr
p1 = p2
end
end
show(can)
while true
angleiters[2] = angles[angleiters[1] % 3 + 1]
angleiters[1] += 1
angleiters[3] = angleiters[3] == 0 ? 1 : 0
draw(can)
yield()
sleep(0.5)
end
|
http://rosettacode.org/wiki/Polynomial_regression
|
Polynomial regression
|
Find an approximating polynomial of known degree for a given data.
Example:
For input data:
x = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
y = {1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321};
The approximating polynomial is:
3 x2 + 2 x + 1
Here, the polynomial's coefficients are (3, 2, 1).
This task is intended as a subtask for Measure relative performance of sorting algorithms implementations.
|
#C.23
|
C#
|
public static double[] Polyfit(double[] x, double[] y, int degree)
{
// Vandermonde matrix
var v = new DenseMatrix(x.Length, degree + 1);
for (int i = 0; i < v.RowCount; i++)
for (int j = 0; j <= degree; j++) v[i, j] = Math.Pow(x[i], j);
var yv = new DenseVector(y).ToColumnMatrix();
QR<double> qr = v.QR();
// Math.Net doesn't have an "economy" QR, so:
// cut R short to square upper triangle, then recompute Q
var r = qr.R.SubMatrix(0, degree + 1, 0, degree + 1);
var q = v.Multiply(r.Inverse());
var p = r.Inverse().Multiply(q.TransposeThisAndMultiply(yv));
return p.Column(0).ToArray();
}
|
http://rosettacode.org/wiki/Power_set
|
Power set
|
A set is a collection (container) of certain values,
without any particular order, and no repeated values.
It corresponds with a finite set in mathematics.
A set can be implemented as an associative array (partial mapping)
in which the value of each key-value pair is ignored.
Given a set S, the power set (or powerset) of S, written P(S), or 2S, is the set of all subsets of S.
Task
By using a library or built-in set type, or by defining a set type with necessary operations, write a function with a set S as input that yields the power set 2S of S.
For example, the power set of {1,2,3,4} is
{{}, {1}, {2}, {1,2}, {3}, {1,3}, {2,3}, {1,2,3}, {4}, {1,4}, {2,4}, {1,2,4}, {3,4}, {1,3,4}, {2,3,4}, {1,2,3,4}}.
For a set which contains n elements, the corresponding power set has 2n elements, including the edge cases of empty set.
The power set of the empty set is the set which contains itself (20 = 1):
P
{\displaystyle {\mathcal {P}}}
(
∅
{\displaystyle \varnothing }
) = {
∅
{\displaystyle \varnothing }
}
And the power set of the set which contains only the empty set, has two subsets, the empty set and the set which contains the empty set (21 = 2):
P
{\displaystyle {\mathcal {P}}}
({
∅
{\displaystyle \varnothing }
}) = {
∅
{\displaystyle \varnothing }
, {
∅
{\displaystyle \varnothing }
} }
Extra credit: Demonstrate that your language supports these last two powersets.
|
#AWK
|
AWK
|
cat power_set.awk
#!/usr/local/bin/gawk -f
# User defined function
function tochar(l,n, r) {
while (l) { n--; if (l%2 != 0) r = r sprintf(" %c ",49+n); l = int(l/2) }; return r
}
# For each input
{ for (i=0;i<=2^NF-1;i++) if (i == 0) printf("empty\n"); else printf("(%s)\n",tochar(i,NF)) }
|
http://rosettacode.org/wiki/Primality_by_trial_division
|
Primality by trial division
|
Task
Write a boolean function that tells whether a given integer is prime.
Remember that 1 and all non-positive numbers are not prime.
Use trial division.
Even numbers greater than 2 may be eliminated right away.
A loop from 3 to √ n will suffice, but other loops are allowed.
Related tasks
count in factors
prime decomposition
AKS test for primes
factors of an integer
Sieve of Eratosthenes
factors of a Mersenne number
trial factoring of a Mersenne number
partition an integer X into N primes
sequence of primes by Trial Division
|
#Arturo
|
Arturo
|
isPrime?: function [n][
if n=2 -> return true
if n=3 -> return true
if or? n=<1 0=n%2 -> return false
high: to :integer sqrt n
loop high..2 .step: 3 'i [
if 0=n%i -> return false
]
return true
]
loop 1..20 'i [
print ["isPrime?" i "=" isPrime? i ]
]
|
http://rosettacode.org/wiki/Price_fraction
|
Price fraction
|
A friend of mine runs a pharmacy. He has a specialized function in his Dispensary application which receives a decimal value of currency and replaces it to a standard value. This value is regulated by a government department.
Task
Given a floating point value between 0.00 and 1.00, rescale according to the following table:
>= 0.00 < 0.06 := 0.10
>= 0.06 < 0.11 := 0.18
>= 0.11 < 0.16 := 0.26
>= 0.16 < 0.21 := 0.32
>= 0.21 < 0.26 := 0.38
>= 0.26 < 0.31 := 0.44
>= 0.31 < 0.36 := 0.50
>= 0.36 < 0.41 := 0.54
>= 0.41 < 0.46 := 0.58
>= 0.46 < 0.51 := 0.62
>= 0.51 < 0.56 := 0.66
>= 0.56 < 0.61 := 0.70
>= 0.61 < 0.66 := 0.74
>= 0.66 < 0.71 := 0.78
>= 0.71 < 0.76 := 0.82
>= 0.76 < 0.81 := 0.86
>= 0.81 < 0.86 := 0.90
>= 0.86 < 0.91 := 0.94
>= 0.91 < 0.96 := 0.98
>= 0.96 < 1.01 := 1.00
|
#C.2B.2B
|
C++
|
#include <iostream>
#include <cmath>
int main( ) {
double froms[ ] = { 0.00 , 0.06 , 0.11 , 0.16 , 0.21 , 0.26 ,
0.31 , 0.36 , 0.41 , 0.46 , 0.51 , 0.56 , 0.61 , 0.66 ,
0.71 , 0.76 , 0.81 , 0.86 , 0.91 , 0.96 } ;
double tos[ ] = { 0.06 , 0.11 , 0.16 , 0.21 , 0.26 , 0.31 ,
0.36 , 0.41 , 0.46 , 0.51 , 0.56 , 0.61 , 0.66 , 0.71 ,
0.76 , 0.81 , 0.86 , 0.91 , 0.96 , 1.01 } ;
double replacements [] = { 0.10 , 0.18 , 0.26 , 0.32 , 0.38 ,
0.44 , 0.50 , 0.54 , 0.58 , 0.62 , 0.66 , 0.70 , 0.74 ,
0.78 , 0.82 , 0.86 , 0.90 , 0.94 , 0.98 , 1.00 } ;
double number = 0.1 ;
std::cout << "Enter a fractional number between 0 and 1 ( 0 to end )!\n" ;
std::cin >> number ;
while ( number != 0 ) {
if ( number < 0 || number > 1 ) {
std::cerr << "Error! Only positive values between 0 and 1 are allowed!\n" ;
return 1 ;
}
int n = 0 ;
while ( ! ( number >= froms[ n ] && number < tos[ n ] ) )
n++ ;
std::cout << "-->" << replacements[ n ] << '\n' ;
std::cout << "Enter a fractional number ( 0 to end )!\n" ;
std::cin >> number ;
}
return 0 ;
}
|
http://rosettacode.org/wiki/Proper_divisors
|
Proper divisors
|
The proper divisors of a positive integer N are those numbers, other than N itself, that divide N without remainder.
For N > 1 they will always include 1, but for N == 1 there are no proper divisors.
Examples
The proper divisors of 6 are 1, 2, and 3.
The proper divisors of 100 are 1, 2, 4, 5, 10, 20, 25, and 50.
Task
Create a routine to generate all the proper divisors of a number.
use it to show the proper divisors of the numbers 1 to 10 inclusive.
Find a number in the range 1 to 20,000 with the most proper divisors. Show the number and just the count of how many proper divisors it has.
Show all output here.
Related tasks
Amicable pairs
Abundant, deficient and perfect number classifications
Aliquot sequence classifications
Factors of an integer
Prime decomposition
|
#Fermat
|
Fermat
|
Func Divisors(n) =
[d]:=[(1)]; {start divisor list with just 1, which is a divisor of everything}
for i = 2 to n\2 do {loop through possible divisors of n}
if Divides(i, n) then [d]:=[d]_[(i)] fi
od;
.;
for n = 1 to 10 do
Divisors(n);
!!(n,' ',[d);
od;
record:=0;
champ:=1;
for n=2 to 20000 do
Divisors(n);
m:=Cols[d]; {this gets the length of the array}
if m > record then
champ:=n;
record:=m;
fi;
od;
!!('The number up to 20,000 with the most divisors was ',champ,' with ',record,' divisors.');
|
http://rosettacode.org/wiki/Probabilistic_choice
|
Probabilistic choice
|
Given a mapping between items and their required probability of occurrence, generate a million items randomly subject to the given probabilities and compare the target probability of occurrence versus the generated values.
The total of all the probabilities should equal one. (Because floating point arithmetic is involved, this is subject to rounding errors).
aleph 1/5.0
beth 1/6.0
gimel 1/7.0
daleth 1/8.0
he 1/9.0
waw 1/10.0
zayin 1/11.0
heth 1759/27720 # adjusted so that probabilities add to 1
Related task
Random number generator (device)
|
#Java
|
Java
|
public class Prob{
static long TRIALS= 1000000;
private static class Expv{
public String name;
public int probcount;
public double expect;
public double mapping;
public Expv(String name, int probcount, double expect, double mapping){
this.name= name;
this.probcount= probcount;
this.expect= expect;
this.mapping= mapping;
}
}
static Expv[] items=
{new Expv("aleph", 0, 0.0, 0.0), new Expv("beth", 0, 0.0, 0.0),
new Expv("gimel", 0, 0.0, 0.0),
new Expv("daleth", 0, 0.0, 0.0),
new Expv("he", 0, 0.0, 0.0), new Expv("waw", 0, 0.0, 0.0),
new Expv("zayin", 0, 0.0, 0.0),
new Expv("heth", 0, 0.0, 0.0)};
public static void main(String[] args){
int i, j;
double rnum, tsum= 0.0;
for(i= 0, rnum= 5.0;i < 7;i++, rnum+= 1.0){
items[i].expect= 1.0 / rnum;
tsum+= items[i].expect;
}
items[7].expect= 1.0 - tsum;
items[0].mapping= 1.0 / 5.0;
for(i= 1;i < 7;i++){
items[i].mapping= items[i - 1].mapping + 1.0 / ((double)i + 5.0);
}
items[7].mapping= 1.0;
for(i= 0;i < TRIALS;i++){
rnum= Math.random();
for(j= 0;j < 8;j++){
if(rnum < items[j].mapping){
items[j].probcount++;
break;
}
}
}
System.out.printf("Trials: %d\n", TRIALS);
System.out.printf("Items: ");
for(i= 0;i < 8;i++)
System.out.printf("%-8s ", items[i].name);
System.out.printf("\nTarget prob.: ");
for(i= 0;i < 8;i++)
System.out.printf("%8.6f ", items[i].expect);
System.out.printf("\nAttained prob.: ");
for(i= 0;i < 8;i++)
System.out.printf("%8.6f ", (double)(items[i].probcount)
/ (double)TRIALS);
System.out.printf("\n");
}
}
|
http://rosettacode.org/wiki/Priority_queue
|
Priority queue
|
A priority queue is somewhat similar to a queue, with an important distinction: each item is added to a priority queue with a priority level, and will be later removed from the queue with the highest priority element first. That is, the items are (conceptually) stored in the queue in priority order instead of in insertion order.
Task
Create a priority queue. The queue must support at least two operations:
Insertion. An element is added to the queue with a priority (a numeric value).
Top item removal. Deletes the element or one of the elements with the current top priority and return it.
Optionally, other operations may be defined, such as peeking (find what current top priority/top element is), merging (combining two priority queues into one), etc.
To test your implementation, insert a number of elements into the queue, each with some random priority.
Then dequeue them sequentially; now the elements should be sorted by priority.
You can use the following task/priority items as input data:
Priority Task
══════════ ════════════════
3 Clear drains
4 Feed cat
5 Make tea
1 Solve RC tasks
2 Tax return
The implementation should try to be efficient. A typical implementation has O(log n) insertion and extraction time, where n is the number of items in the queue.
You may choose to impose certain limits such as small range of allowed priority levels, limited capacity, etc. If so, discuss the reasons behind it.
|
#Groovy
|
Groovy
|
import groovy.transform.Canonical
@Canonical
class Task implements Comparable<Task> {
int priority
String name
int compareTo(Task o) { priority <=> o?.priority }
}
new PriorityQueue<Task>().with {
add new Task(priority: 3, name: 'Clear drains')
add new Task(priority: 4, name: 'Feed cat')
add new Task(priority: 5, name: 'Make tea')
add new Task(priority: 1, name: 'Solve RC tasks')
add new Task(priority: 2, name: 'Tax return')
while (!empty) { println remove() }
}
|
http://rosettacode.org/wiki/Problem_of_Apollonius
|
Problem of Apollonius
|
Task
Implement a solution to the Problem of Apollonius (description on Wikipedia) which is the problem of finding the circle that is tangent to three specified circles (colored black in the diagram below to the right).
There is an algebraic solution which is pretty straightforward.
The solutions to the example in the code are shown in the diagram (below and to the right).
The red circle is "internally tangent" to all three black circles, and the green circle is "externally tangent" to all three black circles.
|
#Racket
|
Racket
|
#lang slideshow
(struct circle (x y r) #:prefab)
(define (apollonius c1 c2 c3 s1 s2 s3)
(define x1 (circle-x c1))
(define y1 (circle-y c1))
(define r1 (circle-r c1))
(define x2 (circle-x c2))
(define y2 (circle-y c2))
(define r2 (circle-r c2))
(define x3 (circle-x c3))
(define y3 (circle-y c3))
(define r3 (circle-r c3))
(define v11 (- (* 2 x2) (* 2 x1)))
(define v12 (- (* 2 y2) (* 2 y1)))
(define v13 (+ (- (* x1 x1) (* x2 x2))
(- (* y1 y1) (* y2 y2))
(- (* r2 r2) (* r1 r1))))
(define v14 (- (* 2 s2 r2) (* 2 s1 r1)))
(define v21 (- (* 2 x3) (* 2 x2)))
(define v22 (- (* 2 y3) (* 2 y2)))
(define v23 (+ (- (* x2 x2) (* x3 x3))
(- (* y2 y2) (* y3 y3))
(- (* r3 r3) (* r2 r2))))
(define v24 (- (* 2 s3 r3) (* 2 s2 r2)))
(define w12 (/ v12 v11))
(define w13 (/ v13 v11))
(define w14 (/ v14 v11))
(define w22 (- (/ v22 v21) w12))
(define w23 (- (/ v23 v21) w13))
(define w24 (- (/ v24 v21) w14))
(define P (- (/ w23 w22)))
(define Q (/ w24 w22))
(define M (- (+ (* w12 P) w13)))
(define N (- w14 (* w12 Q)))
(define a (+ (* N N) (* Q Q) -1))
(define b (+ (- (* 2 M N) (* 2 N x1))
(- (* 2 P Q) (* 2 Q y1))
(* 2 s1 r1)))
(define c (- (+ (* x1 x1) (* M M) (* P P) (* y1 y1))
(+ (* 2 M x1) (* 2 P y1) (* r1 r1))))
(define D (- (* b b) (* 4 a c)))
(define rs (/ (- (+ b (sqrt D))) (* 2 a)))
(define xs (+ M (* N rs)))
(define ys (+ P (* Q rs)))
(circle xs ys rs))
(define c1 (circle 0.0 0.0 1.0))
(define c2 (circle 4.0 0.0 1.0))
(define c3 (circle 2.0 4.0 2.0))
;; print solutions
(apollonius c1 c2 c3 1.0 1.0 1.0)
(apollonius c1 c2 c3 -1.0 -1.0 -1.0)
;; visualize solutions
(require racket/gui/base)
(define (show-circles . circles+colors)
(define f (new frame% [label "Apollonius"] [width 300] [height 300]))
(define c
(new canvas% [parent f]
[paint-callback
(lambda (canvas dc)
(send* dc (set-origin 100 100)
(set-scale 20 20)
(set-pen "black" 1/10 'solid)
(set-brush "white" 'transparent))
(for ([x circles+colors])
(if (string? x)
(send dc set-pen x 1/5 'solid)
(let ([x (circle-x x)] [y (circle-y x)] [r (circle-r x)])
(send dc draw-ellipse (- x r) (- y r) (* 2 r) (* 2 r))))))]))
(send f show #t))
(show-circles "black" c1 c2 c3
"green" (apollonius c1 c2 c3 1.0 1.0 1.0)
"red" (apollonius c1 c2 c3 -1.0 -1.0 -1.0))
|
http://rosettacode.org/wiki/Problem_of_Apollonius
|
Problem of Apollonius
|
Task
Implement a solution to the Problem of Apollonius (description on Wikipedia) which is the problem of finding the circle that is tangent to three specified circles (colored black in the diagram below to the right).
There is an algebraic solution which is pretty straightforward.
The solutions to the example in the code are shown in the diagram (below and to the right).
The red circle is "internally tangent" to all three black circles, and the green circle is "externally tangent" to all three black circles.
|
#Raku
|
Raku
|
class Circle {
has $.x;
has $.y;
has $.r;
method gist { sprintf "%s =%7.3f " xx 3, (:$!x,:$!y,:$!r)».kv }
}
sub circle($x,$y,$r) { Circle.new: :$x, :$y, :$r }
sub solve-Apollonius([\c1, \c2, \c3], [\s1, \s2, \s3]) {
my \𝑣11 = 2 * c2.x - 2 * c1.x;
my \𝑣12 = 2 * c2.y - 2 * c1.y;
my \𝑣13 = c1.x² - c2.x² + c1.y² - c2.y² - c1.r² + c2.r²;
my \𝑣14 = 2 * s2 * c2.r - 2 * s1 * c1.r;
my \𝑣21 = 2 * c3.x - 2 * c2.x;
my \𝑣22 = 2 * c3.y - 2 * c2.y;
my \𝑣23 = c2.x² - c3.x² + c2.y² - c3.y² - c2.r² + c3.r²;
my \𝑣24 = 2 * s3 * c3.r - 2 * s2 * c2.r;
my \𝑤12 = 𝑣12 / 𝑣11;
my \𝑤13 = 𝑣13 / 𝑣11;
my \𝑤14 = 𝑣14 / 𝑣11;
my \𝑤22 = 𝑣22 / 𝑣21 - 𝑤12;
my \𝑤23 = 𝑣23 / 𝑣21 - 𝑤13;
my \𝑤24 = 𝑣24 / 𝑣21 - 𝑤14;
my \𝑃 = -𝑤23 / 𝑤22;
my \𝑄 = 𝑤24 / 𝑤22;
my \𝑀 = -𝑤12 * 𝑃 - 𝑤13;
my \𝑁 = 𝑤14 - 𝑤12 * 𝑄;
my \𝑎 = 𝑁² + 𝑄² - 1;
my \𝑏 = 2 * 𝑀 * 𝑁 - 2 * 𝑁 * c1.x + 2 * 𝑃 * 𝑄 - 2 * 𝑄 * c1.y + 2 * s1 * c1.r;
my \𝑐 = c1.x² + 𝑀² - 2 * 𝑀 * c1.x + 𝑃² + c1.y² - 2 * 𝑃 * c1.y - c1.r²;
my \𝐷 = 𝑏² - 4 * 𝑎 * 𝑐;
my \rs = (-𝑏 - sqrt 𝐷) / (2 * 𝑎);
my \xs = 𝑀 + 𝑁 * rs;
my \ys = 𝑃 + 𝑄 * rs;
circle(xs, ys, rs);
}
my @c = circle(0, 0, 1), circle(4, 0, 1), circle(2, 4, 2);
for ([X] [-1,1] xx 3) -> @i {
say (solve-Apollonius @c, @i).gist;
}
|
http://rosettacode.org/wiki/Program_name
|
Program name
|
The task is to programmatically obtain the name used to invoke the program. (For example determine whether the user ran "python hello.py", or "python hellocaller.py", a program importing the code from "hello.py".)
Sometimes a multiline shebang is necessary in order to provide the script name to a language's internal ARGV.
See also Command-line arguments
Examples from GitHub.
|
#Seed7
|
Seed7
|
$ include "seed7_05.s7i";
const proc: main is func
local
var integer: i is 0;
begin
writeln("Program path: " <& path(PROGRAM));
writeln("Program directory: " <& dir(PROGRAM));
writeln("Program file: " <& file(PROGRAM));
end func;
|
http://rosettacode.org/wiki/Program_name
|
Program name
|
The task is to programmatically obtain the name used to invoke the program. (For example determine whether the user ran "python hello.py", or "python hellocaller.py", a program importing the code from "hello.py".)
Sometimes a multiline shebang is necessary in order to provide the script name to a language's internal ARGV.
See also Command-line arguments
Examples from GitHub.
|
#Sidef
|
Sidef
|
say __MAIN__;
if (__MAIN__ != __FILE__) {
say "This file has been included!";
}
|
http://rosettacode.org/wiki/Pythagorean_triples
|
Pythagorean triples
|
A Pythagorean triple is defined as three positive integers
(
a
,
b
,
c
)
{\displaystyle (a,b,c)}
where
a
<
b
<
c
{\displaystyle a<b<c}
, and
a
2
+
b
2
=
c
2
.
{\displaystyle a^{2}+b^{2}=c^{2}.}
They are called primitive triples if
a
,
b
,
c
{\displaystyle a,b,c}
are co-prime, that is, if their pairwise greatest common divisors
g
c
d
(
a
,
b
)
=
g
c
d
(
a
,
c
)
=
g
c
d
(
b
,
c
)
=
1
{\displaystyle {\rm {gcd}}(a,b)={\rm {gcd}}(a,c)={\rm {gcd}}(b,c)=1}
.
Because of their relationship through the Pythagorean theorem, a, b, and c are co-prime if a and b are co-prime (
g
c
d
(
a
,
b
)
=
1
{\displaystyle {\rm {gcd}}(a,b)=1}
).
Each triple forms the length of the sides of a right triangle, whose perimeter is
P
=
a
+
b
+
c
{\displaystyle P=a+b+c}
.
Task
The task is to determine how many Pythagorean triples there are with a perimeter no larger than 100 and the number of these that are primitive.
Extra credit
Deal with large values. Can your program handle a maximum perimeter of 1,000,000? What about 10,000,000? 100,000,000?
Note: the extra credit is not for you to demonstrate how fast your language is compared to others; you need a proper algorithm to solve them in a timely manner.
Related tasks
Euler's sum of powers conjecture
List comprehensions
Pythagorean quadruples
|
#Raku
|
Raku
|
constant limit = 100;
for [X] [^limit] xx 3 -> (\a, \b, \c) {
say [a, b, c] if a < b < c and a**2 + b**2 == c**2
}
|
http://rosettacode.org/wiki/Program_termination
|
Program termination
|
Task
Show the syntax for a complete stoppage of a program inside a conditional.
This includes all threads/processes which are part of your program.
Explain the cleanup (or lack thereof) caused by the termination (allocated memory, database connections, open files, object finalizers/destructors, run-on-exit hooks, etc.).
Unless otherwise described, no special cleanup outside that provided by the operating system is provided.
|
#PureBasic
|
PureBasic
|
If problem = 1
End
EndIf
|
http://rosettacode.org/wiki/Program_termination
|
Program termination
|
Task
Show the syntax for a complete stoppage of a program inside a conditional.
This includes all threads/processes which are part of your program.
Explain the cleanup (or lack thereof) caused by the termination (allocated memory, database connections, open files, object finalizers/destructors, run-on-exit hooks, etc.).
Unless otherwise described, no special cleanup outside that provided by the operating system is provided.
|
#Python
|
Python
|
import sys
if problem:
sys.exit(1)
|
http://rosettacode.org/wiki/Primality_by_Wilson%27s_theorem
|
Primality by Wilson's theorem
|
Task
Write a boolean function that tells whether a given integer is prime using Wilson's theorem.
By Wilson's theorem, a number p is prime if and only if p divides (p - 1)! + 1.
Remember that 1 and all non-positive integers are not prime.
See also
Cut-the-knot: Wilson's theorem.
Wikipedia: Wilson's theorem
|
#Pascal
|
Pascal
|
program PrimesByWilson;
uses SysUtils;
(* Function to return whether 32-bit unsigned n is prime.
Applies Wilson's theorem with full calculation of (n - 1)! modulo n. *)
function WilsonFullCalc( n : longword) : boolean;
var
f, m : longword;
begin
if n < 2 then begin
result := false; exit;
end;
f := 1;
for m := 2 to n - 1 do begin
f := (uint64(f) * uint64(m)) mod n; // typecast is needed
end;
result := (f = n - 1);
end;
(* Function to return whether 32-bit unsigned n is prime.
Applies Wilson's theorem with a short cut. *)
function WilsonShortCut( n : longword) : boolean;
var
f, g, h, m, m2inc, r : longword;
begin
if n < 2 then begin
result := false; exit;
end;
(* Part 1: Factorial (modulo n) of floor(sqrt(n)) *)
f := 1;
m := 1;
m2inc := 3; // (m + 1)^2 - m^2
// Want to loop while m^2 <= n, but if n is close to 2^32 - 1 then least
// m^2 > n overflows 32 bits. Work round this by looking at r = n - m^2.
r := n - 1;
while r >= m2inc do begin
inc(m);
f := (uint64(f) * uint64(m)) mod n;
dec( r, m2inc);
inc( m2inc, 2);
end;
(* Part 2: Euclid's algorithm: at the end, h = HCF( f, n) *)
h := n;
while f <> 0 do begin
g := h mod f;
h := f;
f := g;
end;
result := (h = 1);
end;
type TPrimalityTest = function( n : longword) : boolean;
procedure ShowPrimes( isPrime : TPrimalityTest;
minValue, maxValue : longword);
var
n : longword;
begin
WriteLn( 'Primes in ', minValue, '..', maxValue);
for n := minValue to maxValue do
if isPrime(n) then Write(' ', n);
WriteLn;
end;
(* Main routine *)
begin
WriteLn( 'By full calculation:');
ShowPrimes( @WilsonFullCalc, 1, 100);
ShowPrimes( @WilsonFullCalc, 1000, 1100);
WriteLn; WriteLn( 'Using the short cut:');
ShowPrimes( @WilsonShortCut, 1, 100);
ShowPrimes( @WilsonShortCut, 1000, 1100);
ShowPrimes( @WilsonShortCut, 4294967195, 4294967295 {= 2^32 - 1});
end.
|
http://rosettacode.org/wiki/Prime_conspiracy
|
Prime conspiracy
|
A recent discovery, quoted from Quantamagazine (March 13, 2016):
Two mathematicians have uncovered a simple, previously unnoticed property of
prime numbers — those numbers that are divisible only by 1 and themselves.
Prime numbers, it seems, have decided preferences about the final digits of
the primes that immediately follow them.
and
This conspiracy among prime numbers seems, at first glance, to violate a
longstanding assumption in number theory: that prime numbers behave much
like random numbers.
─── (original authors from Stanford University):
─── Kannan Soundararajan and Robert Lemke Oliver
The task is to check this assertion, modulo 10.
Lets call i -> j a transition if i is the last decimal digit of a prime, and j the last decimal digit of the following prime.
Task
Considering the first one million primes. Count, for any pair of successive primes, the number of transitions i -> j and print them along with their relative frequency, sorted by i .
You can see that, for a given i , frequencies are not evenly distributed.
Observation
(Modulo 10), primes whose last digit is 9 "prefer" the digit 1 to the digit 9, as its following prime.
Extra credit
Do the same for one hundred million primes.
Example for 10,000 primes
10000 first primes. Transitions prime % 10 → next-prime % 10.
1 → 1 count: 365 frequency: 3.65 %
1 → 3 count: 833 frequency: 8.33 %
1 → 7 count: 889 frequency: 8.89 %
1 → 9 count: 397 frequency: 3.97 %
2 → 3 count: 1 frequency: 0.01 %
3 → 1 count: 529 frequency: 5.29 %
3 → 3 count: 324 frequency: 3.24 %
3 → 5 count: 1 frequency: 0.01 %
3 → 7 count: 754 frequency: 7.54 %
3 → 9 count: 907 frequency: 9.07 %
5 → 7 count: 1 frequency: 0.01 %
7 → 1 count: 655 frequency: 6.55 %
7 → 3 count: 722 frequency: 7.22 %
7 → 7 count: 323 frequency: 3.23 %
7 → 9 count: 808 frequency: 8.08 %
9 → 1 count: 935 frequency: 9.35 %
9 → 3 count: 635 frequency: 6.35 %
9 → 7 count: 541 frequency: 5.41 %
9 → 9 count: 379 frequency: 3.79 %
|
#Python
|
Python
|
def isPrime(n):
if n < 2:
return False
if n % 2 == 0:
return n == 2
if n % 3 == 0:
return n == 3
d = 5
while d * d <= n:
if n % d == 0:
return False
d += 2
if n % d == 0:
return False
d += 4
return True
def generatePrimes():
yield 2
yield 3
p = 5
while p > 0:
if isPrime(p):
yield p
p += 2
if isPrime(p):
yield p
p += 4
g = generatePrimes()
transMap = {}
prev = None
limit = 1000000
for _ in xrange(limit):
prime = next(g)
if prev:
transition = (prev, prime %10)
if transition in transMap:
transMap[transition] += 1
else:
transMap[transition] = 1
prev = prime % 10
print "First {:,} primes. Transitions prime % 10 > next-prime % 10.".format(limit)
for trans in sorted(transMap):
print "{0} -> {1} count {2:5} frequency: {3}%".format(trans[0], trans[1], transMap[trans], 100.0 * transMap[trans] / limit)
|
http://rosettacode.org/wiki/Prime_decomposition
|
Prime decomposition
|
The prime decomposition of a number is defined as a list of prime numbers
which when all multiplied together, are equal to that number.
Example
12 = 2 × 2 × 3, so its prime decomposition is {2, 2, 3}
Task
Write a function which returns an array or collection which contains the prime decomposition of a given number
n
{\displaystyle n}
greater than 1.
If your language does not have an isPrime-like function available,
you may assume that you have a function which determines
whether a number is prime (note its name before your code).
If you would like to test code from this task, you may use code from trial division or the Sieve of Eratosthenes.
Note: The program must not be limited by the word size of your computer or some other artificial limit; it should work for any number regardless of size (ignoring the physical limits of RAM etc).
Related tasks
count in factors
factors of an integer
Sieve of Eratosthenes
primality by trial division
factors of a Mersenne number
trial factoring of a Mersenne number
partition an integer X into N primes
sequence of primes by Trial Division
|
#C.23
|
C#
|
using System;
using System.Collections.Generic;
namespace PrimeDecomposition
{
class Program
{
static void Main(string[] args)
{
GetPrimes(12);
}
static List<int> GetPrimes(decimal n)
{
List<int> storage = new List<int>();
while (n > 1)
{
int i = 1;
while (true)
{
if (IsPrime(i))
{
if (((decimal)n / i) == Math.Round((decimal) n / i))
{
n /= i;
storage.Add(i);
break;
}
}
i++;
}
}
return storage;
}
static bool IsPrime(int n)
{
if (n <= 1) return false;
for (int i = 2; i <= Math.Sqrt(n); i++)
if (n % i == 0) return false;
return true;
}
}
}
|
http://rosettacode.org/wiki/Pointers_and_references
|
Pointers and references
|
Basic Data Operation
This is a basic data operation. It represents a fundamental action on a basic data type.
You may see other such operations in the Basic Data Operations category, or:
Integer Operations
Arithmetic |
Comparison
Boolean Operations
Bitwise |
Logical
String Operations
Concatenation |
Interpolation |
Comparison |
Matching
Memory Operations
Pointers & references |
Addresses
In this task, the goal is to demonstrate common operations on pointers and references. These examples show pointer operations on the stack, which can be dangerous and is rarely done. Pointers and references are commonly used along with Memory allocation on the heap.
|
#AutoHotkey
|
AutoHotkey
|
VarSetCapacity(var, 100) ; allocate memory
NumPut(87, var, 0, "Char") ; store 87 at offset 0
MsgBox % NumGet(var, 0, "Char") ; get character at offset 0 (87)
MsgBox % &var ; address of contents pointed to by var structure
MsgBox % *&var ; integer at address of var contents (87)
|
http://rosettacode.org/wiki/Pointers_and_references
|
Pointers and references
|
Basic Data Operation
This is a basic data operation. It represents a fundamental action on a basic data type.
You may see other such operations in the Basic Data Operations category, or:
Integer Operations
Arithmetic |
Comparison
Boolean Operations
Bitwise |
Logical
String Operations
Concatenation |
Interpolation |
Comparison |
Matching
Memory Operations
Pointers & references |
Addresses
In this task, the goal is to demonstrate common operations on pointers and references. These examples show pointer operations on the stack, which can be dangerous and is rarely done. Pointers and references are commonly used along with Memory allocation on the heap.
|
#BBC_BASIC
|
BBC BASIC
|
REM Pointer to integer variable:
pointer_to_varA = ^varA%
!pointer_to_varA = 123456
PRINT !pointer_to_varA
REM Pointer to variant variable:
pointer_to_varB = ^varB
|pointer_to_varB = PI
PRINT |pointer_to_varB
REM Pointer to procedure:
PROCmyproc : REM conventional call to initialise
pointer_to_myproc = ^PROCmyproc
PROC(pointer_to_myproc)
REM Pointer to function:
pointer_to_myfunc = ^FNmyfunc
PRINT FN(pointer_to_myfunc)
END
DEF PROCmyproc
PRINT "Executing myproc"
ENDPROC
DEF FNmyfunc
= "Returned from myfunc"
|
http://rosettacode.org/wiki/Plot_coordinate_pairs
|
Plot coordinate pairs
|
Task
Plot a function represented as x, y numerical arrays.
Post the resulting image for the following input arrays (taken from Python's Example section on Time a function):
x = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
y = {2.7, 2.8, 31.4, 38.1, 58.0, 76.2, 100.5, 130.0, 149.3, 180.0};
This task is intended as a subtask for Measure relative performance of sorting algorithms implementations.
|
#AArch64_Assembly
|
AArch64 Assembly
|
/* ARM assembly AARCH64 Raspberry PI 3B */
/* program areaPlot64.s */
/*******************************************/
/* Constantes file */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly*/
.include "../includeConstantesARM64.inc"
.equ HAUTEUR, 22
.equ LARGEUR, 50
.equ MARGEGAUCHE, 10
/*******************************************/
/* Structures */
/********************************************/
/* structure for points */
.struct 0
point_posX:
.struct point_posX + 8
point_posY:
.struct point_posY + 8
point_end:
/*******************************************/
/* Initialized data */
/*******************************************/
.data
szMessError: .asciz "Number of points too large !! \n"
szCarriageReturn: .asciz "\n"
szMessMovePos: .ascii "\033[" // cursor position
posY: .byte '0'
.byte '6'
.ascii ";"
posX: .byte '0'
.byte '3'
.asciz "H*"
szMessEchelleX: .asciz "Y^ X="
szClear1: .byte 0x1B
.byte 'c' // other console clear
.byte 0
szMessPosEch: .ascii "\033[" // scale cursor position
posY1: .byte '0'
.byte '0'
.ascii ";"
posX1: .byte '0'
.byte '0'
.asciz "H"
//x = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
//y = {2.7, 2.8, 31.4, 38.1, 58.0, 76.2, 100.5, 130.0, 149.3, 180.0};
/* areas points */
tbPoints: .quad 0 // 1
.quad 27 // Data * 10 for integer operation
.quad 1 // 2
.quad 28
.quad 2 // 3
.quad 314
.quad 3 // 4
.quad 381
.quad 4 // 5
.quad 580
.quad 5 // 6
.quad 762
.quad 6 // 7
.quad 1005
.quad 7 // 8
.quad 1300
.quad 8 // 9
.quad 1493
.quad 9 // 10
.quad 1800
/*******************************************/
/* UnInitialized data */
/*******************************************/
.bss
sZoneConv: .skip 30
/*******************************************/
/* code section */
/*******************************************/
.text
.global main
main: // entry of program
ldr x0,qAdrtbPoints // area address
mov x1,10 // size
mov x2,LARGEUR
mov x3,HAUTEUR
bl plotArea
b 100f
100: // standard end of the program
mov x0, 0 // return code
mov x8,EXIT // request to exit program
svc 0 // perform the system call
qAdrsZoneConv: .quad sZoneConv
qAdrszCarriageReturn: .quad szCarriageReturn
qAdrtbPoints: .quad tbPoints
/************************************/
/* create graph */
/************************************/
/* x0 contains area points address */
/* x1 contains number points */
/* x2 contains graphic weight */
/* x3 contains graphic height */
/* REMARK : no save x9-x20 registers */
plotArea:
stp x2,lr,[sp,-16]! // save registers
stp x3,x4,[sp,-16]! // save registers
cmp x1,x2
bge 99f
mov x9,x0
mov x4,x1
ldr x10,qAdrposX
ldr x11,qAdrposY
mov x12,#0 // indice
mov x13,point_end // element area size
mov x17,0 // Y maxi
mov x19,-1 // Y Mini
1: //search mini maxi
madd x14,x12,x13,x0 // load coord Y
ldr x15,[x14,point_posY]
cmp x15,x17
csel x17,x15,x17,hi // maxi ?
cmp x15,x19
csel x19,x15,x19,lo // mini ?
add x12,x12,#1
cmp x12,x1 // end ?
blt 1b // no -> loop
// compute ratio
udiv x15,x17,x3 // ratio = maxi / height
add x15,x15,1 // for adjust
ldr x0,qAdrszClear1 // clear screen
bl affichageMess
udiv x20,x2,x4 // compute interval X = weight / number points
mov x12,0 // indice
2: // loop begin for display point
madd x14,x12,x13,x9 // charge X coord point
ldr x16,[x14,point_posX]
mul x16,x20,x12 // interval * indice
add x0,x16,MARGEGAUCHE // + left margin
mov x1,x10 // conversion ascii and store
bl convPos
ldr x18,[x14,point_posY] // charge Y coord point
udiv x18,x18,x15 // divide by ratio
sub x0,x3,x18 // inversion position ligne
mov x1,x11 // conversion ascii and store
bl convPos
ldr x0,qAdrszMessMovePos // display * at position X,Y
bl affichageMess
add x12,x12,1 // next point
cmp x12,x4 // end ?
blt 2b // no -> loop
// display left scale
// display Y Mini
mov x0,0
ldr x1,qAdrposX1
bl convPos
mov x0,HAUTEUR
ldr x1,qAdrposY1
bl convPos
ldr x0,qAdrszMessPosEch
bl affichageMess
mov x0,x19
ldr x1,qAdrsZoneConv
bl conversion10
ldr x0,qAdrsZoneConv
bl affichageMess
// display Y Maxi
mov x0,0
ldr x1,qAdrposX1
bl convPos
mov x0,0
ldr x1,qAdrposY1
bl convPos
ldr x0,qAdrszMessPosEch
bl affichageMess
mov x0,x17
ldr x1,qAdrsZoneConv
bl conversion10
ldr x0,qAdrsZoneConv
bl affichageMess
// display average value
mov x0,0
ldr x1,qAdrposX1
bl convPos
mov x0,HAUTEUR/2
add x0,x0,#1
ldr x1,qAdrposY1
bl convPos
ldr x0,qAdrszMessPosEch
bl affichageMess
lsr x0,x17,#1
ldr x1,qAdrsZoneConv
bl conversion10
ldr x0,qAdrsZoneConv
bl affichageMess
// display X scale
mov x0,0
ldr x1,qAdrposX1
bl convPos
mov x0,HAUTEUR+1
ldr x1,qAdrposY1
bl convPos
ldr x0,qAdrszMessPosEch
bl affichageMess
ldr x0,qAdrszMessEchelleX
bl affichageMess
mov x12,0 // indice
mov x19,MARGEGAUCHE
10:
udiv x20,x2,x4
madd x0,x20,x12,x19
ldr x1,qAdrposX1
bl convPos
mov x0,HAUTEUR+1
ldr x1,qAdrposY1
bl convPos
ldr x0,qAdrszMessPosEch
bl affichageMess
madd x14,x12,x13,x9 // load X coord point
ldr x0,[x14,point_posX]
ldr x1,qAdrsZoneConv
bl conversion10
ldr x0,qAdrsZoneConv
bl affichageMess
add x12,x12,1
cmp x12,x4
blt 10b
ldr x0,qAdrszCarriageReturn
bl affichageMess
mov x0,0 // return code
b 100f
99: // error
ldr x0,qAdrszMessError
bl affichageMess
mov x0,-1 // return code
100:
ldp x3,x4,[sp],16 // restaur 2 registers
ldp x2,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
qAdrszMessMovePos: .quad szMessMovePos
qAdrszClear1: .quad szClear1
qAdrposX: .quad posX
qAdrposY: .quad posY
qAdrposX1: .quad posX1
qAdrposY1: .quad posY1
qAdrszMessEchelleX: .quad szMessEchelleX
qAdrszMessPosEch: .quad szMessPosEch
qAdrszMessError: .quad szMessError
/************************************/
/* conv position in ascii and store at address */
/************************************/
/* x0 contains position */
/* x1 contains string address */
convPos:
stp x2,lr,[sp,-16]! // save registers
stp x3,x4,[sp,-16]! // save registers
mov x2,10
udiv x3,x0,x2
add x4,x3,48 // convert in ascii
strb w4,[x1] // store posX
msub x4,x3,x2,x0
add x4,x4,48
strb w4,[x1,1]
100:
ldp x3,x4,[sp],16 // restaur 2 registers
ldp x2,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/********************************************************/
/* File Include fonctions */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"
|
http://rosettacode.org/wiki/Polymorphism
|
Polymorphism
|
Task
Create two classes Point(x,y) and Circle(x,y,r) with a polymorphic function print, accessors for (x,y,r), copy constructor, assignment and destructor and every possible default constructors
|
#ALGOL_68
|
ALGOL 68
|
# Algol 68 provides for polymorphic operators but not procedures #
# define the CIRCLE and POINT modes #
MODE POINT = STRUCT( REAL x, y );
MODE CIRCLE = STRUCT( REAL x, y, r );
# PRINT operator #
OP PRINT = ( POINT p )VOID: print( ( "Point(", x OF p, ",", y OF p, ")" ) );
OP PRINT = ( CIRCLE c )VOID: print( ( "Circle(", r OF c, " @ ", x OF c, ",", y OF c, ")" ) );
# getters #
OP XCOORD = ( POINT p )REAL: x OF p;
OP YCOORD = ( POINT p )REAL: y OF p;
OP XCOORD = ( CIRCLE c )REAL: x OF c;
OP YCOORD = ( CIRCLE c )REAL: y OF c;
OP RADIUS = ( CIRCLE c )REAL: r OF c;
# setters #
# the setters are dyadic operators so need a priority - we make them lowest #
# priority, like PLUSAB etc. #
# They could have the same names as the getters but this seems clearer? #
PRIO SETXCOORD = 1
, SETYCOORD = 1
, SETRADIUS = 1
;
# the setters return the POINT/CIRCLE being modified so we can write e.g. #
# "PRINT ( p SETXCOORD 3 )" #
OP SETXCOORD = ( REF POINT p, REAL x )REF POINT: ( x OF p := x; p );
OP SETYCOORD = ( REF POINT p, REAL y )REF POINT: ( y OF p := y; p );
OP SETXCOORD = ( REF CIRCLE c, REAL x )REF CIRCLE: ( x OF c := x; c );
OP SETYCOORD = ( REF CIRCLE c, REAL y )REF CIRCLE: ( y OF c := y; c );
OP SETRADIUS = ( REF CIRCLE c, REAL r )REF CIRCLE: ( r OF c := r; c );
# operands of an operator are not automatically coerced from INT to REAL so #
# we also need these operators #
OP SETXCOORD = ( REF POINT p, INT x )REF POINT: ( x OF p := x; p );
OP SETYCOORD = ( REF POINT p, INT y )REF POINT: ( y OF p := y; p );
OP SETXCOORD = ( REF CIRCLE c, INT x )REF CIRCLE: ( x OF c := x; c );
OP SETYCOORD = ( REF CIRCLE c, INT y )REF CIRCLE: ( y OF c := y; c );
OP SETRADIUS = ( REF CIRCLE c, INT r )REF CIRCLE: ( r OF c := r; c );
# copy constructors #
# A copy constructor is not needed as assignment will generate a copy #
# e.g.: "POINT pa, pb; pa := ...; pb := pa; ..." will make pb a copy of pa #
# assignment #
# It is not possible to redefine the assignment "operator" in Algol 68 but #
# assignment is automatically provided so no code need be written for e.g. #
# "CIRCLE c1 := ...." #
# destructors #
# Algol 68 does not include destructors. A particular postlude could, #
# in theory be provided if specific cleanup was requried, but this would #
# occur at the end of the program, not at the end of the lifetime of the #
# object. #
# default constructor #
# Algol 68 automatically provides generators HEAP and LOC, which will #
# create new objects of the specified MODE, e.g. HEAP CIRCLE will create a #
# new CIRCLE. HEAP allocates apace on the heap, LOC allocates in on the #
# stack (so the new item disappears when the enclosing block procedure or #
# operator finishes) #
# a suitable "display" (value list enclosed in "(" and ")") can be cast to #
# the relevent MODE, allowing us to write e.g.: #
# "POINT( 3.1, 2.2 )" where we need a new item. #
# "constructors" with other than all the fields in the correct order could #
# be provided as procedures but each would need a distinct name #
# e.g. #
PROC new circle at the origin = ( REAL r )REF CIRCLE:
( ( HEAP CIRCLE SETRADIUS r ) SETXCOORD 0 ) SETYCOORD 0;
PROC new point at the origin = REF POINT:
( HEAP POINT SETXCOORD 0 ) SETYCOORD 0;
# examples of use #
BEGIN
CIRCLE c1 := CIRCLE( 1.1, 2.4, 4.1 );
POINT p1 := new point at the origin;
PRINT c1; newline( stand out );
# move c1 so it is centred on p1 #
( c1 SETXCOORD XCOORD p1 ) SETYCOORD YCOORD p1;
PRINT c1; newline( stand out )
END
|
http://rosettacode.org/wiki/Poker_hand_analyser
|
Poker hand analyser
|
Task
Create a program to parse a single five card poker hand and rank it according to this list of poker hands.
A poker hand is specified as a space separated list of five playing cards.
Each input card has two characters indicating face and suit.
Example
2d (two of diamonds).
Faces are: a, 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k
Suits are: h (hearts), d (diamonds), c (clubs), and s (spades), or
alternatively, the unicode card-suit characters: ♥ ♦ ♣ ♠
Duplicate cards are illegal.
The program should analyze a single hand and produce one of the following outputs:
straight-flush
four-of-a-kind
full-house
flush
straight
three-of-a-kind
two-pair
one-pair
high-card
invalid
Examples
2♥ 2♦ 2♣ k♣ q♦: three-of-a-kind
2♥ 5♥ 7♦ 8♣ 9♠: high-card
a♥ 2♦ 3♣ 4♣ 5♦: straight
2♥ 3♥ 2♦ 3♣ 3♦: full-house
2♥ 7♥ 2♦ 3♣ 3♦: two-pair
2♥ 7♥ 7♦ 7♣ 7♠: four-of-a-kind
10♥ j♥ q♥ k♥ a♥: straight-flush
4♥ 4♠ k♠ 5♦ 10♠: one-pair
q♣ 10♣ 7♣ 6♣ q♣: invalid
The programs output for the above examples should be displayed here on this page.
Extra credit
use the playing card characters introduced with Unicode 6.0 (U+1F0A1 - U+1F0DE).
allow two jokers
use the symbol joker
duplicates would be allowed (for jokers only)
five-of-a-kind would then be the highest hand
More extra credit examples
joker 2♦ 2♠ k♠ q♦: three-of-a-kind
joker 5♥ 7♦ 8♠ 9♦: straight
joker 2♦ 3♠ 4♠ 5♠: straight
joker 3♥ 2♦ 3♠ 3♦: four-of-a-kind
joker 7♥ 2♦ 3♠ 3♦: three-of-a-kind
joker 7♥ 7♦ 7♠ 7♣: five-of-a-kind
joker j♥ q♥ k♥ A♥: straight-flush
joker 4♣ k♣ 5♦ 10♠: one-pair
joker k♣ 7♣ 6♣ 4♣: flush
joker 2♦ joker 4♠ 5♠: straight
joker Q♦ joker A♠ 10♠: straight
joker Q♦ joker A♦ 10♦: straight-flush
joker 2♦ 2♠ joker q♦: four-of-a-kind
Related tasks
Playing cards
Card shuffles
Deal cards_for_FreeCell
War Card_Game
Go Fish
|
#AutoHotkey
|
AutoHotkey
|
PokerHand(hand){
StringUpper, hand, hand
Sort, hand, FCardSort D%A_Space%
cardSeq := RegExReplace(hand, "[^2-9TJQKA]")
Straight:= InStr("23456789TJQKA", cardSeq) || (cardSeq = "2345A") ? true : false
hand := cardSeq = "2345A" ? RegExReplace(hand, "(.*)\h(A.)", "$2 $1") : hand
Royal := InStr(hand, "A") ? "Royal": "Straight"
return (hand ~= "[2-9TJQKA](.)\h.\1\h.\1\h.\1\h.\1") && (Straight) ? hand "`t" Royal " Flush"
: (hand ~= "([2-9TJQKA]).*?\1.*?\1.*?\1") ? hand "`tFour of a Kind"
: (hand ~= "^([2-9TJQKA]).\h\1.\h(?!\1)([2-9TJQKA]).\h\2.\h\2.$") ? hand "`tFull House" ; xxyyy
: (hand ~= "^([2-9TJQKA]).\h\1.\h\1.\h(?!\1)([2-9TJQKA]).\h\2.$") ? hand "`tFull House" ; xxxyy
: (hand ~= "[2-9TJQKA](.)\h.\1\h.\1\h.\1\h.\1") ? hand "`tFlush"
: (Straight) ? hand "`tStraight"
: (hand ~= "([2-9TJQKA]).*?\1.*?\1") ? hand "`tThree of a Kind"
: (hand ~= "([2-9TJQKA]).\h\1.*?([2-9TJQKA]).\h\2") ? hand "`tTwo Pair"
: (hand ~= "([2-9TJQKA]).\h\1") ? hand "`tOne Pair"
: hand "`tHigh Card"
}
CardSort(a, b){
a := SubStr(a, 1, 1), b := SubStr(b, 1, 1)
a := (a = "T") ? 10 : (a = "J") ? 11 : (a = "Q") ? 12 : (a = "K") ? 13 : a
b := (b = "T") ? 10 : (b = "J") ? 11 : (b = "Q") ? 12 : (b = "K") ? 13 : b
return a > b ? 1 : a < b ? -1 : 0
}
|
http://rosettacode.org/wiki/Population_count
|
Population count
|
Population count
You are encouraged to solve this task according to the task description, using any language you may know.
The population count is the number of 1s (ones) in the binary representation of a non-negative integer.
Population count is also known as:
pop count
popcount
sideways sum
bit summation
Hamming weight
For example, 5 (which is 101 in binary) has a population count of 2.
Evil numbers are non-negative integers that have an even population count.
Odious numbers are positive integers that have an odd population count.
Task
write a function (or routine) to return the population count of a non-negative integer.
all computation of the lists below should start with 0 (zero indexed).
display the pop count of the 1st thirty powers of 3 (30, 31, 32, 33, 34, ∙∙∙ 329).
display the 1st thirty evil numbers.
display the 1st thirty odious numbers.
display each list of integers on one line (which may or may not include a title), each set of integers being shown should be properly identified.
See also
The On-Line Encyclopedia of Integer Sequences: A000120 population count.
The On-Line Encyclopedia of Integer Sequences: A000069 odious numbers.
The On-Line Encyclopedia of Integer Sequences: A001969 evil numbers.
|
#ALGOL_W
|
ALGOL W
|
begin
% returns the population count (number of bits on) of the non-negative integer n %
integer procedure populationCount( integer value n ) ;
begin
integer v, count;
v := n;
count := 0;
while v > 0 do begin
if odd( v ) then count := count + 1;
v := v div 2
end while_v_gt_0 ;
count
end populationCount ;
% returns the sum of population counts of the elements of the array n %
% the bounds of n must be 1 :: length %
integer procedure arrayPopulationCount( integer array n ( * ); integer value length ) ;
begin
integer count;
count := 0;
for i := 1 until length do count := count + populationCount( n( i ) );
count
end arrayPopulationCount ;
begin %task requirements %
integer array power( 1 :: 8 );
integer n, count, carry;
% population counts of the first 30 powers of three %
% Algol W integers are 32-bit, so we simulate 64-bit with an array of integers %
% the only operation we need is multiplication by 3 %
% we use 8 bits of each number %
% start with 3^0, which is 1 %
for i := 1 until 8 do power( i ) := 0;
power( 1 ) := 1;
write( i_w := 1, s_w := 0, "3^x population: ", arrayPopulationCount( power, 8 ) );
for p := 1 until 29 do begin
carry := 0;
for b := 1 until 8 do begin
integer bValue;
bValue := ( power( b ) * 3 ) + carry;
carry := bValue div 256;
power( b ) := bValue rem 256
end for_b ;
writeon( i_w := 1, s_w := 0, " ", arrayPopulationCount( power, 8 ) )
end for_p ;
% evil numbers (even population count) %
write( "evil numbers:" );
n := 0;
count := 0;
while count < 30 do begin
if not odd( populationCount( n ) ) then begin
writeon( i_w := 1, s_w := 0, " ", n );
count := count + 1
end if_not_odd_populationCount ;
n := n + 1
end evil_numbers_loop ;
% odious numbers (odd population count %
write( "odious numbers:" );
n := 0;
count := 0;
while count < 30 do begin
if odd( populationCount( n ) ) then begin
writeon( i_w := 1, s_w := 0, " ", n );
count := count + 1
end if_odd_populationCount ;
n := n + 1
end odious_numbers_loop
end
end.
|
http://rosettacode.org/wiki/Polynomial_long_division
|
Polynomial long division
|
This page uses content from Wikipedia. The original article was at Polynomial long division. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree.
Let us suppose a polynomial is represented by a vector,
x
{\displaystyle x}
(i.e., an ordered collection of coefficients) so that the
i
{\displaystyle i}
th element keeps the coefficient of
x
i
{\displaystyle x^{i}}
, and the multiplication by a monomial is a shift of the vector's elements "towards right" (injecting ones from left) followed by a multiplication of each element by the coefficient of the monomial.
Then a pseudocode for the polynomial long division using the conventions described above could be:
degree(P):
return the index of the last non-zero element of P;
if all elements are 0, return -∞
polynomial_long_division(N, D) returns (q, r):
// N, D, q, r are vectors
if degree(D) < 0 then error
q ← 0
while degree(N) ≥ degree(D)
d ← D shifted right by (degree(N) - degree(D))
q(degree(N) - degree(D)) ← N(degree(N)) / d(degree(d))
// by construction, degree(d) = degree(N) of course
d ← d * q(degree(N) - degree(D))
N ← N - d
endwhile
r ← N
return (q, r)
Note: vector * scalar multiplies each element of the vector by the scalar; vectorA - vectorB subtracts each element of the vectorB from the element of the vectorA with "the same index". The vectors in the pseudocode are zero-based.
Error handling (for allocations or for wrong inputs) is not mandatory.
Conventions can be different; in particular, note that if the first coefficient in the vector is the highest power of x for the polynomial represented by the vector, then the algorithm becomes simpler.
Example for clarification
This example is from Wikipedia, but changed to show how the given pseudocode works.
0 1 2 3
----------------------
N: -42 0 -12 1 degree = 3
D: -3 1 0 0 degree = 1
d(N) - d(D) = 2, so let's shift D towards right by 2:
N: -42 0 -12 1
d: 0 0 -3 1
N(3)/d(3) = 1, so d is unchanged. Now remember that "shifting by 2"
is like multiplying by x2, and the final multiplication
(here by 1) is the coefficient of this monomial. Let's store this
into q:
0 1 2
---------------
q: 0 0 1
now compute N - d, and let it be the "new" N, and let's loop
N: -42 0 -9 0 degree = 2
D: -3 1 0 0 degree = 1
d(N) - d(D) = 1, right shift D by 1 and let it be d
N: -42 0 -9 0
d: 0 -3 1 0 * -9/1 = -9
q: 0 -9 1
d: 0 27 -9 0
N ← N - d
N: -42 -27 0 0 degree = 1
D: -3 1 0 0 degree = 1
looping again... d(N)-d(D)=0, so no shift is needed; we
multiply D by -27 (= -27/1) storing the result in d, then
q: -27 -9 1
and
N: -42 -27 0 0 -
d: 81 -27 0 0 =
N: -123 0 0 0 (last N)
d(N) < d(D), so now r ← N, and the result is:
0 1 2
-------------
q: -27 -9 1 → x2 - 9x - 27
r: -123 0 0 → -123
Related task
Polynomial derivative
|
#C.2B.2B
|
C++
|
#include <iostream>
#include <iterator>
#include <vector>
using namespace std;
typedef vector<double> Poly;
// does: prints all members of vector
// input: c - ASCII char with the name of the vector
// A - reference to polynomial (vector)
void Print(char name, const Poly &A) {
cout << name << "(" << A.size()-1 << ") = [ ";
copy(A.begin(), A.end(), ostream_iterator<decltype(A[0])>(cout, " "));
cout << "]\n";
}
int main() {
Poly N, D, d, q, r; // vectors - N / D == q && N % D == r
size_t dN, dD, dd, dq, dr; // degrees of vectors
size_t i; // loop counter
// setting the degrees of vectors
cout << "Enter the degree of N: ";
cin >> dN;
cout << "Enter the degree of D: ";
cin >> dD;
dq = dN-dD;
dr = dN-dD;
if( dD < 1 || dN < 1 ) {
cerr << "Error: degree of D and N must be positive.\n";
return 1;
}
// allocation and initialization of vectors
N.resize(dN+1);
cout << "Enter the coefficients of N:"<<endl;
for ( i = 0; i <= dN; i++ ) {
cout << "N[" << i << "]= ";
cin >> N[i];
}
D.resize(dN+1);
cout << "Enter the coefficients of D:"<<endl;
for ( i = 0; i <= dD; i++ ) {
cout << "D[" << i << "]= ";
cin >> D[i];
}
d.resize(dN+1);
q.resize(dq+1);
r.resize(dr+1);
cout << "-- Procedure --" << endl << endl;
if( dN >= dD ) {
while(dN >= dD) {
// d equals D shifted right
d.assign(d.size(), 0);
for( i = 0 ; i <= dD ; i++ )
d[i+dN-dD] = D[i];
dd = dN;
Print( 'd', d );
// calculating one element of q
q[dN-dD] = N[dN]/d[dd];
Print( 'q', q );
// d equals d * q[dN-dD]
for( i = 0 ; i < dq + 1 ; i++ )
d[i] = d[i] * q[dN-dD];
Print( 'd', d );
// N equals N - d
for( i = 0 ; i < dN + 1 ; i++ )
N[i] = N[i] - d[i];
dN--;
Print( 'N', N );
cout << "-----------------------" << endl << endl;
}
}
// r equals N
for( i = 0 ; i <= dN ; i++ )
r[i] = N[i];
cout << "=========================" << endl << endl;
cout << "-- Result --" << endl << endl;
Print( 'q', q );
Print( 'r', r );
}
|
http://rosettacode.org/wiki/Polymorphic_copy
|
Polymorphic copy
|
An object is polymorphic when its specific type may vary.
The types a specific value may take, is called class.
It is trivial to copy an object if its type is known:
int x;
int y = x;
Here x is not polymorphic, so y is declared of same type (int) as x.
But if the specific type of x were unknown, then y could not be declared of any specific type.
The task: let a polymorphic object contain an instance of some specific type S derived from a type T.
The type T is known.
The type S is possibly unknown until run time.
The objective is to create an exact copy of such polymorphic object (not to create a reference, nor a pointer to).
Let further the type T have a method overridden by S.
This method is to be called on the copy to demonstrate that the specific type of the copy is indeed S.
|
#Delphi
|
Delphi
|
program PolymorphicCopy;
type
T = class
function Name:String; virtual;
function Clone:T; virtual;
end;
S = class(T)
function Name:String; override;
function Clone:T; override;
end;
function T.Name :String; begin Exit('T') end;
function T.Clone:T; begin Exit(T.Create)end;
function S.Name :String; begin Exit('S') end;
function S.Clone:T; begin Exit(S.Create)end;
procedure Main;
var
Original, Clone :T;
begin
Original := S.Create;
Clone := Original.Clone;
WriteLn(Original.Name);
WriteLn(Clone.Name);
end;
begin
Main;
end.
|
http://rosettacode.org/wiki/Polyspiral
|
Polyspiral
|
A Polyspiral is a spiral made of multiple line segments, whereby each segment is larger (or smaller) than the previous one by a given amount. Each segment also changes direction at a given angle.
Task
Animate a series of polyspirals, by drawing a complete spiral then incrementing the angle, and (after clearing the background) drawing the next, and so on. Every spiral will be a frame of the animation. The animation may stop as it goes full circle or continue indefinitely. The given input values may be varied.
If animation is not practical in your programming environment, you may show a single frame instead.
Pseudo code
set incr to 0.0
// animation loop
WHILE true
incr = (incr + 0.05) MOD 360
x = width / 2
y = height / 2
length = 5
angle = incr
// spiral loop
FOR 1 TO 150
drawline
change direction by angle
length = length + 3
angle = (angle + incr) MOD 360
ENDFOR
|
#Kotlin
|
Kotlin
|
// version 1.1.0
import java.awt.*
import java.awt.event.ActionEvent
import javax.swing.*
class PolySpiral() : JPanel() {
private var inc = 0.0
init {
preferredSize = Dimension(640, 640)
background = Color.white
Timer(40) {
inc = (inc + 0.05) % 360.0
repaint()
}.start()
}
private fun drawSpiral(g: Graphics2D, length: Int, angleIncrement: Double) {
var x1 = width / 2.0
var y1 = height / 2.0
var len = length
var angle = angleIncrement
for (i in 0 until 150) {
g.setColor(Color.getHSBColor(i / 150f, 1.0f, 1.0f))
val x2 = x1 + Math.cos(angle) * len
val y2 = y1 - Math.sin(angle) * len
g.drawLine(x1.toInt(), y1.toInt(), x2.toInt(), y2.toInt())
x1 = x2
y1 = y2
len += 3
angle = (angle + angleIncrement) % (Math.PI * 2.0)
}
}
override protected fun paintComponent(gg: Graphics) {
super.paintComponent(gg)
val g = gg as Graphics2D
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
drawSpiral(g, 5, Math.toRadians(inc))
}
}
fun main(args: Array<String>) {
SwingUtilities.invokeLater {
val f = JFrame()
f.defaultCloseOperation = JFrame.EXIT_ON_CLOSE
f.title = "PolySpiral"
f.setResizable(true)
f.add(PolySpiral(), BorderLayout.CENTER)
f.pack()
f.setLocationRelativeTo(null)
f.setVisible(true)
}
}
|
http://rosettacode.org/wiki/Polynomial_regression
|
Polynomial regression
|
Find an approximating polynomial of known degree for a given data.
Example:
For input data:
x = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
y = {1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321};
The approximating polynomial is:
3 x2 + 2 x + 1
Here, the polynomial's coefficients are (3, 2, 1).
This task is intended as a subtask for Measure relative performance of sorting algorithms implementations.
|
#C.2B.2B
|
C++
|
#include <algorithm>
#include <iostream>
#include <numeric>
#include <vector>
void polyRegression(const std::vector<int>& x, const std::vector<int>& y) {
int n = x.size();
std::vector<int> r(n);
std::iota(r.begin(), r.end(), 0);
double xm = std::accumulate(x.begin(), x.end(), 0.0) / x.size();
double ym = std::accumulate(y.begin(), y.end(), 0.0) / y.size();
double x2m = std::transform_reduce(r.begin(), r.end(), 0.0, std::plus<double>{}, [](double a) {return a * a; }) / r.size();
double x3m = std::transform_reduce(r.begin(), r.end(), 0.0, std::plus<double>{}, [](double a) {return a * a * a; }) / r.size();
double x4m = std::transform_reduce(r.begin(), r.end(), 0.0, std::plus<double>{}, [](double a) {return a * a * a * a; }) / r.size();
double xym = std::transform_reduce(x.begin(), x.end(), y.begin(), 0.0, std::plus<double>{}, std::multiplies<double>{});
xym /= fmin(x.size(), y.size());
double x2ym = std::transform_reduce(x.begin(), x.end(), y.begin(), 0.0, std::plus<double>{}, [](double a, double b) { return a * a * b; });
x2ym /= fmin(x.size(), y.size());
double sxx = x2m - xm * xm;
double sxy = xym - xm * ym;
double sxx2 = x3m - xm * x2m;
double sx2x2 = x4m - x2m * x2m;
double sx2y = x2ym - x2m * ym;
double b = (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);
double c = (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);
double a = ym - b * xm - c * x2m;
auto abc = [a, b, c](int xx) {
return a + b * xx + c * xx*xx;
};
std::cout << "y = " << a << " + " << b << "x + " << c << "x^2" << std::endl;
std::cout << " Input Approximation" << std::endl;
std::cout << " x y y1" << std::endl;
auto xit = x.cbegin();
auto xend = x.cend();
auto yit = y.cbegin();
auto yend = y.cend();
while (xit != xend && yit != yend) {
printf("%2d %3d %5.1f\n", *xit, *yit, abc(*xit));
xit = std::next(xit);
yit = std::next(yit);
}
}
int main() {
using namespace std;
vector<int> x(11);
iota(x.begin(), x.end(), 0);
vector<int> y{ 1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321 };
polyRegression(x, y);
return 0;
}
|
http://rosettacode.org/wiki/Power_set
|
Power set
|
A set is a collection (container) of certain values,
without any particular order, and no repeated values.
It corresponds with a finite set in mathematics.
A set can be implemented as an associative array (partial mapping)
in which the value of each key-value pair is ignored.
Given a set S, the power set (or powerset) of S, written P(S), or 2S, is the set of all subsets of S.
Task
By using a library or built-in set type, or by defining a set type with necessary operations, write a function with a set S as input that yields the power set 2S of S.
For example, the power set of {1,2,3,4} is
{{}, {1}, {2}, {1,2}, {3}, {1,3}, {2,3}, {1,2,3}, {4}, {1,4}, {2,4}, {1,2,4}, {3,4}, {1,3,4}, {2,3,4}, {1,2,3,4}}.
For a set which contains n elements, the corresponding power set has 2n elements, including the edge cases of empty set.
The power set of the empty set is the set which contains itself (20 = 1):
P
{\displaystyle {\mathcal {P}}}
(
∅
{\displaystyle \varnothing }
) = {
∅
{\displaystyle \varnothing }
}
And the power set of the set which contains only the empty set, has two subsets, the empty set and the set which contains the empty set (21 = 2):
P
{\displaystyle {\mathcal {P}}}
({
∅
{\displaystyle \varnothing }
}) = {
∅
{\displaystyle \varnothing }
, {
∅
{\displaystyle \varnothing }
} }
Extra credit: Demonstrate that your language supports these last two powersets.
|
#BBC_BASIC
|
BBC BASIC
|
DIM list$(3) : list$() = "1", "2", "3", "4"
PRINT FNpowerset(list$())
END
DEF FNpowerset(list$())
IF DIM(list$(),1) > 31 ERROR 100, "Set too large to represent as integer"
LOCAL i%, j%, s$
s$ = "{"
FOR i% = 0 TO (2 << DIM(list$(),1)) - 1
s$ += "{"
FOR j% = 0 TO DIM(list$(),1)
IF i% AND (1 << j%) s$ += list$(j%) + ","
NEXT
IF RIGHT$(s$) = "," s$ = LEFT$(s$)
s$ += "},"
NEXT i%
= LEFT$(s$) + "}"
|
http://rosettacode.org/wiki/Primality_by_trial_division
|
Primality by trial division
|
Task
Write a boolean function that tells whether a given integer is prime.
Remember that 1 and all non-positive numbers are not prime.
Use trial division.
Even numbers greater than 2 may be eliminated right away.
A loop from 3 to √ n will suffice, but other loops are allowed.
Related tasks
count in factors
prime decomposition
AKS test for primes
factors of an integer
Sieve of Eratosthenes
factors of a Mersenne number
trial factoring of a Mersenne number
partition an integer X into N primes
sequence of primes by Trial Division
|
#AutoHotkey
|
AutoHotkey
|
MsgBox % IsPrime(1995937)
Loop
MsgBox % A_Index-3 . " is " . (IsPrime(A_Index-3) ? "" : "not ") . "prime."
IsPrime(n,k=2) { ; testing primality with trial divisors not multiple of 2,3,5, up to sqrt(n)
d := k+(k<7 ? 1+(k>2) : SubStr("6-----4---2-4---2-4---6-----2",Mod(k,30),1))
Return n < 3 ? n>1 : Mod(n,k) ? (d*d <= n ? IsPrime(n,d) : 1) : 0
}
|
http://rosettacode.org/wiki/Price_fraction
|
Price fraction
|
A friend of mine runs a pharmacy. He has a specialized function in his Dispensary application which receives a decimal value of currency and replaces it to a standard value. This value is regulated by a government department.
Task
Given a floating point value between 0.00 and 1.00, rescale according to the following table:
>= 0.00 < 0.06 := 0.10
>= 0.06 < 0.11 := 0.18
>= 0.11 < 0.16 := 0.26
>= 0.16 < 0.21 := 0.32
>= 0.21 < 0.26 := 0.38
>= 0.26 < 0.31 := 0.44
>= 0.31 < 0.36 := 0.50
>= 0.36 < 0.41 := 0.54
>= 0.41 < 0.46 := 0.58
>= 0.46 < 0.51 := 0.62
>= 0.51 < 0.56 := 0.66
>= 0.56 < 0.61 := 0.70
>= 0.61 < 0.66 := 0.74
>= 0.66 < 0.71 := 0.78
>= 0.71 < 0.76 := 0.82
>= 0.76 < 0.81 := 0.86
>= 0.81 < 0.86 := 0.90
>= 0.86 < 0.91 := 0.94
>= 0.91 < 0.96 := 0.98
>= 0.96 < 1.01 := 1.00
|
#Clipper
|
Clipper
|
FUNCTION PriceFraction( npQuantDispensed )
LOCAL aPriceFraction := { {0,.06,.1},;
{.06,.11,.18}, ;
{.11,.16,.26}, ;
{.16,.21,.32}, ;
{.21,.26,.38}, ;
{.26,.31,.44}, ;
{.31,.36,.5}, ;
{.36,.41,.54}, ;
{.41,.46,.58}, ;
{.46,.51,.62}, ;
{.51,.56,.66}, ;
{.56,.61,.7}, ;
{.61,.66,.74}, ;
{.66,.71,.78}, ;
{.71,.76,.82}, ;
{.76,.81,.86}, ;
{.81,.86,.9}, ;
{.86,.91,.94}, ;
{.91,.96,.98} }
LOCAL nResult
LOCAL nScan
IF npQuantDispensed = 0
nResult = 0
ELSEIF npQuantDispensed >= .96
nResult = 1
ELSE
nScan := ASCAN( aPriceFraction, ;
{ |aItem| npQuantDispensed >= aItem[ 1 ] .AND.;
npQuantDispensed < aItem[ 2 ] } )
nResult := aPriceFraction[ nScan ][ 3 ]
END IF
RETURN nResult
|
http://rosettacode.org/wiki/Price_fraction
|
Price fraction
|
A friend of mine runs a pharmacy. He has a specialized function in his Dispensary application which receives a decimal value of currency and replaces it to a standard value. This value is regulated by a government department.
Task
Given a floating point value between 0.00 and 1.00, rescale according to the following table:
>= 0.00 < 0.06 := 0.10
>= 0.06 < 0.11 := 0.18
>= 0.11 < 0.16 := 0.26
>= 0.16 < 0.21 := 0.32
>= 0.21 < 0.26 := 0.38
>= 0.26 < 0.31 := 0.44
>= 0.31 < 0.36 := 0.50
>= 0.36 < 0.41 := 0.54
>= 0.41 < 0.46 := 0.58
>= 0.46 < 0.51 := 0.62
>= 0.51 < 0.56 := 0.66
>= 0.56 < 0.61 := 0.70
>= 0.61 < 0.66 := 0.74
>= 0.66 < 0.71 := 0.78
>= 0.71 < 0.76 := 0.82
>= 0.76 < 0.81 := 0.86
>= 0.81 < 0.86 := 0.90
>= 0.86 < 0.91 := 0.94
>= 0.91 < 0.96 := 0.98
>= 0.96 < 1.01 := 1.00
|
#Clojure
|
Clojure
|
(def values [10 18 26 32 38 44 50 54 58 62 66 70 74 78 82 86 90 94 98 100])
(defn price [v]
(format "%.2f" (double (/ (values (int (/ (- (* v 100) 1) 5))) 100))))
|
http://rosettacode.org/wiki/Proper_divisors
|
Proper divisors
|
The proper divisors of a positive integer N are those numbers, other than N itself, that divide N without remainder.
For N > 1 they will always include 1, but for N == 1 there are no proper divisors.
Examples
The proper divisors of 6 are 1, 2, and 3.
The proper divisors of 100 are 1, 2, 4, 5, 10, 20, 25, and 50.
Task
Create a routine to generate all the proper divisors of a number.
use it to show the proper divisors of the numbers 1 to 10 inclusive.
Find a number in the range 1 to 20,000 with the most proper divisors. Show the number and just the count of how many proper divisors it has.
Show all output here.
Related tasks
Amicable pairs
Abundant, deficient and perfect number classifications
Aliquot sequence classifications
Factors of an integer
Prime decomposition
|
#Forth
|
Forth
|
: .proper-divisors
dup 1 ?do
dup i mod 0= if i . then
loop cr drop
;
: proper-divisors-count
0 swap
dup 1 ?do
dup i mod 0= if swap 1 + swap then
loop drop
;
: rosetta-proper-divisors
cr
11 1 do
i . ." : " i .proper-divisors
loop
1 0
20000 2 do
i proper-divisors-count
2dup < if nip nip i swap else drop then
loop
swap cr . ." has " . ." divisors" cr
;
rosetta-proper-divisors
|
http://rosettacode.org/wiki/Probabilistic_choice
|
Probabilistic choice
|
Given a mapping between items and their required probability of occurrence, generate a million items randomly subject to the given probabilities and compare the target probability of occurrence versus the generated values.
The total of all the probabilities should equal one. (Because floating point arithmetic is involved, this is subject to rounding errors).
aleph 1/5.0
beth 1/6.0
gimel 1/7.0
daleth 1/8.0
he 1/9.0
waw 1/10.0
zayin 1/11.0
heth 1759/27720 # adjusted so that probabilities add to 1
Related task
Random number generator (device)
|
#JavaScript
|
JavaScript
|
var probabilities = {
aleph: 1/5.0,
beth: 1/6.0,
gimel: 1/7.0,
daleth: 1/8.0,
he: 1/9.0,
waw: 1/10.0,
zayin: 1/11.0,
heth: 1759/27720
};
var sum = 0;
var iterations = 1000000;
var cumulative = {};
var randomly = {};
for (var name in probabilities) {
sum += probabilities[name];
cumulative[name] = sum;
randomly[name] = 0;
}
for (var i = 0; i < iterations; i++) {
var r = Math.random();
for (var name in cumulative) {
if (r <= cumulative[name]) {
randomly[name]++;
break;
}
}
}
for (var name in probabilities)
// using WSH
WScript.Echo(name + "\t" + probabilities[name] + "\t" + randomly[name]/iterations);
|
http://rosettacode.org/wiki/Priority_queue
|
Priority queue
|
A priority queue is somewhat similar to a queue, with an important distinction: each item is added to a priority queue with a priority level, and will be later removed from the queue with the highest priority element first. That is, the items are (conceptually) stored in the queue in priority order instead of in insertion order.
Task
Create a priority queue. The queue must support at least two operations:
Insertion. An element is added to the queue with a priority (a numeric value).
Top item removal. Deletes the element or one of the elements with the current top priority and return it.
Optionally, other operations may be defined, such as peeking (find what current top priority/top element is), merging (combining two priority queues into one), etc.
To test your implementation, insert a number of elements into the queue, each with some random priority.
Then dequeue them sequentially; now the elements should be sorted by priority.
You can use the following task/priority items as input data:
Priority Task
══════════ ════════════════
3 Clear drains
4 Feed cat
5 Make tea
1 Solve RC tasks
2 Tax return
The implementation should try to be efficient. A typical implementation has O(log n) insertion and extraction time, where n is the number of items in the queue.
You may choose to impose certain limits such as small range of allowed priority levels, limited capacity, etc. If so, discuss the reasons behind it.
|
#Haskell
|
Haskell
|
import Data.PQueue.Prio.Min
main = print (toList (fromList [(3, "Clear drains"),(4, "Feed cat"),(5, "Make tea"),(1, "Solve RC tasks"), (2, "Tax return")]))
|
http://rosettacode.org/wiki/Problem_of_Apollonius
|
Problem of Apollonius
|
Task
Implement a solution to the Problem of Apollonius (description on Wikipedia) which is the problem of finding the circle that is tangent to three specified circles (colored black in the diagram below to the right).
There is an algebraic solution which is pretty straightforward.
The solutions to the example in the code are shown in the diagram (below and to the right).
The red circle is "internally tangent" to all three black circles, and the green circle is "externally tangent" to all three black circles.
|
#REXX
|
REXX
|
/*REXX program solves the problem of Apollonius, named after the Greek Apollonius of */
/*────────────────────────────────────── Perga [Pergæus] (circa 262 BCE ──► 190 BCE). */
numeric digits 15; x1= 0; y1= 0; r1= 1
x2= 4; y2= 0; r2= 1
x3= 2; y3= 4; r3= 2
call tell 'external tangent: ', Apollonius( 1, 1, 1)
call tell 'internal tangent: ', Apollonius(-1, -1, -1)
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
Apollonius: parse arg s1,s2,s3 /*could be internal or external tangent*/
numeric digits digits() * 3 /*reduce rounding with thrice digits. */
va= x2*2 - x1*2; vb= y2*2 - y1*2
vc= x1**2 - x2**2 + y1**2 - y2**2 - r1**2 + r2**2
vd= s2*r2*2 - s1*r1*2; ve= x3*2 - x2*2; vf= y3*2 - y2*2
vg= x2**2 - x3**2 + y2**2 - y3**2 - r2**2 + r3**2; vh= s3*r3*2 - s2*r2*2
vj= vb/va; vk= vc/va; vm= vd/va; vn= vf/ve - vj
vp= vg/ve - vk; vr= vh/ve - vm; p = -vp/vn; q = vr/vn
m = -vj*p - vk; n = vm - vj*q
a = n**2 + q**2 - 1
b = (m*n - n*x1 + p*q - q*y1 + s1*r1) * 2
c = x1**2 + y1**2 + m**2 - r1**2 + p**2 - (m*x1 + p*y1) * 2
$r= (-b - sqrt(b**2 - a*c*4) ) / (a+a)
return (m + n*$r) (p + q*$r) ($r) /*return 3 arguments.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); h=d+6; numeric digits
m.=9; numeric form; parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g*.5'e'_%2
do j=0 while h>9; m.j=h; h= h % 2 + 1; end /*j*/
do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g) * .5; end /*k*/; return g
/*──────────────────────────────────────────────────────────────────────────────────────*/
tell: parse arg _,a b c; w=digits()+4; say _ left(a/1,w%2) left(b/1,w) left(c/1,w); return
|
http://rosettacode.org/wiki/Program_name
|
Program name
|
The task is to programmatically obtain the name used to invoke the program. (For example determine whether the user ran "python hello.py", or "python hellocaller.py", a program importing the code from "hello.py".)
Sometimes a multiline shebang is necessary in order to provide the script name to a language's internal ARGV.
See also Command-line arguments
Examples from GitHub.
|
#Smalltalk
|
Smalltalk
|
"exec" "gst" "-f" "$0" "$0" "$@"
"exit"
| program |
program := Smalltalk getArgv: 1.
Transcript show: 'Program: ', program; cr.
|
http://rosettacode.org/wiki/Program_name
|
Program name
|
The task is to programmatically obtain the name used to invoke the program. (For example determine whether the user ran "python hello.py", or "python hellocaller.py", a program importing the code from "hello.py".)
Sometimes a multiline shebang is necessary in order to provide the script name to a language's internal ARGV.
See also Command-line arguments
Examples from GitHub.
|
#Standard_ML
|
Standard ML
|
#!/usr/bin/env sml
let
val program = CommandLine.name ()
in
print ("Program: " ^ program ^ "\n")
end;
|
http://rosettacode.org/wiki/Pythagorean_triples
|
Pythagorean triples
|
A Pythagorean triple is defined as three positive integers
(
a
,
b
,
c
)
{\displaystyle (a,b,c)}
where
a
<
b
<
c
{\displaystyle a<b<c}
, and
a
2
+
b
2
=
c
2
.
{\displaystyle a^{2}+b^{2}=c^{2}.}
They are called primitive triples if
a
,
b
,
c
{\displaystyle a,b,c}
are co-prime, that is, if their pairwise greatest common divisors
g
c
d
(
a
,
b
)
=
g
c
d
(
a
,
c
)
=
g
c
d
(
b
,
c
)
=
1
{\displaystyle {\rm {gcd}}(a,b)={\rm {gcd}}(a,c)={\rm {gcd}}(b,c)=1}
.
Because of their relationship through the Pythagorean theorem, a, b, and c are co-prime if a and b are co-prime (
g
c
d
(
a
,
b
)
=
1
{\displaystyle {\rm {gcd}}(a,b)=1}
).
Each triple forms the length of the sides of a right triangle, whose perimeter is
P
=
a
+
b
+
c
{\displaystyle P=a+b+c}
.
Task
The task is to determine how many Pythagorean triples there are with a perimeter no larger than 100 and the number of these that are primitive.
Extra credit
Deal with large values. Can your program handle a maximum perimeter of 1,000,000? What about 10,000,000? 100,000,000?
Note: the extra credit is not for you to demonstrate how fast your language is compared to others; you need a proper algorithm to solve them in a timely manner.
Related tasks
Euler's sum of powers conjecture
List comprehensions
Pythagorean quadruples
|
#REXX
|
REXX
|
/*REXX program counts the number of Pythagorean triples that exist given a maximum */
/*──────────────────── perimeter of N, and also counts how many of them are primitives.*/
parse arg N . /*obtain optional argument from the CL.*/
if N=='' | N=="," then N= 100 /*Not specified? Then use the default.*/
do j=1 for N; @.j= j*j; end /*pre-compute some squares. */
N66= N * 2%3 /*calculate 2/3 of N (for a+b). */
T= 0; P= 0 /*set the number of Triples, Primitives*/
do a=3 to N%3 /*limit side to 1/3 of the perimeter.*/
do b= a+1 /*the triangle can't be isosceles. */
ab= a + b /*compute a partial perimeter (2 sides)*/
if ab>=N66 then iterate a /*is a+b≥66% perimeter? Try different A*/
aabb= @.a + @.b /*compute the sum of a²+b² (shortcut)*/
do c=b+1 /*compute the value of the third side. */
if ab+c > N then iterate a /*is a+b+c>perimeter ? Try different A.*/
if @.c >aabb then iterate b /*is c² > a²+b² ? Try " B.*/
if @.c\==aabb then iterate /*is c² ¬= a²+b² ? Try " C.*/
T= T + 1 /*eureka. We found a Pythagorean triple*/
P= P + (gcd(a, b)==1) /*is this triple a primitive triple? */
end /*c*/
end /*b*/
end /*a*/
_= left('', 7) /*for padding the output with 7 blanks.*/
say 'max perimeter =' N _ "Pythagorean triples =" T _ 'primitives =' P
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
gcd: procedure; parse arg x,y; do until y==0; parse value x//y y with y x; end; return x
|
http://rosettacode.org/wiki/Program_termination
|
Program termination
|
Task
Show the syntax for a complete stoppage of a program inside a conditional.
This includes all threads/processes which are part of your program.
Explain the cleanup (or lack thereof) caused by the termination (allocated memory, database connections, open files, object finalizers/destructors, run-on-exit hooks, etc.).
Unless otherwise described, no special cleanup outside that provided by the operating system is provided.
|
#QB64
|
QB64
|
INPUT "Press any key...", a$
IF 1 THEN SYSTEM
|
http://rosettacode.org/wiki/Program_termination
|
Program termination
|
Task
Show the syntax for a complete stoppage of a program inside a conditional.
This includes all threads/processes which are part of your program.
Explain the cleanup (or lack thereof) caused by the termination (allocated memory, database connections, open files, object finalizers/destructors, run-on-exit hooks, etc.).
Unless otherwise described, no special cleanup outside that provided by the operating system is provided.
|
#R
|
R
|
if(problem) q(status=10)
|
http://rosettacode.org/wiki/Program_termination
|
Program termination
|
Task
Show the syntax for a complete stoppage of a program inside a conditional.
This includes all threads/processes which are part of your program.
Explain the cleanup (or lack thereof) caused by the termination (allocated memory, database connections, open files, object finalizers/destructors, run-on-exit hooks, etc.).
Unless otherwise described, no special cleanup outside that provided by the operating system is provided.
|
#Racket
|
Racket
|
#lang racket
(run-stuff)
(when (something-bad-happened) (exit 1))
|
http://rosettacode.org/wiki/Primality_by_Wilson%27s_theorem
|
Primality by Wilson's theorem
|
Task
Write a boolean function that tells whether a given integer is prime using Wilson's theorem.
By Wilson's theorem, a number p is prime if and only if p divides (p - 1)! + 1.
Remember that 1 and all non-positive integers are not prime.
See also
Cut-the-knot: Wilson's theorem.
Wikipedia: Wilson's theorem
|
#Perl
|
Perl
|
use strict;
use warnings;
use feature 'say';
use ntheory qw(factorial);
my($ends_in_7, $ends_in_3);
sub is_wilson_prime {
my($n) = @_;
$n > 1 or return 0;
(factorial($n-1) % $n) == ($n-1) ? 1 : 0;
}
for (0..50) {
my $m = 3 + 10 * $_;
$ends_in_3 .= "$m " if is_wilson_prime($m);
my $n = 7 + 10 * $_;
$ends_in_7 .= "$n " if is_wilson_prime($n);
}
say $ends_in_3;
say $ends_in_7;
|
http://rosettacode.org/wiki/Primality_by_Wilson%27s_theorem
|
Primality by Wilson's theorem
|
Task
Write a boolean function that tells whether a given integer is prime using Wilson's theorem.
By Wilson's theorem, a number p is prime if and only if p divides (p - 1)! + 1.
Remember that 1 and all non-positive integers are not prime.
See also
Cut-the-knot: Wilson's theorem.
Wikipedia: Wilson's theorem
|
#Phix
|
Phix
|
function wilson(integer n)
integer facmod = 1
for i=2 to n-1 do
facmod = remainder(facmod*i,n)
end for
return facmod+1=n
end function
atom t0 = time()
sequence primes = {}
integer p = 2
while length(primes)<1015 do
if wilson(p) then
primes &= p
end if
p += 1
end while
printf(1,"The first 25 primes: %V\n",{primes[1..25]})
printf(1," builtin: %V\n",{get_primes(-25)})
printf(1,"primes[1000..1015]: %V\n",{primes[1000..1015]})
printf(1," builtin: %V\n",{get_primes(-1015)[1000..1015]})
?elapsed(time()-t0)
|
http://rosettacode.org/wiki/Prime_conspiracy
|
Prime conspiracy
|
A recent discovery, quoted from Quantamagazine (March 13, 2016):
Two mathematicians have uncovered a simple, previously unnoticed property of
prime numbers — those numbers that are divisible only by 1 and themselves.
Prime numbers, it seems, have decided preferences about the final digits of
the primes that immediately follow them.
and
This conspiracy among prime numbers seems, at first glance, to violate a
longstanding assumption in number theory: that prime numbers behave much
like random numbers.
─── (original authors from Stanford University):
─── Kannan Soundararajan and Robert Lemke Oliver
The task is to check this assertion, modulo 10.
Lets call i -> j a transition if i is the last decimal digit of a prime, and j the last decimal digit of the following prime.
Task
Considering the first one million primes. Count, for any pair of successive primes, the number of transitions i -> j and print them along with their relative frequency, sorted by i .
You can see that, for a given i , frequencies are not evenly distributed.
Observation
(Modulo 10), primes whose last digit is 9 "prefer" the digit 1 to the digit 9, as its following prime.
Extra credit
Do the same for one hundred million primes.
Example for 10,000 primes
10000 first primes. Transitions prime % 10 → next-prime % 10.
1 → 1 count: 365 frequency: 3.65 %
1 → 3 count: 833 frequency: 8.33 %
1 → 7 count: 889 frequency: 8.89 %
1 → 9 count: 397 frequency: 3.97 %
2 → 3 count: 1 frequency: 0.01 %
3 → 1 count: 529 frequency: 5.29 %
3 → 3 count: 324 frequency: 3.24 %
3 → 5 count: 1 frequency: 0.01 %
3 → 7 count: 754 frequency: 7.54 %
3 → 9 count: 907 frequency: 9.07 %
5 → 7 count: 1 frequency: 0.01 %
7 → 1 count: 655 frequency: 6.55 %
7 → 3 count: 722 frequency: 7.22 %
7 → 7 count: 323 frequency: 3.23 %
7 → 9 count: 808 frequency: 8.08 %
9 → 1 count: 935 frequency: 9.35 %
9 → 3 count: 635 frequency: 6.35 %
9 → 7 count: 541 frequency: 5.41 %
9 → 9 count: 379 frequency: 3.79 %
|
#R
|
R
|
suppressMessages(library(gmp))
limit <- 1e6
result <- vector('numeric', 99)
prev_prime <- 2
count <- 0
getOutput <- function(transition) {
if (result[transition] == 0) return()
second <- transition %% 10
first <- (transition - second) / 10
cat(first,"->",second,"count:", sprintf("%6d",result[transition]), "frequency:",
sprintf("%5.2f%%\n",result[transition]*100/limit))
}
while (count <= limit) {
count <- count + 1
next_prime <- nextprime(prev_prime)
transition <- 10*(asNumeric(prev_prime) %% 10) + (asNumeric(next_prime) %% 10)
prev_prime <- next_prime
result[transition] <- result[transition] + 1
}
cat(sprintf("%d",limit),"first primes. Transitions prime % 10 -> next-prime % 10\n")
invisible(sapply(1:99,getOutput))
|
http://rosettacode.org/wiki/Prime_decomposition
|
Prime decomposition
|
The prime decomposition of a number is defined as a list of prime numbers
which when all multiplied together, are equal to that number.
Example
12 = 2 × 2 × 3, so its prime decomposition is {2, 2, 3}
Task
Write a function which returns an array or collection which contains the prime decomposition of a given number
n
{\displaystyle n}
greater than 1.
If your language does not have an isPrime-like function available,
you may assume that you have a function which determines
whether a number is prime (note its name before your code).
If you would like to test code from this task, you may use code from trial division or the Sieve of Eratosthenes.
Note: The program must not be limited by the word size of your computer or some other artificial limit; it should work for any number regardless of size (ignoring the physical limits of RAM etc).
Related tasks
count in factors
factors of an integer
Sieve of Eratosthenes
primality by trial division
factors of a Mersenne number
trial factoring of a Mersenne number
partition an integer X into N primes
sequence of primes by Trial Division
|
#C.2B.2B
|
C++
|
#include <iostream>
#include <gmpxx.h>
// This function template works for any type representing integers or
// nonnegative integers, and has the standard operator overloads for
// arithmetic and comparison operators, as well as explicit conversion
// from int.
//
// OutputIterator must be an output iterator with value_type Integer.
// It receives the prime factors.
template<typename Integer, typename OutputIterator>
void decompose(Integer n, OutputIterator out)
{
Integer i(2);
while (n != 1)
{
while (n % i == Integer(0))
{
*out++ = i;
n /= i;
}
++i;
}
}
// this is an output iterator similar to std::ostream_iterator, except
// that it outputs the separation string *before* the value, but not
// before the first value (i.e. it produces an infix notation).
template<typename T> class infix_ostream_iterator:
public std::iterator<T, std::output_iterator_tag>
{
class Proxy;
friend class Proxy;
class Proxy
{
public:
Proxy(infix_ostream_iterator& iter): iterator(iter) {}
Proxy& operator=(T const& value)
{
if (!iterator.first)
{
iterator.stream << iterator.infix;
}
iterator.stream << value;
}
private:
infix_ostream_iterator& iterator;
};
public:
infix_ostream_iterator(std::ostream& os, char const* inf):
stream(os),
first(true),
infix(inf)
{
}
infix_ostream_iterator& operator++() { first = false; return *this; }
infix_ostream_iterator operator++(int)
{
infix_ostream_iterator prev(*this);
++*this;
return prev;
}
Proxy operator*() { return Proxy(*this); }
private:
std::ostream& stream;
bool first;
char const* infix;
};
int main()
{
std::cout << "please enter a positive number: ";
mpz_class number;
std::cin >> number;
if (number <= 0)
std::cout << "this number is not positive!\n;";
else
{
std::cout << "decomposition: ";
decompose(number, infix_ostream_iterator<mpz_class>(std::cout, " * "));
std::cout << "\n";
}
}
|
http://rosettacode.org/wiki/Pointers_and_references
|
Pointers and references
|
Basic Data Operation
This is a basic data operation. It represents a fundamental action on a basic data type.
You may see other such operations in the Basic Data Operations category, or:
Integer Operations
Arithmetic |
Comparison
Boolean Operations
Bitwise |
Logical
String Operations
Concatenation |
Interpolation |
Comparison |
Matching
Memory Operations
Pointers & references |
Addresses
In this task, the goal is to demonstrate common operations on pointers and references. These examples show pointer operations on the stack, which can be dangerous and is rarely done. Pointers and references are commonly used along with Memory allocation on the heap.
|
#C_and_C.2B.2B
|
C and C++
|
int var = 3;
int *pointer = &var;
|
http://rosettacode.org/wiki/Pointers_and_references
|
Pointers and references
|
Basic Data Operation
This is a basic data operation. It represents a fundamental action on a basic data type.
You may see other such operations in the Basic Data Operations category, or:
Integer Operations
Arithmetic |
Comparison
Boolean Operations
Bitwise |
Logical
String Operations
Concatenation |
Interpolation |
Comparison |
Matching
Memory Operations
Pointers & references |
Addresses
In this task, the goal is to demonstrate common operations on pointers and references. These examples show pointer operations on the stack, which can be dangerous and is rarely done. Pointers and references are commonly used along with Memory allocation on the heap.
|
#C.23
|
C#
|
static void Main(string[] args)
{
int p;
p = 1;
Console.WriteLine("Ref Before: " + p);
Value(ref p);
Console.WriteLine("Ref After : " + p);
p = 1;
Console.WriteLine("Val Before: " + p);
Value(p);
Console.WriteLine("Val After : " + p);
Console.ReadLine();
}
private static void Value(ref int Value)
{
Value += 1;
}
private static void Value(int Value)
{
Value += 1;
}
|
http://rosettacode.org/wiki/Plot_coordinate_pairs
|
Plot coordinate pairs
|
Task
Plot a function represented as x, y numerical arrays.
Post the resulting image for the following input arrays (taken from Python's Example section on Time a function):
x = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
y = {2.7, 2.8, 31.4, 38.1, 58.0, 76.2, 100.5, 130.0, 149.3, 180.0};
This task is intended as a subtask for Measure relative performance of sorting algorithms implementations.
|
#Action.21
|
Action!
|
INCLUDE "D2:REAL.ACT" ;from the Action! Tool Kit
DEFINE PTR="CARD"
DEFINE BUF_SIZE="100"
DEFINE REAL_SIZE="3"
TYPE Settings=[
INT xMin,xMax,xStep,yMin,yMax,yStep
INT xLeft,xRight,yTop,yBottom
INT tickLength]
BYTE ARRAY xs(BUF_SIZE),ys(BUF_SIZE)
BYTE count=[0]
PTR FUNC GetXPtr(BYTE i)
RETURN (xs+3*i)
PTR FUNC GetYPtr(BYTE i)
RETURN (ys+3*i)
PROC AddPoint(CHAR ARRAY xstr,ystr)
REAL POINTER p
p=GetXPtr(count) ValR(xstr,p)
p=GetYPtr(count) ValR(ystr,p)
count==+1
RETURN
PROC InitData()
AddPoint("0.0","2.7")
AddPoint("1.0","2.8")
AddPoint("2.0","31.4")
AddPoint("3.0","38.1")
AddPoint("4.0","58.0")
AddPoint("5.0","76.2")
AddPoint("6.0","100.5")
AddPoint("7.0","130.0")
AddPoint("8.0","149.3")
AddPoint("9.0","180.0")
RETURN
INT FUNC GetXPos(Settings POINTER s INT x)
INT res
res=x*(s.xRight-s.xLeft)/(s.xMax-s.xMin)+s.xLeft
RETURN (res)
INT FUNC GetYPos(Settings POINTER s INT y)
INT res
res=y*(s.yTop-s.yBottom)/(s.yMax-s.yMin)+s.yBottom
RETURN (res)
INT FUNC GetXPosR(Settings POINTER s REAL POINTER x)
REAL nom,denom,div,tmp
INT res
IntToReal(s.xRight-s.xLeft,tmp)
RealMult(tmp,x,nom)
IntToReal(s.xMax-s.xMin,denom)
RealDiv(nom,denom,div)
res=RealToInt(div)+s.xLeft
RETURN (res)
INT FUNC GetYPosR(Settings POINTER s REAL POINTER y)
REAL nom,denom,div,tmp
INT res
IntToReal(s.yBottom-s.yTop,tmp)
RealMult(tmp,y,nom)
IntToReal(s.yMax-s.yMin,denom)
RealDiv(nom,denom,div)
res=-RealToInt(div)+s.yBottom
RETURN (res)
BYTE FUNC AtasciiToInternal(CHAR c)
BYTE c2
c2=c&$7F
IF c2<32 THEN
RETURN (c+64)
ELSEIF c2<96 THEN
RETURN (c-32)
FI
RETURN (c)
PROC CharOut(INT x,y CHAR c)
BYTE i,j,v
PTR addr
addr=$E000+AtasciiToInternal(c)*8;
FOR j=0 TO 7
DO
v=Peek(addr)
i=8
WHILE i>0
DO
IF v&1 THEN
Plot(x+i,y+j)
FI
v=v RSH 1
i==-1
OD
addr==+1
OD
RETURN
PROC TextOut(INT x,y CHAR ARRAY text)
BYTE i
FOR i=1 TO text(0)
DO
CharOut(x,y,text(i))
x==+8
OD
RETURN
PROC DrawAxes(Settings POINTER s)
INT i,x,y
CHAR ARRAY t(10)
Plot(s.xLeft,s.yTop)
DrawTo(s.xLeft,s.yBottom)
DrawTo(s.xRight,s.yBottom)
FOR i=s.xMin TO s.xMax STEP s.xStep
DO
x=GetXPos(s,i)
Plot(x,s.yBottom)
DrawTo(x,s.yBottom+s.tickLength)
StrI(i,t)
TextOut(x-t(0)*4,s.yBottom+s.tickLength+1,t)
OD
FOR i=s.yMin TO s.yMax STEP s.yStep
DO
y=GetYPos(s,i)
Plot(s.xLeft-s.tickLength,y)
DrawTo(s.xLeft,y)
StrI(i,t)
TextOut(s.xLeft-s.tickLength-1-t(0)*8,y-4,t)
OD
RETURN
PROC DrawPoint(INT x,y)
Plot(x-1,y-1) DrawTo(x+1,y-1)
DrawTo(x+1,y+1) DrawTo(x-1,y+1)
DrawTo(x-1,y-1)
RETURN
PROC DrawSeries(Settings POINTER s)
INT i,x,y,prevX,prevY
REAL POINTER p
FOR i=0 TO count-1
DO
p=GetXPtr(i) x=GetXPosR(s,p)
p=GetYPtr(i) y=GetYPosR(s,p)
DrawPoint(x,y)
IF i>0 THEN
Plot(prevX,prevY)
DrawTo(x,y)
FI
prevX=x prevY=y
OD
RETURN
PROC DrawPlot(Settings POINTER s)
DrawAxes(s)
DrawSeries(s)
RETURN
PROC Main()
BYTE CH=$02FC,COLOR1=$02C5,COLOR2=$02C6
Settings s
Graphics(8+16)
Color=1
COLOR1=$0C
COLOR2=$02
InitData()
s.xMin=0 s.xMax=9 s.xStep=1
s.yMin=0 s.yMax=180 s.yStep=20
s.xLeft=30 s.xRight=311 s.yTop=8 s.yBottom=177
s.tickLength=3
DrawPlot(s)
DO UNTIL CH#$FF OD
CH=$FF
RETURN
|
http://rosettacode.org/wiki/Plot_coordinate_pairs
|
Plot coordinate pairs
|
Task
Plot a function represented as x, y numerical arrays.
Post the resulting image for the following input arrays (taken from Python's Example section on Time a function):
x = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
y = {2.7, 2.8, 31.4, 38.1, 58.0, 76.2, 100.5, 130.0, 149.3, 180.0};
This task is intended as a subtask for Measure relative performance of sorting algorithms implementations.
|
#Ada
|
Ada
|
with Gtk.Main;
with Gtk.Window; use Gtk.Window;
with Gtk.Widget; use Gtk.Widget;
with Gtk.Handlers; use Gtk.Handlers;
with Glib; use Glib;
with Gtk.Extra.Plot; use Gtk.Extra.Plot;
with Gtk.Extra.Plot_Data; use Gtk.Extra.Plot_Data;
with Gtk.Extra.Plot_Canvas; use Gtk.Extra.Plot_Canvas;
with Gtk.Extra.Plot_Canvas.Plot; use Gtk.Extra.Plot_Canvas.Plot;
procedure PlotCoords is
package Handler is new Callback (Gtk_Widget_Record);
Window : Gtk_Window;
Plot : Gtk_Plot;
PCP : Gtk_Plot_Canvas_Plot;
Canvas : Gtk_Plot_Canvas;
PlotData : Gtk_Plot_Data;
x, y, dx, dy : Gdouble_Array_Access;
procedure ExitMain (Object : access Gtk_Widget_Record'Class) is
begin
Destroy (Object); Gtk.Main.Main_Quit;
end ExitMain;
begin
x := new Gdouble_Array'(0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0);
y := new Gdouble_Array'(2.7, 2.8, 31.4, 38.1, 58.0, 76.2, 100.5, 130.0, 149.3, 180.0);
Gtk.Main.Init;
Gtk_New (Window);
Set_Title (Window, "Plot coordinate pairs with GtkAda");
Gtk_New (PlotData);
Set_Points (PlotData, x, y, dx, dy);
Gtk_New (Plot);
Add_Data (Plot, PlotData);
Autoscale (Plot); Show (PlotData);
Hide_Legends (Plot);
Gtk_New (PCP, Plot); Show (Plot);
Gtk_New (Canvas, 500, 500); Show (Canvas);
Put_Child (Canvas, PCP, 0.15, 0.15, 0.85, 0.85);
Add (Window, Canvas);
Show_All (Window);
Handler.Connect (Window, "destroy",
Handler.To_Marshaller (ExitMain'Access));
Gtk.Main.Main;
end PlotCoords;
|
http://rosettacode.org/wiki/Polymorphism
|
Polymorphism
|
Task
Create two classes Point(x,y) and Circle(x,y,r) with a polymorphic function print, accessors for (x,y,r), copy constructor, assignment and destructor and every possible default constructors
|
#Arturo
|
Arturo
|
define :point [x,y][
init: [
ensure -> is? :floating this\x
ensure -> is? :floating this\y
]
print: [
render "point (x: |this\x|, y: |this\y|)"
]
]
define :circle [center,radius][
init: [
ensure -> is? :point this\center
ensure -> is? :floating this\radius
]
print: [
render "circle (center: |this\center|, radius: |this\radius|)"
]
]
p: to :point [10.0, 20.0]
c: to :circle @[p, 10.0]
inspect p
inspect c
print p
print c
|
http://rosettacode.org/wiki/Polymorphism
|
Polymorphism
|
Task
Create two classes Point(x,y) and Circle(x,y,r) with a polymorphic function print, accessors for (x,y,r), copy constructor, assignment and destructor and every possible default constructors
|
#AutoHotkey
|
AutoHotkey
|
MyPoint := new Point(1, 8)
MyPoint.Print()
MyCircle := new Circle(4, 7, 9)
MyCircle2 := MyCircle.Copy()
MyCircle.SetX(2) ;Assignment method
MyCircle.y := 3 ;Direct assignment
MyCircle.Print()
MyCircle2.Print()
MyCircle.SetX(100), MyCircle.SetY(1000), MyCircle.r := 10000
MsgBox, % MyCircle.__Class
. "`n`nx:`t" MyCircle.GetX()
. "`ny:`t" MyCircle.y
. "`nr:`t" MyCircle.GetR()
return
class Point
{
Copy()
{
return this.Clone()
}
GetX()
{
return this.x
}
GetY()
{
return this.y
}
__New(x, y)
{
this.x := x
this.y := y
}
Print()
{
MsgBox, % this.__Class
. "`n`nx:`t" this.x
. "`ny:`t" this.y
}
SetX(aValue)
{
this.x := aValue
}
SetY(aValue)
{
this.y := aValue
}
}
class Circle extends Point
{
GetR()
{
return this.r
}
__New(x, y, r)
{
this.r := r
base.__New(x, y)
}
Print()
{
MsgBox, % this.__Class
. "`n`nx:`t" this.x
. "`ny:`t" this.y
. "`nr:`t" this.r
}
SetR(aValue)
{
this.r := aValue
}
}
|
http://rosettacode.org/wiki/Poker_hand_analyser
|
Poker hand analyser
|
Task
Create a program to parse a single five card poker hand and rank it according to this list of poker hands.
A poker hand is specified as a space separated list of five playing cards.
Each input card has two characters indicating face and suit.
Example
2d (two of diamonds).
Faces are: a, 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k
Suits are: h (hearts), d (diamonds), c (clubs), and s (spades), or
alternatively, the unicode card-suit characters: ♥ ♦ ♣ ♠
Duplicate cards are illegal.
The program should analyze a single hand and produce one of the following outputs:
straight-flush
four-of-a-kind
full-house
flush
straight
three-of-a-kind
two-pair
one-pair
high-card
invalid
Examples
2♥ 2♦ 2♣ k♣ q♦: three-of-a-kind
2♥ 5♥ 7♦ 8♣ 9♠: high-card
a♥ 2♦ 3♣ 4♣ 5♦: straight
2♥ 3♥ 2♦ 3♣ 3♦: full-house
2♥ 7♥ 2♦ 3♣ 3♦: two-pair
2♥ 7♥ 7♦ 7♣ 7♠: four-of-a-kind
10♥ j♥ q♥ k♥ a♥: straight-flush
4♥ 4♠ k♠ 5♦ 10♠: one-pair
q♣ 10♣ 7♣ 6♣ q♣: invalid
The programs output for the above examples should be displayed here on this page.
Extra credit
use the playing card characters introduced with Unicode 6.0 (U+1F0A1 - U+1F0DE).
allow two jokers
use the symbol joker
duplicates would be allowed (for jokers only)
five-of-a-kind would then be the highest hand
More extra credit examples
joker 2♦ 2♠ k♠ q♦: three-of-a-kind
joker 5♥ 7♦ 8♠ 9♦: straight
joker 2♦ 3♠ 4♠ 5♠: straight
joker 3♥ 2♦ 3♠ 3♦: four-of-a-kind
joker 7♥ 2♦ 3♠ 3♦: three-of-a-kind
joker 7♥ 7♦ 7♠ 7♣: five-of-a-kind
joker j♥ q♥ k♥ A♥: straight-flush
joker 4♣ k♣ 5♦ 10♠: one-pair
joker k♣ 7♣ 6♣ 4♣: flush
joker 2♦ joker 4♠ 5♠: straight
joker Q♦ joker A♠ 10♠: straight
joker Q♦ joker A♦ 10♦: straight-flush
joker 2♦ 2♠ joker q♦: four-of-a-kind
Related tasks
Playing cards
Card shuffles
Deal cards_for_FreeCell
War Card_Game
Go Fish
|
#C
|
C
|
#include <stdio.h>
#include <ctype.h>
#include <string.h>
#include <stdlib.h>
#define TRUE 1
#define FALSE 0
#define FACES "23456789tjqka"
#define SUITS "shdc"
typedef int bool;
typedef struct {
int face; /* FACES map to 0..12 respectively */
char suit;
} card;
card cards[5];
int compare_card(const void *a, const void *b) {
card c1 = *(card *)a;
card c2 = *(card *)b;
return c1.face - c2.face;
}
bool equals_card(card c1, card c2) {
if (c1.face == c2.face && c1.suit == c2.suit) return TRUE;
return FALSE;
}
bool are_distinct() {
int i, j;
for (i = 0; i < 4; ++i)
for (j = i + 1; j < 5; ++j)
if (equals_card(cards[i], cards[j])) return FALSE;
return TRUE;
}
bool is_straight() {
int i;
qsort(cards, 5, sizeof(card), compare_card);
if (cards[0].face + 4 == cards[4].face) return TRUE;
if (cards[4].face == 12 && cards[0].face == 0 &&
cards[3].face == 3) return TRUE;
return FALSE;
}
bool is_flush() {
int i;
char suit = cards[0].suit;
for (i = 1; i < 5; ++i) if (cards[i].suit != suit) return FALSE;
return TRUE;
}
const char *analyze_hand(const char *hand) {
int i, j, gs = 0;
char suit, *cp;
bool found, flush, straight;
int groups[13];
if (strlen(hand) != 14) return "invalid";
for (i = 0; i < 14; i += 3) {
cp = strchr(FACES, tolower(hand[i]));
if (cp == NULL) return "invalid";
j = i / 3;
cards[j].face = cp - FACES;
suit = tolower(hand[i + 1]);
cp = strchr(SUITS, suit);
if (cp == NULL) return "invalid";
cards[j].suit = suit;
}
if (!are_distinct()) return "invalid";
for (i = 0; i < 13; ++i) groups[i] = 0;
for (i = 0; i < 5; ++i) groups[cards[i].face]++;
for (i = 0; i < 13; ++i) if (groups[i] > 0) gs++;
switch(gs) {
case 2:
found = FALSE;
for (i = 0; i < 13; ++i) if (groups[i] == 4) {
found = TRUE;
break;
}
if (found) return "four-of-a-kind";
return "full-house";
case 3:
found = FALSE;
for (i = 0; i < 13; ++i) if (groups[i] == 3) {
found = TRUE;
break;
}
if (found) return "three-of-a-kind";
return "two-pairs";
case 4:
return "one-pair";
default:
flush = is_flush();
straight = is_straight();
if (flush && straight)
return "straight-flush";
else if (flush)
return "flush";
else if (straight)
return "straight";
else
return "high-card";
}
}
int main(){
int i;
const char *type;
const char *hands[10] = {
"2h 2d 2c kc qd",
"2h 5h 7d 8c 9s",
"ah 2d 3c 4c 5d",
"2h 3h 2d 3c 3d",
"2h 7h 2d 3c 3d",
"2h 7h 7d 7c 7s",
"th jh qh kh ah",
"4h 4s ks 5d ts",
"qc tc 7c 6c 4c",
"ah ah 7c 6c 4c"
};
for (i = 0; i < 10; ++i) {
type = analyze_hand(hands[i]);
printf("%s: %s\n", hands[i], type);
}
return 0;
}
|
http://rosettacode.org/wiki/Population_count
|
Population count
|
Population count
You are encouraged to solve this task according to the task description, using any language you may know.
The population count is the number of 1s (ones) in the binary representation of a non-negative integer.
Population count is also known as:
pop count
popcount
sideways sum
bit summation
Hamming weight
For example, 5 (which is 101 in binary) has a population count of 2.
Evil numbers are non-negative integers that have an even population count.
Odious numbers are positive integers that have an odd population count.
Task
write a function (or routine) to return the population count of a non-negative integer.
all computation of the lists below should start with 0 (zero indexed).
display the pop count of the 1st thirty powers of 3 (30, 31, 32, 33, 34, ∙∙∙ 329).
display the 1st thirty evil numbers.
display the 1st thirty odious numbers.
display each list of integers on one line (which may or may not include a title), each set of integers being shown should be properly identified.
See also
The On-Line Encyclopedia of Integer Sequences: A000120 population count.
The On-Line Encyclopedia of Integer Sequences: A000069 odious numbers.
The On-Line Encyclopedia of Integer Sequences: A001969 evil numbers.
|
#APL
|
APL
|
APL (DYALOG APL)
popDemo←{⎕IO←0
N←⍵
⍝ popCount: Does a popCount of integers (8-32 bits) or floats (64-bits) that can be represented as integers
popCount←{
i2bits←{∊+/2⊥⍣¯1⊣⍵} ⍝ Use ⊥⍣¯1 (inverted decode) for ⊤ (encode) to automatically detect nubits needed
+/i2bits ⍵ ⍝ Count the bits
}¨
act3←popCount 3*⍳N
M←N×2
actEvil←N↑{⍵/⍨0=2|popCount ⍵}⍳M
actOdious←N↑{⍵/⍨1=2|popCount ⍵}⍳M
⎕←'powers 3'act3
⎕←'evil 'actEvil
⎕←'odious 'actOdious
⍝ Extra: Validate answers are correct
⍝ Actual answers
ans3←1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
ansEvil←0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
ansOdious←1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
'***Passes' '***Fails'⊃⍨(ans3≢act3)∨(actEvil≢ansEvil)∨(actOdious≢ansOdious)
}
|
http://rosettacode.org/wiki/Polynomial_long_division
|
Polynomial long division
|
This page uses content from Wikipedia. The original article was at Polynomial long division. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree.
Let us suppose a polynomial is represented by a vector,
x
{\displaystyle x}
(i.e., an ordered collection of coefficients) so that the
i
{\displaystyle i}
th element keeps the coefficient of
x
i
{\displaystyle x^{i}}
, and the multiplication by a monomial is a shift of the vector's elements "towards right" (injecting ones from left) followed by a multiplication of each element by the coefficient of the monomial.
Then a pseudocode for the polynomial long division using the conventions described above could be:
degree(P):
return the index of the last non-zero element of P;
if all elements are 0, return -∞
polynomial_long_division(N, D) returns (q, r):
// N, D, q, r are vectors
if degree(D) < 0 then error
q ← 0
while degree(N) ≥ degree(D)
d ← D shifted right by (degree(N) - degree(D))
q(degree(N) - degree(D)) ← N(degree(N)) / d(degree(d))
// by construction, degree(d) = degree(N) of course
d ← d * q(degree(N) - degree(D))
N ← N - d
endwhile
r ← N
return (q, r)
Note: vector * scalar multiplies each element of the vector by the scalar; vectorA - vectorB subtracts each element of the vectorB from the element of the vectorA with "the same index". The vectors in the pseudocode are zero-based.
Error handling (for allocations or for wrong inputs) is not mandatory.
Conventions can be different; in particular, note that if the first coefficient in the vector is the highest power of x for the polynomial represented by the vector, then the algorithm becomes simpler.
Example for clarification
This example is from Wikipedia, but changed to show how the given pseudocode works.
0 1 2 3
----------------------
N: -42 0 -12 1 degree = 3
D: -3 1 0 0 degree = 1
d(N) - d(D) = 2, so let's shift D towards right by 2:
N: -42 0 -12 1
d: 0 0 -3 1
N(3)/d(3) = 1, so d is unchanged. Now remember that "shifting by 2"
is like multiplying by x2, and the final multiplication
(here by 1) is the coefficient of this monomial. Let's store this
into q:
0 1 2
---------------
q: 0 0 1
now compute N - d, and let it be the "new" N, and let's loop
N: -42 0 -9 0 degree = 2
D: -3 1 0 0 degree = 1
d(N) - d(D) = 1, right shift D by 1 and let it be d
N: -42 0 -9 0
d: 0 -3 1 0 * -9/1 = -9
q: 0 -9 1
d: 0 27 -9 0
N ← N - d
N: -42 -27 0 0 degree = 1
D: -3 1 0 0 degree = 1
looping again... d(N)-d(D)=0, so no shift is needed; we
multiply D by -27 (= -27/1) storing the result in d, then
q: -27 -9 1
and
N: -42 -27 0 0 -
d: 81 -27 0 0 =
N: -123 0 0 0 (last N)
d(N) < d(D), so now r ← N, and the result is:
0 1 2
-------------
q: -27 -9 1 → x2 - 9x - 27
r: -123 0 0 → -123
Related task
Polynomial derivative
|
#Clojure
|
Clojure
|
(defn grevlex [term1 term2]
(let [grade1 (reduce +' term1)
grade2 (reduce +' term2)
comp (- grade2 grade1)] ;; total degree
(if (not= 0 comp)
comp
(loop [term1 term1
term2 term2]
(if (empty? term1)
0
(let [grade1 (last term1)
grade2 (last term2)
comp (- grade1 grade2)] ;; differs from grlex because terms are flipped from above
(if (not= 0 comp)
comp
(recur (pop term1)
(pop term2)))))))))
(defn mul
;; transducer
([poly1] ;; completion
(fn
([] poly1)
([poly2] (mul poly1 poly2))
([poly2 & more] (mul poly1 poly2 more))))
([poly1 poly2]
(let [product (atom (transient (sorted-map-by grevlex)))]
(doall ;; `for` is lazy so must to be forced for side-effects
(for [term1 poly1
term2 poly2
:let [vars (mapv +' (key term1) (key term2))
coeff (* (val term1) (val term2))]]
(if (contains? @product vars)
(swap! product assoc! vars (+ (get @product vars) coeff))
(swap! product assoc! vars coeff))))
(->> product
(deref)
(persistent!)
(denull))))
([poly1 poly2 & more]
(reduce mul (mul poly1 poly2) more)))
(defn compl [term1 term2]
(map (fn [x y]
(cond
(and (zero? x) (not= 0 y)) nil
(< x y) nil
(>= x y) (- x y)))
term1
term2))
(defn s-poly [f g]
(let [f-vars (first f)
g-vars (first g)
lcm (compl f-vars g-vars)]
(if (not-any? nil? lcm)
{(vec lcm)
(/ (second f) (second g))})))
(defn divide [f g]
(loop [f f
g g
result (transient {})
remainder {}]
(if (empty? f)
(list (persistent! result)
(->> remainder
(filter #(not (nil? %)))
(into (sorted-map-by grevlex))))
(let [term1 (first f)
term2 (first g)
s-term (s-poly term1 term2)]
(if (nil? s-term)
(recur (dissoc f (first term1))
(dissoc g (first term2))
result
(conj remainder term1))
(recur (sub f (mul g s-term))
g
(conj! result s-term)
remainder))))))
(deftest divide-tests
(is (= (divide {[1 1] 2, [1 0] 3, [0 1] 5, [0 0] 7}
{[1 1] 2, [1 0] 3, [0 1] 5, [0 0] 7})
'({[0 0] 1} {})))
(is (= (divide {[1 1] 2, [1 0] 3, [0 1] 5, [0 0] 7}
{[0 0] 1})
'({[1 1] 2, [1 0] 3, [0 1] 5, [0 0] 7} {})))
(is (= (divide {[1 1] 2, [1 0] 10, [0 1] 3, [0 0] 15}
{[0 1] 1, [0 0] 5})
'({[1 0] 2, [0 0] 3} {})))
(is (= (divide {[1 1] 2, [1 0] 10, [0 1] 3, [0 0] 15}
{[1 0] 2, [0 0] 3})
'({[0 1] 1, [0 0] 5} {}))))
|
http://rosettacode.org/wiki/Polymorphic_copy
|
Polymorphic copy
|
An object is polymorphic when its specific type may vary.
The types a specific value may take, is called class.
It is trivial to copy an object if its type is known:
int x;
int y = x;
Here x is not polymorphic, so y is declared of same type (int) as x.
But if the specific type of x were unknown, then y could not be declared of any specific type.
The task: let a polymorphic object contain an instance of some specific type S derived from a type T.
The type T is known.
The type S is possibly unknown until run time.
The objective is to create an exact copy of such polymorphic object (not to create a reference, nor a pointer to).
Let further the type T have a method overridden by S.
This method is to be called on the copy to demonstrate that the specific type of the copy is indeed S.
|
#E
|
E
|
def deSubgraphKit := <elib:serial.deSubgraphKit>
def copy(object) {
return deSubgraphKit.recognize(object, deSubgraphKit.makeBuilder())
}
|
http://rosettacode.org/wiki/Polymorphic_copy
|
Polymorphic copy
|
An object is polymorphic when its specific type may vary.
The types a specific value may take, is called class.
It is trivial to copy an object if its type is known:
int x;
int y = x;
Here x is not polymorphic, so y is declared of same type (int) as x.
But if the specific type of x were unknown, then y could not be declared of any specific type.
The task: let a polymorphic object contain an instance of some specific type S derived from a type T.
The type T is known.
The type S is possibly unknown until run time.
The objective is to create an exact copy of such polymorphic object (not to create a reference, nor a pointer to).
Let further the type T have a method overridden by S.
This method is to be called on the copy to demonstrate that the specific type of the copy is indeed S.
|
#EchoLisp
|
EchoLisp
|
(lib 'types)
(lib 'struct)
(struct T (integer:x)) ;; super class
(struct S T (integer:y)) ;; sub class
(struct K (T:box)) ;; container class, box must be of type T, or derived
(define k-source (K (S 33 42)))
(define k-copy (copy k-source))
k-source
→ #<K> (#<S> (33 42)) ;; new container, with a S in box
k-copy
→ #<K> (#<S> (33 42)) ;; copied S type
(set-S-y! (K-box k-source) 666) ;; modify k-source.box.y
k-source
→ #<K> (#<S> (33 666)) ;; modified
k-copy
→ #<K> (#<S> (33 42)) ;; unmodified
(K "string-inside") ;; trying to put a string in the container box
😡 error: T : type-check failure : string-inside → 'K:box'
|
http://rosettacode.org/wiki/Polyspiral
|
Polyspiral
|
A Polyspiral is a spiral made of multiple line segments, whereby each segment is larger (or smaller) than the previous one by a given amount. Each segment also changes direction at a given angle.
Task
Animate a series of polyspirals, by drawing a complete spiral then incrementing the angle, and (after clearing the background) drawing the next, and so on. Every spiral will be a frame of the animation. The animation may stop as it goes full circle or continue indefinitely. The given input values may be varied.
If animation is not practical in your programming environment, you may show a single frame instead.
Pseudo code
set incr to 0.0
// animation loop
WHILE true
incr = (incr + 0.05) MOD 360
x = width / 2
y = height / 2
length = 5
angle = incr
// spiral loop
FOR 1 TO 150
drawline
change direction by angle
length = length + 3
angle = (angle + incr) MOD 360
ENDFOR
|
#Lua
|
Lua
|
function love.load ()
love.window.setTitle("Polyspiral")
incr = 0
end
function love.update (dt)
incr = (incr + 0.05) % 360
x1 = love.graphics.getWidth() / 2
y1 = love.graphics.getHeight() / 2
length = 5
angle = incr
end
function love.draw ()
for i = 1, 150 do
x2 = x1 + math.cos(angle) * length
y2 = y1 + math.sin(angle) * length
love.graphics.line(x1, y1, x2, y2)
x1, y1 = x2, y2
length = length + 3
angle = (angle + incr) % 360
end
end
|
http://rosettacode.org/wiki/Polyspiral
|
Polyspiral
|
A Polyspiral is a spiral made of multiple line segments, whereby each segment is larger (or smaller) than the previous one by a given amount. Each segment also changes direction at a given angle.
Task
Animate a series of polyspirals, by drawing a complete spiral then incrementing the angle, and (after clearing the background) drawing the next, and so on. Every spiral will be a frame of the animation. The animation may stop as it goes full circle or continue indefinitely. The given input values may be varied.
If animation is not practical in your programming environment, you may show a single frame instead.
Pseudo code
set incr to 0.0
// animation loop
WHILE true
incr = (incr + 0.05) MOD 360
x = width / 2
y = height / 2
length = 5
angle = incr
// spiral loop
FOR 1 TO 150
drawline
change direction by angle
length = length + 3
angle = (angle + incr) MOD 360
ENDFOR
|
#Mathematica.2FWolfram_Language
|
Mathematica/Wolfram Language
|
linedata = {};
Dynamic[Graphics[Line[linedata], PlotRange -> 1000]]
Do[
linedata = AnglePath[{#, \[Theta]} & /@ Range[5, 300, 3]];
Pause[0.1];
,
{\[Theta], Subdivide[0.1, 1, 100]}
]
|
http://rosettacode.org/wiki/Polynomial_regression
|
Polynomial regression
|
Find an approximating polynomial of known degree for a given data.
Example:
For input data:
x = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
y = {1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321};
The approximating polynomial is:
3 x2 + 2 x + 1
Here, the polynomial's coefficients are (3, 2, 1).
This task is intended as a subtask for Measure relative performance of sorting algorithms implementations.
|
#Common_Lisp
|
Common Lisp
|
;; Least square fit of a polynomial of order n the x-y-curve.
(defun polyfit (x y n)
(let* ((m (cadr (array-dimensions x)))
(A (make-array `(,m ,(+ n 1)) :initial-element 0)))
(loop for i from 0 to (- m 1) do
(loop for j from 0 to n do
(setf (aref A i j)
(expt (aref x 0 i) j))))
(lsqr A (mtp y))))
|
http://rosettacode.org/wiki/Power_set
|
Power set
|
A set is a collection (container) of certain values,
without any particular order, and no repeated values.
It corresponds with a finite set in mathematics.
A set can be implemented as an associative array (partial mapping)
in which the value of each key-value pair is ignored.
Given a set S, the power set (or powerset) of S, written P(S), or 2S, is the set of all subsets of S.
Task
By using a library or built-in set type, or by defining a set type with necessary operations, write a function with a set S as input that yields the power set 2S of S.
For example, the power set of {1,2,3,4} is
{{}, {1}, {2}, {1,2}, {3}, {1,3}, {2,3}, {1,2,3}, {4}, {1,4}, {2,4}, {1,2,4}, {3,4}, {1,3,4}, {2,3,4}, {1,2,3,4}}.
For a set which contains n elements, the corresponding power set has 2n elements, including the edge cases of empty set.
The power set of the empty set is the set which contains itself (20 = 1):
P
{\displaystyle {\mathcal {P}}}
(
∅
{\displaystyle \varnothing }
) = {
∅
{\displaystyle \varnothing }
}
And the power set of the set which contains only the empty set, has two subsets, the empty set and the set which contains the empty set (21 = 2):
P
{\displaystyle {\mathcal {P}}}
({
∅
{\displaystyle \varnothing }
}) = {
∅
{\displaystyle \varnothing }
, {
∅
{\displaystyle \varnothing }
} }
Extra credit: Demonstrate that your language supports these last two powersets.
|
#BQN
|
BQN
|
P ← (⥊·↕2⥊˜≠)/¨<
|
http://rosettacode.org/wiki/Primality_by_trial_division
|
Primality by trial division
|
Task
Write a boolean function that tells whether a given integer is prime.
Remember that 1 and all non-positive numbers are not prime.
Use trial division.
Even numbers greater than 2 may be eliminated right away.
A loop from 3 to √ n will suffice, but other loops are allowed.
Related tasks
count in factors
prime decomposition
AKS test for primes
factors of an integer
Sieve of Eratosthenes
factors of a Mersenne number
trial factoring of a Mersenne number
partition an integer X into N primes
sequence of primes by Trial Division
|
#AutoIt
|
AutoIt
|
#cs ----------------------------------------------------------------------------
AutoIt Version: 3.3.8.1
Author: Alexander Alvonellos
Script Function:
Perform primality test on a given integer $number.
RETURNS: TRUE/FALSE
#ce ----------------------------------------------------------------------------
Func main()
ConsoleWrite("The primes up to 100 are: " & @LF)
For $i = 1 To 100 Step 1
If(isPrime($i)) Then
If($i <> 97) Then
ConsoleWrite($i & ", ")
Else
ConsoleWrite($i)
EndIf
EndIf
Next
EndFunc
Func isPrime($n)
If($n < 2) Then Return False
If($n = 2) Then Return True
If(BitAnd($n, 1) = 0) Then Return False
For $i = 3 To Sqrt($n) Step 2
If(Mod($n, $i) = 0) Then Return False
Next
Return True
EndFunc
main()
|
http://rosettacode.org/wiki/Price_fraction
|
Price fraction
|
A friend of mine runs a pharmacy. He has a specialized function in his Dispensary application which receives a decimal value of currency and replaces it to a standard value. This value is regulated by a government department.
Task
Given a floating point value between 0.00 and 1.00, rescale according to the following table:
>= 0.00 < 0.06 := 0.10
>= 0.06 < 0.11 := 0.18
>= 0.11 < 0.16 := 0.26
>= 0.16 < 0.21 := 0.32
>= 0.21 < 0.26 := 0.38
>= 0.26 < 0.31 := 0.44
>= 0.31 < 0.36 := 0.50
>= 0.36 < 0.41 := 0.54
>= 0.41 < 0.46 := 0.58
>= 0.46 < 0.51 := 0.62
>= 0.51 < 0.56 := 0.66
>= 0.56 < 0.61 := 0.70
>= 0.61 < 0.66 := 0.74
>= 0.66 < 0.71 := 0.78
>= 0.71 < 0.76 := 0.82
>= 0.76 < 0.81 := 0.86
>= 0.81 < 0.86 := 0.90
>= 0.86 < 0.91 := 0.94
>= 0.91 < 0.96 := 0.98
>= 0.96 < 1.01 := 1.00
|
#Common_Lisp
|
Common Lisp
|
(defun scale (value)
(cond ((minusp value) (error "invalid value: ~A" value))
((< value 0.06) 0.10)
((< value 0.11) 0.18)
((< value 0.16) 0.26)
((< value 0.21) 0.32)
((< value 0.26) 0.38)
((< value 0.31) 0.44)
((< value 0.36) 0.50)
((< value 0.41) 0.54)
((< value 0.46) 0.58)
((< value 0.51) 0.62)
((< value 0.56) 0.66)
((< value 0.61) 0.70)
((< value 0.66) 0.74)
((< value 0.71) 0.78)
((< value 0.76) 0.82)
((< value 0.81) 0.86)
((< value 0.86) 0.90)
((< value 0.91) 0.94)
((< value 0.96) 0.98)
((< value 1.01) 1.00)
(t (error "invalid value: ~A" value))))
|
http://rosettacode.org/wiki/Proper_divisors
|
Proper divisors
|
The proper divisors of a positive integer N are those numbers, other than N itself, that divide N without remainder.
For N > 1 they will always include 1, but for N == 1 there are no proper divisors.
Examples
The proper divisors of 6 are 1, 2, and 3.
The proper divisors of 100 are 1, 2, 4, 5, 10, 20, 25, and 50.
Task
Create a routine to generate all the proper divisors of a number.
use it to show the proper divisors of the numbers 1 to 10 inclusive.
Find a number in the range 1 to 20,000 with the most proper divisors. Show the number and just the count of how many proper divisors it has.
Show all output here.
Related tasks
Amicable pairs
Abundant, deficient and perfect number classifications
Aliquot sequence classifications
Factors of an integer
Prime decomposition
|
#Fortran
|
Fortran
|
function icntprop(num )
icnt=0
do i=1 , num-1
if (mod(num , i) .eq. 0) then
icnt = icnt + 1
if (num .lt. 11) print *,' ',i
end if
end do
icntprop = icnt
end function
limit = 20000
maxcnt = 0
print *,'N divisors'
do j=1,limit,1
if (j .lt. 11) print *,j
icnt = icntprop(j)
if (icnt .gt. maxcnt) then
maxcnt = icnt
maxj = j
end if
end do
print *,' '
print *,' from 1 to ',limit
print *,maxj,' has max proper divisors: ',maxcnt
end
|
http://rosettacode.org/wiki/Probabilistic_choice
|
Probabilistic choice
|
Given a mapping between items and their required probability of occurrence, generate a million items randomly subject to the given probabilities and compare the target probability of occurrence versus the generated values.
The total of all the probabilities should equal one. (Because floating point arithmetic is involved, this is subject to rounding errors).
aleph 1/5.0
beth 1/6.0
gimel 1/7.0
daleth 1/8.0
he 1/9.0
waw 1/10.0
zayin 1/11.0
heth 1759/27720 # adjusted so that probabilities add to 1
Related task
Random number generator (device)
|
#Julia
|
Julia
|
using Printf
p = [1/i for i in 5:11]
plen = length(p)
q = [0.0, [sum(p[1:i]) for i = 1:plen]]
plab = [char(i) for i in 0x05d0:(0x05d0+plen)]
hi = 10^6
push!(p, 1.0 - sum(p))
plen += 1
accum = zeros(Int, plen)
for i in 1:hi
accum[sum(rand() .>= q)] += 1
end
r = accum/hi
println("Rates at which items are selected (", hi, " trials).")
println(" Item Expected Actual")
for i in 1:plen
println(@sprintf(" \u2067%s %8.6f %8.6f", plab[i], p[i], r[i]))
end
println()
println("Rates at which items are selected (", hi, " trials).")
println(" Item Count Expected Actual")
for i in 1:plen
println(@sprintf(" %s yields %6d %8.6f %8.6f",
plab[i], accum[i], p[i], r[i]))
end
|
http://rosettacode.org/wiki/Probabilistic_choice
|
Probabilistic choice
|
Given a mapping between items and their required probability of occurrence, generate a million items randomly subject to the given probabilities and compare the target probability of occurrence versus the generated values.
The total of all the probabilities should equal one. (Because floating point arithmetic is involved, this is subject to rounding errors).
aleph 1/5.0
beth 1/6.0
gimel 1/7.0
daleth 1/8.0
he 1/9.0
waw 1/10.0
zayin 1/11.0
heth 1759/27720 # adjusted so that probabilities add to 1
Related task
Random number generator (device)
|
#Kotlin
|
Kotlin
|
// version 1.0.6
fun main(args: Array<String>) {
val letters = arrayOf("aleph", "beth", "gimel", "daleth", "he", "waw", "zayin", "heth")
val actual = IntArray(8)
val probs = doubleArrayOf(1/5.0, 1/6.0, 1/7.0, 1/8.0, 1/9.0, 1/10.0, 1/11.0, 0.0)
val cumProbs = DoubleArray(8)
cumProbs[0] = probs[0]
for (i in 1..6) cumProbs[i] = cumProbs[i - 1] + probs[i]
cumProbs[7] = 1.0
probs[7] = 1.0 - cumProbs[6]
val n = 1000000
(1..n).forEach {
val rand = Math.random()
when {
rand <= cumProbs[0] -> actual[0]++
rand <= cumProbs[1] -> actual[1]++
rand <= cumProbs[2] -> actual[2]++
rand <= cumProbs[3] -> actual[3]++
rand <= cumProbs[4] -> actual[4]++
rand <= cumProbs[5] -> actual[5]++
rand <= cumProbs[6] -> actual[6]++
else -> actual[7]++
}
}
var sumActual = 0.0
println("Letter\t Actual Expected")
println("------\t-------- --------")
for (i in 0..7) {
val generated = actual[i].toDouble() / n
println("${letters[i]}\t${String.format("%8.6f %8.6f", generated, probs[i])}")
sumActual += generated
}
println("\t-------- --------")
println("\t${"%8.6f".format(sumActual)} 1.000000")
}
|
http://rosettacode.org/wiki/Priority_queue
|
Priority queue
|
A priority queue is somewhat similar to a queue, with an important distinction: each item is added to a priority queue with a priority level, and will be later removed from the queue with the highest priority element first. That is, the items are (conceptually) stored in the queue in priority order instead of in insertion order.
Task
Create a priority queue. The queue must support at least two operations:
Insertion. An element is added to the queue with a priority (a numeric value).
Top item removal. Deletes the element or one of the elements with the current top priority and return it.
Optionally, other operations may be defined, such as peeking (find what current top priority/top element is), merging (combining two priority queues into one), etc.
To test your implementation, insert a number of elements into the queue, each with some random priority.
Then dequeue them sequentially; now the elements should be sorted by priority.
You can use the following task/priority items as input data:
Priority Task
══════════ ════════════════
3 Clear drains
4 Feed cat
5 Make tea
1 Solve RC tasks
2 Tax return
The implementation should try to be efficient. A typical implementation has O(log n) insertion and extraction time, where n is the number of items in the queue.
You may choose to impose certain limits such as small range of allowed priority levels, limited capacity, etc. If so, discuss the reasons behind it.
|
#Icon_and_Unicon
|
Icon and Unicon
|
import Utils # For Closure class
import Collections # For Heap (dense priority queue) class
procedure main()
pq := Heap(, Closure("[]",Arg,1) )
pq.add([3, "Clear drains"])
pq.add([4, "Feed cat"])
pq.add([5, "Make tea"])
pq.add([1, "Solve RC tasks"])
pq.add([2, "Tax return"])
while task := pq.get() do write(task[1]," -> ",task[2])
end
|
http://rosettacode.org/wiki/Problem_of_Apollonius
|
Problem of Apollonius
|
Task
Implement a solution to the Problem of Apollonius (description on Wikipedia) which is the problem of finding the circle that is tangent to three specified circles (colored black in the diagram below to the right).
There is an algebraic solution which is pretty straightforward.
The solutions to the example in the code are shown in the diagram (below and to the right).
The red circle is "internally tangent" to all three black circles, and the green circle is "externally tangent" to all three black circles.
|
#Ruby
|
Ruby
|
class Circle
def initialize(x, y, r)
@x, @y, @r = [x, y, r].map(&:to_f)
end
attr_reader :x, :y, :r
def self.apollonius(c1, c2, c3, s1=1, s2=1, s3=1)
x1, y1, r1 = c1.x, c1.y, c1.r
x2, y2, r2 = c2.x, c2.y, c2.r
x3, y3, r3 = c3.x, c3.y, c3.r
v11 = 2*x2 - 2*x1
v12 = 2*y2 - 2*y1
v13 = x1**2 - x2**2 + y1**2 - y2**2 - r1**2 + r2**2
v14 = 2*s2*r2 - 2*s1*r1
v21 = 2*x3 - 2*x2
v22 = 2*y3 - 2*y2
v23 = x2**2 - x3**2 + y2**2 - y3**2 - r2**2 + r3**2
v24 = 2*s3*r3 - 2*s2*r2
w12 = v12/v11
w13 = v13/v11
w14 = v14/v11
w22 = v22/v21 - w12
w23 = v23/v21 - w13
w24 = v24/v21 - w14
p = -w23/w22
q = w24/w22
m = -w12*p - w13
n = w14 - w12*q
a = n**2 + q**2 - 1
b = 2*m*n - 2*n*x1 + 2*p*q - 2*q*y1 + 2*s1*r1
c = x1**2 + m**2 - 2*m*x1 + p**2 + y1**2 - 2*p*y1 - r1**2
d = b**2 - 4*a*c
rs = (-b - Math.sqrt(d)) / (2*a)
xs = m + n*rs
ys = p + q*rs
self.new(xs, ys, rs)
end
def to_s
"Circle: x=#{@x}, y=#{@y}, r=#{@r}"
end
end
puts c1 = Circle.new(0, 0, 1)
puts c2 = Circle.new(2, 4, 2)
puts c3 = Circle.new(4, 0, 1)
puts Circle.apollonius(c1, c2, c3)
puts Circle.apollonius(c1, c2, c3, -1, -1, -1)
|
http://rosettacode.org/wiki/Program_name
|
Program name
|
The task is to programmatically obtain the name used to invoke the program. (For example determine whether the user ran "python hello.py", or "python hellocaller.py", a program importing the code from "hello.py".)
Sometimes a multiline shebang is necessary in order to provide the script name to a language's internal ARGV.
See also Command-line arguments
Examples from GitHub.
|
#Tcl
|
Tcl
|
#!/usr/bin/env tclsh
proc main {args} {
set program $::argv0
puts "Program: $program"
}
if {$::argv0 eq [info script]} {
main {*}$::argv
}
|
http://rosettacode.org/wiki/Program_name
|
Program name
|
The task is to programmatically obtain the name used to invoke the program. (For example determine whether the user ran "python hello.py", or "python hellocaller.py", a program importing the code from "hello.py".)
Sometimes a multiline shebang is necessary in order to provide the script name to a language's internal ARGV.
See also Command-line arguments
Examples from GitHub.
|
#TXR
|
TXR
|
#!/usr/local/bin/txr -B
@(bind my-name @self-path)
|
http://rosettacode.org/wiki/Pythagorean_triples
|
Pythagorean triples
|
A Pythagorean triple is defined as three positive integers
(
a
,
b
,
c
)
{\displaystyle (a,b,c)}
where
a
<
b
<
c
{\displaystyle a<b<c}
, and
a
2
+
b
2
=
c
2
.
{\displaystyle a^{2}+b^{2}=c^{2}.}
They are called primitive triples if
a
,
b
,
c
{\displaystyle a,b,c}
are co-prime, that is, if their pairwise greatest common divisors
g
c
d
(
a
,
b
)
=
g
c
d
(
a
,
c
)
=
g
c
d
(
b
,
c
)
=
1
{\displaystyle {\rm {gcd}}(a,b)={\rm {gcd}}(a,c)={\rm {gcd}}(b,c)=1}
.
Because of their relationship through the Pythagorean theorem, a, b, and c are co-prime if a and b are co-prime (
g
c
d
(
a
,
b
)
=
1
{\displaystyle {\rm {gcd}}(a,b)=1}
).
Each triple forms the length of the sides of a right triangle, whose perimeter is
P
=
a
+
b
+
c
{\displaystyle P=a+b+c}
.
Task
The task is to determine how many Pythagorean triples there are with a perimeter no larger than 100 and the number of these that are primitive.
Extra credit
Deal with large values. Can your program handle a maximum perimeter of 1,000,000? What about 10,000,000? 100,000,000?
Note: the extra credit is not for you to demonstrate how fast your language is compared to others; you need a proper algorithm to solve them in a timely manner.
Related tasks
Euler's sum of powers conjecture
List comprehensions
Pythagorean quadruples
|
#Ring
|
Ring
|
size = 100
sum = 0
prime = 0
for i = 1 to size
for j = i + 1 to size
for k = 1 to size
if pow(i,2) + pow(j,2) = pow(k,2) and (i+j+k) < 101
if gcd(i,j) = 1 prime += 1 ok
sum += 1
see "" + i + " " + j + " " + k + nl ok
next
next
next
see "Total : " + sum + nl
see "Primitives : " + prime + nl
func gcd gcd, b
while b
c = gcd
gcd = b
b = c % b
end
return gcd
|
http://rosettacode.org/wiki/Program_termination
|
Program termination
|
Task
Show the syntax for a complete stoppage of a program inside a conditional.
This includes all threads/processes which are part of your program.
Explain the cleanup (or lack thereof) caused by the termination (allocated memory, database connections, open files, object finalizers/destructors, run-on-exit hooks, etc.).
Unless otherwise described, no special cleanup outside that provided by the operating system is provided.
|
#Raku
|
Raku
|
if $problem { exit $error-code }
|
http://rosettacode.org/wiki/Program_termination
|
Program termination
|
Task
Show the syntax for a complete stoppage of a program inside a conditional.
This includes all threads/processes which are part of your program.
Explain the cleanup (or lack thereof) caused by the termination (allocated memory, database connections, open files, object finalizers/destructors, run-on-exit hooks, etc.).
Unless otherwise described, no special cleanup outside that provided by the operating system is provided.
|
#REBOL
|
REBOL
|
if error? try [6 / 0] [quit]
|
http://rosettacode.org/wiki/Primality_by_Wilson%27s_theorem
|
Primality by Wilson's theorem
|
Task
Write a boolean function that tells whether a given integer is prime using Wilson's theorem.
By Wilson's theorem, a number p is prime if and only if p divides (p - 1)! + 1.
Remember that 1 and all non-positive integers are not prime.
See also
Cut-the-knot: Wilson's theorem.
Wikipedia: Wilson's theorem
|
#Plain_English
|
Plain English
|
To run:
Start up.
Show some primes (via Wilson's theorem).
Wait for the escape key.
Shut down.
The maximum representable factorial is a number equal to 12. \32-bit signed
To show some primes (via Wilson's theorem):
If a counter is past the maximum representable factorial, exit.
If the counter is prime (via Wilson's theorem), write "" then the counter then " " on the console without advancing.
Repeat.
A prime is a number.
A factorial is a number.
To find a factorial of a number:
Put 1 into the factorial.
Loop.
If a counter is past the number, exit.
Multiply the factorial by the counter.
Repeat.
To decide if a number is prime (via Wilson's theorem):
If the number is less than 1, say no.
Find a factorial of the number minus 1. Bump the factorial.
If the factorial is evenly divisible by the number, say yes.
Say no.
|
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