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http://rosettacode.org/wiki/Achilles_numbers | Achilles numbers |
This page uses content from Wikipedia. The original article was at Achilles number. 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)
An Achilles number is a number that is powerful but imperfect. Named after Achilles, a hero of the Trojan war, who was also powerful but imperfect.
A positive integer n is a powerful number if, for every prime factor p of n, p2 is also a divisor.
In other words, every prime factor appears at least squared in the factorization.
All Achilles numbers are powerful. However, not all powerful numbers are Achilles numbers: only those that cannot be represented as mk, where m and k are positive integers greater than 1.
A strong Achilles number is an Achilles number whose Euler totient (𝜑) is also an Achilles number.
E.G.
108 is a powerful number. Its prime factorization is 22 × 33, and thus its prime factors are 2 and 3. Both 22 = 4 and 32 = 9 are divisors of 108. However, 108 cannot be represented as mk, where m and k are positive integers greater than 1, so 108 is an Achilles number.
360 is not an Achilles number because it is not powerful. One of its prime factors is 5 but 360 is not divisible by 52 = 25.
Finally, 784 is not an Achilles number. It is a powerful number, because not only are 2 and 7 its only prime factors, but also 22 = 4 and 72 = 49 are divisors of it. Nonetheless, it is a perfect power; its square root is an even integer, so it is not an Achilles number.
500 = 22 × 53 is a strong Achilles number as its Euler totient, 𝜑(500), is 200 = 23 × 52 which is also an Achilles number.
Task
Find and show the first 50 Achilles numbers.
Find and show at least the first 20 strong Achilles numbers.
For at least 2 through 5, show the count of Achilles numbers with that many digits.
See also
Wikipedia: Achilles number
OEIS:A052486 - Achilles numbers - powerful but imperfect numbers
OEIS:A194085 - Strong Achilles numbers: Achilles numbers m such that phi(m) is also an Achilles number
Related task: Powerful numbers
Related task: Totient function
| #XPL0 | XPL0 | func GCD(N, D); \Return the greatest common divisor of N and D
int N, D; \numerator and denominator
int R;
[if D > N then
[R:= D; D:= N; N:= R]; \swap D and N
while D > 0 do
[R:= rem(N/D);
N:= D;
D:= R;
];
return N;
]; \GCD
func Totient(N); \Return the totient of N
int N, Phi, M;
[Phi:= 0;
for M:= 1 to N do
if GCD(M, N) = 1 then Phi:= Phi+1;
return Phi;
];
func Powerful(N0); \Return 'true' if N0 is a powerful number
int N0, N, F, Q, L;
[if N0 <= 1 then return false;
N:= N0; F:= 2;
L:= sqrt(N0);
loop [Q:= N/F;
if rem(0) = 0 then \found a factor
[if rem(N0/(F*F)) then return false;
N:= Q;
if F>N then quit;
]
else [F:= F+1;
if F > L then
[if rem(N0/(N*N)) then return false;
quit;
];
];
];
return true;
];
func Achilles(N); \Return 'true' if N is an Achilles number
int N, M, A;
[if not Powerful(N) then return false;
M:= 2;
A:= M*M;
repeat loop [if A = N then return false;
if A > N then quit;
A:= A*M;
];
M:= M+1;
A:= M*M;
until A > N;
return true;
];
int Cnt, N, Pwr, Start;
[Cnt:= 0;
N:= 1;
loop [if Achilles(N) then
[IntOut(0, N);
Cnt:= Cnt+1;
if Cnt >= 50 then quit;
if rem(Cnt/10) then ChOut(0, 9) else CrLf(0);
];
N:= N+1;
];
CrLf(0); CrLf(0);
Cnt:= 0;
N:= 1;
loop [if Achilles(N) then
if Achilles(Totient(N)) then
[IntOut(0, N);
Cnt:= Cnt+1;
if Cnt >= 20 then quit;
if rem(Cnt/10) then ChOut(0, 9) else CrLf(0);
];
N:= N+1;
];
CrLf(0); CrLf(0);
for Pwr:= 1 to 6 do
[IntOut(0, Pwr); Text(0, ": ");
Start:= fix(Pow(10.0, float(Pwr-1)));
Cnt:= 0;
for N:= Start to Start*10-1 do
if Achilles(N) then Cnt:= Cnt+1;
IntOut(0, Cnt); CrLf(0);
];
] |
http://rosettacode.org/wiki/Aliquot_sequence_classifications | Aliquot sequence classifications | An aliquot sequence of a positive integer K is defined recursively as the first member
being K and subsequent members being the sum of the Proper divisors of the previous term.
If the terms eventually reach 0 then the series for K is said to terminate.
There are several classifications for non termination:
If the second term is K then all future terms are also K and so the sequence repeats from the first term with period 1 and K is called perfect.
If the third term would be repeating K then the sequence repeats with period 2 and K is called amicable.
If the Nth term would be repeating K for the first time, with N > 3 then the sequence repeats with period N - 1 and K is called sociable.
Perfect, amicable and sociable numbers eventually repeat the original number K; there are other repetitions...
Some K have a sequence that eventually forms a periodic repetition of period 1 but of a number other than K, for example 95 which forms the sequence 95, 25, 6, 6, 6, ... such K are called aspiring.
K that have a sequence that eventually forms a periodic repetition of period >= 2 but of a number other than K, for example 562 which forms the sequence 562, 284, 220, 284, 220, ... such K are called cyclic.
And finally:
Some K form aliquot sequences that are not known to be either terminating or periodic; these K are to be called non-terminating.
For the purposes of this task, K is to be classed as non-terminating if it has not been otherwise classed after generating 16 terms or if any term of the sequence is greater than 2**47 = 140,737,488,355,328.
Task
Create routine(s) to generate the aliquot sequence of a positive integer enough to classify it according to the classifications given above.
Use it to display the classification and sequences of the numbers one to ten inclusive.
Use it to show the classification and sequences of the following integers, in order:
11, 12, 28, 496, 220, 1184, 12496, 1264460, 790, 909, 562, 1064, 1488, and optionally 15355717786080.
Show all output on this page.
Related tasks
Abundant, deficient and perfect number classifications. (Classifications from only the first two members of the whole sequence).
Proper divisors
Amicable pairs
| #jq | jq | # "until" is available in more recent versions of jq
# than jq 1.4
def until(cond; next):
def _until:
if cond then . else (next|_until) end;
_until;
# unordered
def proper_divisors:
. as $n
| if $n > 1 then 1,
( range(2; 1 + (sqrt|floor)) as $i
| if ($n % $i) == 0 then $i,
(($n / $i) | if . == $i then empty else . end)
else empty
end)
else empty
end;
# sum of proper divisors, or 0
def pdsum:
[proper_divisors] | add // 0;
# input is n
# maxlen defaults to 16;
# maxterm defaults to 2^47
def aliquot(maxlen; maxterm):
(maxlen // 15) as $maxlen
| (maxterm // 40737488355328) as $maxterm
| if . == 0 then "terminating at 0"
else
# [s, slen, new] = [[n], 1, n]
[ [.], 1, .]
| until( type == "string" or .[1] > $maxlen or .[2] > $maxterm;
.[0] as $s | .[1] as $slen
| ($s | .[length-1] | pdsum) as $new
| if ($s|index($new)) then
if $s[0] == $new then
if $slen == 1 then "perfect \($s)"
elif $slen == 2 then "amicable: \($s)"
else "sociable of length \($slen): \($s)"
end
elif ($s | .[length-1]) == $new then "aspiring: \($s)"
else "cyclic back to \($new): \($s)"
end
elif $new == 0 then "terminating: \($s + [0])"
else [ ($s + [$new]), ($slen + 1), $new ]
end )
| if type == "string" then . else "non-terminating: \(.[0])" end
end;
def task:
def pp: "\(.): \(aliquot(null;null))";
(range(1; 11) | pp),
"",
((11, 12, 28, 496, 220, 1184, 12496, 1264460,
790, 909, 562, 1064, 1488, 15355717786080) | pp);
task |
http://rosettacode.org/wiki/Add_a_variable_to_a_class_instance_at_runtime | Add a variable to a class instance at runtime | Demonstrate how to dynamically add variables to an object (a class instance) at runtime.
This is useful when the methods/variables of an instance are based on a data file that isn't available until runtime. Hal Fulton gives an example of creating an OO CSV parser at An Exercise in Metaprogramming with Ruby. This is referred to as "monkeypatching" by Pythonistas and some others.
| #REBOL | REBOL |
rebol [
Title: "Add Variables to Class at Runtime"
URL: http://rosettacode.org/wiki/Adding_variables_to_a_class_instance_at_runtime
]
; As I understand it, a REBOL object can only ever have whatever
; properties it was born with. However, this is somewhat offset by the
; fact that every instance can serve as a prototype for a new object
; that also has the new parameter you want to add.
; Here I create an empty instance of the base object (x), then add the
; new instance variable while creating a new object prototyped from
; x. I assign the new object to x, et voila', a dynamically added
; variable.
x: make object! [] ; Empty object.
x: make x [
newvar: "forty-two" ; New property.
]
print "Empty object modifed with 'newvar' property:"
probe x
; A slightly more interesting example:
starfighter: make object! [
model: "unknown"
pilot: none
]
x-wing: make starfighter [
model: "Incom T-65 X-wing"
]
squadron: reduce [
make x-wing [pilot: "Luke Skywalker"]
make x-wing [pilot: "Wedge Antilles"]
make starfighter [
model: "Slayn & Korpil B-wing"
pilot: "General Salm"
]
]
; Adding new property here.
squadron/1: make squadron/1 [deathstar-removal-expert: yes]
print [crlf "Fighter squadron:"]
foreach pilot squadron [probe pilot]
|
http://rosettacode.org/wiki/Add_a_variable_to_a_class_instance_at_runtime | Add a variable to a class instance at runtime | Demonstrate how to dynamically add variables to an object (a class instance) at runtime.
This is useful when the methods/variables of an instance are based on a data file that isn't available until runtime. Hal Fulton gives an example of creating an OO CSV parser at An Exercise in Metaprogramming with Ruby. This is referred to as "monkeypatching" by Pythonistas and some others.
| #Red | Red | person: make object! [
name: none
age: none
]
people: reduce [make person [name: "fred" age: 20] make person [name: "paul" age: 21]]
people/1: make people/1 [skill: "fishing"]
foreach person people [
print reduce [person/age "year old" person/name "is good at" any [select person 'skill "nothing"]]
] |
http://rosettacode.org/wiki/Add_a_variable_to_a_class_instance_at_runtime | Add a variable to a class instance at runtime | Demonstrate how to dynamically add variables to an object (a class instance) at runtime.
This is useful when the methods/variables of an instance are based on a data file that isn't available until runtime. Hal Fulton gives an example of creating an OO CSV parser at An Exercise in Metaprogramming with Ruby. This is referred to as "monkeypatching" by Pythonistas and some others.
| #Ring | Ring | o1 = new point
addattribute(o1,"x")
addattribute(o1,"y")
addattribute(o1,"z")
see o1 {x=10 y=20 z=30}
class point |
http://rosettacode.org/wiki/Address_of_a_variable | Address of a variable |
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
Task
Demonstrate how to get the address of a variable and how to set the address of a variable.
| #R | R |
x <- 5
y <- x
pryr::address(x)
pryr::address(y)
y <- y + 1
pryr::address(x)
pryr::address(y)
|
http://rosettacode.org/wiki/Address_of_a_variable | Address of a variable |
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
Task
Demonstrate how to get the address of a variable and how to set the address of a variable.
| #Racket | Racket | #lang racket
(require ffi/unsafe)
(define (madness v) ; i'm so sorry
(cast v _racket _gcpointer)) |
http://rosettacode.org/wiki/Address_of_a_variable | Address of a variable |
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
Task
Demonstrate how to get the address of a variable and how to set the address of a variable.
| #Raku | Raku | my $x;
say $x.WHERE;
my $y := $x; # alias
say $y.WHERE; # same address as $x
say "Same variable" if $y =:= $x;
$x = 42;
say $y; # 42
|
http://rosettacode.org/wiki/AKS_test_for_primes | AKS test for primes | The AKS algorithm for testing whether a number is prime is a polynomial-time algorithm based on an elementary theorem about Pascal triangles.
The theorem on which the test is based can be stated as follows:
a number
p
{\displaystyle p}
is prime if and only if all the coefficients of the polynomial expansion of
(
x
−
1
)
p
−
(
x
p
−
1
)
{\displaystyle (x-1)^{p}-(x^{p}-1)}
are divisible by
p
{\displaystyle p}
.
Example
Using
p
=
3
{\displaystyle p=3}
:
(x-1)^3 - (x^3 - 1)
= (x^3 - 3x^2 + 3x - 1) - (x^3 - 1)
= -3x^2 + 3x
And all the coefficients are divisible by 3, so 3 is prime.
Note:
This task is not the AKS primality test. It is an inefficient exponential time algorithm discovered in the late 1600s and used as an introductory lemma in the AKS derivation.
Task
Create a function/subroutine/method that given
p
{\displaystyle p}
generates the coefficients of the expanded polynomial representation of
(
x
−
1
)
p
{\displaystyle (x-1)^{p}}
.
Use the function to show here the polynomial expansions of
(
x
−
1
)
p
{\displaystyle (x-1)^{p}}
for
p
{\displaystyle p}
in the range 0 to at least 7, inclusive.
Use the previous function in creating another function that when given
p
{\displaystyle p}
returns whether
p
{\displaystyle p}
is prime using the theorem.
Use your test to generate a list of all primes under 35.
As a stretch goal, generate all primes under 50 (needs integers larger than 31-bit).
References
Agrawal-Kayal-Saxena (AKS) primality test (Wikipedia)
Fool-Proof Test for Primes - Numberphile (Video). The accuracy of this video is disputed -- at best it is an oversimplification.
| #Erlang | Erlang | #! /usr/bin/escript
-import(lists, [all/2, seq/2, zip/2]).
iterate(F, X) -> fun() -> [X | iterate(F, F(X))] end.
take(0, _lazy) -> [];
take(N, Lazy) ->
[Value | Next] = Lazy(),
[Value | take(N-1, Next)].
pascal() -> iterate(fun (Row) -> [1 | sum_adj(Row)] end, [1]).
sum_adj([_] = L) -> L;
sum_adj([A, B | _] = Row) -> [A+B | sum_adj(tl(Row))].
show_binomial(Row) ->
Degree = length(Row) - 1,
["(x - 1)^", integer_to_list(Degree), " =", binomial_rhs(Row, 1, Degree)].
show_x(0) -> "";
show_x(1) -> "x";
show_x(N) -> [$x, $^ | integer_to_list(N)].
binomial_rhs([], _, _) -> [];
binomial_rhs([Coef | Coefs], Sgn, Exp) ->
SignChar = if Sgn > 0 -> $+; true -> $- end,
[$ , SignChar, $ , integer_to_list(Coef), show_x(Exp) | binomial_rhs(Coefs, -Sgn, Exp-1)].
primerow(Row, N) -> all(fun (Coef) -> (Coef =:= 1) or (Coef rem N =:= 0) end, Row).
main(_) ->
[io:format("~s~n", [show_binomial(Row)]) || Row <- take(8, pascal())],
io:format("~nThe primes upto 50: ~p~n",
[[N || {Row, N} <- zip(tl(tl(take(51, pascal()))), seq(2, 50)),
primerow(Row, N)]]).
|
http://rosettacode.org/wiki/Additive_primes | Additive primes | Definitions
In mathematics, additive primes are prime numbers for which the sum of their decimal digits are also primes.
Task
Write a program to determine (and show here) all additive primes less than 500.
Optionally, show the number of additive primes.
Also see
the OEIS entry: A046704 additive primes.
the prime-numbers entry: additive primes.
the geeks for geeks entry: additive prime number.
the prime-numbers fandom: additive primes.
| #Julia | Julia | using Primes
let
p = primesmask(500)
println("Additive primes under 500:")
pcount = 0
for i in 2:499
if p[i] && p[sum(digits(i))]
pcount += 1
print(lpad(i, 4), pcount % 20 == 0 ? "\n" : "")
end
end
println("\n\n$pcount additive primes found.")
end
|
http://rosettacode.org/wiki/Additive_primes | Additive primes | Definitions
In mathematics, additive primes are prime numbers for which the sum of their decimal digits are also primes.
Task
Write a program to determine (and show here) all additive primes less than 500.
Optionally, show the number of additive primes.
Also see
the OEIS entry: A046704 additive primes.
the prime-numbers entry: additive primes.
the geeks for geeks entry: additive prime number.
the prime-numbers fandom: additive primes.
| #Kotlin | Kotlin | fun isPrime(n: Int): Boolean {
if (n <= 3) return n > 1
if (n % 2 == 0 || n % 3 == 0) return false
var i = 5
while (i * i <= n) {
if (n % i == 0 || n % (i + 2) == 0) return false
i += 6
}
return true
}
fun digitSum(n: Int): Int {
var sum = 0
var num = n
while (num > 0) {
sum += num % 10
num /= 10
}
return sum
}
fun main() {
var additivePrimes = 0
for (i in 2 until 500) {
if (isPrime(i) and isPrime(digitSum(i))) {
additivePrimes++
print("$i ")
}
}
println("\nFound $additivePrimes additive primes less than 500")
} |
http://rosettacode.org/wiki/Additive_primes | Additive primes | Definitions
In mathematics, additive primes are prime numbers for which the sum of their decimal digits are also primes.
Task
Write a program to determine (and show here) all additive primes less than 500.
Optionally, show the number of additive primes.
Also see
the OEIS entry: A046704 additive primes.
the prime-numbers entry: additive primes.
the geeks for geeks entry: additive prime number.
the prime-numbers fandom: additive primes.
| #Ksh | Ksh | #!/bin/ksh
# Prime numbers for which the sum of their decimal digits are also primes
# # Variables:
#
integer MAX_n=500
# # Functions:
#
# # Function _isprime(n) return 1 for prime, 0 for not prime
#
function _isprime {
typeset _n ; integer _n=$1
typeset _i ; integer _i
(( _n < 2 )) && return 0
for (( _i=2 ; _i*_i<=_n ; _i++ )); do
(( ! ( _n % _i ) )) && return 0
done
return 1
}
# # Function _sumdigits(n) return sum of n's digits
#
function _sumdigits {
typeset _n ; _n=$1
typeset _i _sum ; integer _i _sum=0
for ((_i=0; _i<${#_n}; _i++)); do
(( _sum+=${_n:${_i}:1} ))
done
echo ${_sum}
}
######
# main #
######
integer i digsum
for ((i=2; i<MAX_n; i++)); do
_isprime ${i} && (( ! $? )) && continue
digsum=$(_sumdigits ${i})
_isprime ${digsum} ; (( $? )) && printf "%4d " ${i}
done
print |
http://rosettacode.org/wiki/Almost_prime | Almost prime | A k-Almost-prime is a natural number
n
{\displaystyle n}
that is the product of
k
{\displaystyle k}
(possibly identical) primes.
Example
1-almost-primes, where
k
=
1
{\displaystyle k=1}
, are the prime numbers themselves.
2-almost-primes, where
k
=
2
{\displaystyle k=2}
, are the semiprimes.
Task
Write a function/method/subroutine/... that generates k-almost primes and use it to create a table here of the first ten members of k-Almost primes for
1
<=
K
<=
5
{\displaystyle 1<=K<=5}
.
Related tasks
Semiprime
Category:Prime Numbers
| #jq | jq | # Recent versions of jq (version > 1.4) have the following definition of "until":
def until(cond; next):
def _until:
if cond then . else (next|_until) end;
_until;
# relatively_prime(previous) tests whether the input integer is prime
# relative to the primes in the array "previous":
def relatively_prime(previous):
. as $in
| (previous|length) as $plen
# state: [found, ix]
| [false, 0]
| until( .[0] or .[1] >= $plen;
[ ($in % previous[.[1]]) == 0, .[1] + 1] )
| .[0] | not ;
# Emit a stream in increasing order of all primes (from 2 onwards)
# that are less than or equal to mx:
def primes(mx):
# The helper function, next, has arity 0 for tail recursion optimization;
# it expects its input to be the array of previously found primes:
def next:
. as $previous
| ($previous | .[length-1]) as $last
| if ($last >= mx) then empty
else ((2 + $last)
| until( relatively_prime($previous) ; . + 2)) as $nextp
| if $nextp <= mx
then $nextp, (( $previous + [$nextp] ) | next)
else empty
end
end;
if mx <= 1 then empty
elif mx == 2 then 2
else (2, 3, ( [2,3] | next))
end
;
# Return an array of the distinct prime factors of . in increasing order
def prime_factors:
# Return an array of prime factors of . given that "primes"
# is an array of relevant primes:
def pf(primes):
if . <= 1 then []
else . as $in
| if ($in | relatively_prime(primes)) then [$in]
else reduce primes[] as $p
([];
if ($in % $p) != 0 then .
else . + [$p] + (($in / $p) | pf(primes))
end)
end
| unique
end;
if . <= 1 then []
else . as $in
| pf( [ primes( (1+$in) | sqrt | floor) ] )
end;
# Return an array of prime factors of . repeated according to their multiplicities:
def prime_factors_with_multiplicities:
# Emit p according to the multiplicity of p
# in the input integer assuming p > 1
def multiplicity(p):
if . < p then empty
elif . == p then p
elif (. % p) == 0 then
((./p) | recurse( if (. % p) == 0 then (. / p) else empty end) | p)
else empty
end;
if . <= 1 then []
else . as $in
| prime_factors as $primes
| if ($in|relatively_prime($primes)) then [$in]
else reduce $primes[] as $p
([];
if ($in % $p) == 0 then . + [$in|multiplicity($p)] else . end )
end
end; |
http://rosettacode.org/wiki/Almost_prime | Almost prime | A k-Almost-prime is a natural number
n
{\displaystyle n}
that is the product of
k
{\displaystyle k}
(possibly identical) primes.
Example
1-almost-primes, where
k
=
1
{\displaystyle k=1}
, are the prime numbers themselves.
2-almost-primes, where
k
=
2
{\displaystyle k=2}
, are the semiprimes.
Task
Write a function/method/subroutine/... that generates k-almost primes and use it to create a table here of the first ten members of k-Almost primes for
1
<=
K
<=
5
{\displaystyle 1<=K<=5}
.
Related tasks
Semiprime
Category:Prime Numbers
| #Julia | Julia | using Primes
isalmostprime(n::Integer, k::Integer) = sum(values(factor(n))) == k
function almostprimes(N::Integer, k::Integer) # return first N almost-k primes
P = Vector{typeof(k)}(undef,N)
i = 0; n = 2
while i < N
if isalmostprime(n, k) P[i += 1] = n end
n += 1
end
return P
end
for k in 1:5
println("$k-Almost-primes: ", join(almostprimes(10, k), ", "), "...")
end |
http://rosettacode.org/wiki/Anagrams | Anagrams | When two or more words are composed of the same characters, but in a different order, they are called anagrams.
Task[edit]
Using the word list at http://wiki.puzzlers.org/pub/wordlists/unixdict.txt,
find the sets of words that share the same characters that contain the most words in them.
Related tasks
Word plays
Ordered words
Palindrome detection
Semordnilap
Anagrams
Anagrams/Deranged anagrams
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
| #EchoLisp | EchoLisp |
(require 'struct)
(require 'hash)
(require 'sql)
(require 'words)
(require 'dico.fr.no-accent)
(define mots-français (words-select #:any null 999999))
(string-delimiter "")
(define (string-sort str)
(list->string (list-sort string<? (string->list str))))
(define (ana-sort H words) ;; bump counter for each word
(for ((w words))
#:continue (< (string-length w) 4)
(let [(key (string-sort w))] (hash-set H key (1+ (hash-ref! H key 0))))))
;; input w word
;; output : list of matching words
(define (anagrams w words)
(set! w (string-sort w))
(make-set
(for/list (( ana words))
#:when (string=? w (string-sort ana))
ana)))
(define (task words)
(define H (make-hash))
(ana-sort H words) ;; build counters key= sorted-string, value = count
(hash-get-keys H ;; extract max count values
(for/fold (hmax 0) ((h H) )
#:when (>= (cdr h) hmax)
(cdr h))
))
|
http://rosettacode.org/wiki/Angle_difference_between_two_bearings | Angle difference between two bearings | Finding the angle between two bearings is often confusing.[1]
Task
Find the angle which is the result of the subtraction b2 - b1, where b1 and b2 are the bearings.
Input bearings are expressed in the range -180 to +180 degrees.
The result is also expressed in the range -180 to +180 degrees.
Compute the angle for the following pairs:
20 degrees (b1) and 45 degrees (b2)
-45 and 45
-85 and 90
-95 and 90
-45 and 125
-45 and 145
29.4803 and -88.6381
-78.3251 and -159.036
Optional extra
Allow the input bearings to be any (finite) value.
Test cases
-70099.74233810938 and 29840.67437876723
-165313.6666297357 and 33693.9894517456
1174.8380510598456 and -154146.66490124757
60175.77306795546 and 42213.07192354373
| #Raku | Raku | sub infix:<∠> (Real $b1, Real $b2) {
(my $b = ($b2 - $b1 + 720) % 360) > 180 ?? $b - 360 !! $b;
}
for 20, 45,
-45, 45,
-85, 90,
-95, 90,
-45, 125,
-45, 145,
29.4803, -88.6381,
-78.3251, -159.036,
-70099.74233810938, 29840.67437876723,
-165313.6666297357, 33693.9894517456,
1174.8380510598456, -154146.66490124757,
60175.77306795546, 42213.07192354373
-> $b1, $b2 { printf "%10.2f %10.2f = %8.2f\n", $b1, $b2, $b1 ∠ $b2 } |
http://rosettacode.org/wiki/Anagrams/Deranged_anagrams | Anagrams/Deranged anagrams | Two or more words are said to be anagrams if they have the same characters, but in a different order.
By analogy with derangements we define a deranged anagram as two words with the same characters, but in which the same character does not appear in the same position in both words.
Task[edit]
Use the word list at unixdict to find and display the longest deranged anagram.
Related tasks
Permutations/Derangements
Best shuffle
Word plays
Ordered words
Palindrome detection
Semordnilap
Anagrams
Anagrams/Deranged anagrams
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
| #Ruby | Ruby | def deranged?(a, b)
a.chars.zip(b.chars).all? {|char_a, char_b| char_a != char_b}
end
def find_derangements(list)
list.combination(2) {|a,b| return a,b if deranged?(a,b)}
nil
end
require 'open-uri'
anagram = open('http://www.puzzlers.org/pub/wordlists/unixdict.txt') do |f|
f.read.split.group_by {|s| s.each_char.sort}
end
anagram = anagram.select{|k,list| list.size>1}.sort_by{|k,list| -k.size}
anagram.each do |k,list|
if derangements = find_derangements(list)
puts "Longest derangement anagram: #{derangements}"
break
end
end |
http://rosettacode.org/wiki/Anonymous_recursion | Anonymous recursion | While implementing a recursive function, it often happens that we must resort to a separate helper function to handle the actual recursion.
This is usually the case when directly calling the current function would waste too many resources (stack space, execution time), causing unwanted side-effects, and/or the function doesn't have the right arguments and/or return values.
So we end up inventing some silly name like foo2 or foo_helper. I have always found it painful to come up with a proper name, and see some disadvantages:
You have to think up a name, which then pollutes the namespace
Function is created which is called from nowhere else
The program flow in the source code is interrupted
Some languages allow you to embed recursion directly in-place. This might work via a label, a local gosub instruction, or some special keyword.
Anonymous recursion can also be accomplished using the Y combinator.
Task
If possible, demonstrate this by writing the recursive version of the fibonacci function (see Fibonacci sequence) which checks for a negative argument before doing the actual recursion.
| #Perl | Perl | sub recur (&@) {
my $f = shift;
local *recurse = $f;
$f->(@_);
}
sub fibo {
my $n = shift;
$n < 0 and die 'Negative argument';
recur {
my $m = shift;
$m < 3 ? 1 : recurse($m - 1) + recurse($m - 2);
} $n;
} |
http://rosettacode.org/wiki/Amicable_pairs | Amicable pairs | Two integers
N
{\displaystyle N}
and
M
{\displaystyle M}
are said to be amicable pairs if
N
≠
M
{\displaystyle N\neq M}
and the sum of the proper divisors of
N
{\displaystyle N}
(
s
u
m
(
p
r
o
p
D
i
v
s
(
N
)
)
{\displaystyle \mathrm {sum} (\mathrm {propDivs} (N))}
)
=
M
{\displaystyle =M}
as well as
s
u
m
(
p
r
o
p
D
i
v
s
(
M
)
)
=
N
{\displaystyle \mathrm {sum} (\mathrm {propDivs} (M))=N}
.
Example
1184 and 1210 are an amicable pair, with proper divisors:
1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592 and
1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605 respectively.
Task
Calculate and show here the Amicable pairs below 20,000; (there are eight).
Related tasks
Proper divisors
Abundant, deficient and perfect number classifications
Aliquot sequence classifications and its amicable classification.
| #PARI.2FGP | PARI/GP | for(x=1,20000,my(y=sigma(x)-x); if(y>x && x == sigma(y)-y,print(x" "y))) |
http://rosettacode.org/wiki/Animate_a_pendulum | Animate a pendulum |
One good way of making an animation is by simulating a physical system and illustrating the variables in that system using a dynamically changing graphical display.
The classic such physical system is a simple gravity pendulum.
Task
Create a simple physical model of a pendulum and animate it.
| #Racket | Racket |
#lang racket
(require 2htdp/image 2htdp/universe)
(define (pendulum)
(define (accel θ) (- (sin θ)))
(define θ (/ pi 2.5))
(define θ′ 0)
(define θ′′ (accel (/ pi 2.5)))
(define (x θ) (+ 200 (* 150 (sin θ))))
(define (y θ) (* 150 (cos θ)))
(λ (n)
(define p-image (underlay/xy (add-line (empty-scene 400 200) 200 0 (x θ) (y θ) "black")
(- (x θ) 5) (- (y θ) 5) (circle 5 "solid" "blue")))
(set! θ (+ θ (* θ′ 0.04)))
(set! θ′ (+ θ′ (* (accel θ) 0.04)))
p-image))
(animate (pendulum))
|
http://rosettacode.org/wiki/Amb | Amb | Define and give an example of the Amb operator.
The Amb operator (short for "ambiguous") expresses nondeterminism. This doesn't refer to randomness (as in "nondeterministic universe") but is closely related to the term as it is used in automata theory ("non-deterministic finite automaton").
The Amb operator takes a variable number of expressions (or values if that's simpler in the language) and yields a correct one which will satisfy a constraint in some future computation, thereby avoiding failure.
Problems whose solution the Amb operator naturally expresses can be approached with other tools, such as explicit nested iterations over data sets, or with pattern matching. By contrast, the Amb operator appears integrated into the language. Invocations of Amb are not wrapped in any visible loops or other search patterns; they appear to be independent.
Essentially Amb(x, y, z) splits the computation into three possible futures: a future in which the value x is yielded, a future in which the value y is yielded and a future in which the value z is yielded. The future which leads to a successful subsequent computation is chosen. The other "parallel universes" somehow go away. Amb called with no arguments fails.
For simplicity, one of the domain values usable with Amb may denote failure, if that is convenient. For instance, it is convenient if a Boolean false denotes failure, so that Amb(false) fails, and thus constraints can be expressed using Boolean expressions like Amb(x * y == 8) which unless x and y add to four.
A pseudo-code program which satisfies this constraint might look like:
let x = Amb(1, 2, 3)
let y = Amb(7, 6, 4, 5)
Amb(x * y = 8)
print x, y
The output is 2 4 because Amb(1, 2, 3) correctly chooses the future in which x has value 2, Amb(7, 6, 4, 5) chooses 4 and consequently Amb(x * y = 8) produces a success.
Alternatively, failure could be represented using strictly Amb():
unless x * y = 8 do Amb()
Or else Amb could take the form of two operators or functions: one for producing values and one for enforcing constraints:
let x = Ambsel(1, 2, 3)
let y = Ambsel(4, 5, 6)
Ambassert(x * y = 8)
print x, y
where Ambassert behaves like Amb() if the Boolean expression is false, otherwise it allows the future computation to take place, without yielding any value.
The task is to somehow implement Amb, and demonstrate it with a program which chooses one word from each of the following four sets of character strings to generate a four-word sentence:
"the" "that" "a"
"frog" "elephant" "thing"
"walked" "treaded" "grows"
"slowly" "quickly"
The constraint to be satisfied is that the last character of each word (other than the last) is the same as the first character of its successor.
The only successful sentence is "that thing grows slowly"; other combinations do not satisfy the constraint and thus fail.
The goal of this task isn't to simply process the four lists of words with explicit, deterministic program flow such as nested iteration, to trivially demonstrate the correct output. The goal is to implement the Amb operator, or a facsimile thereof that is possible within the language limitations.
| #jq | jq | def amb: .[];
def joins:
(.[0][-1:]) as $left
| (.[1][0:1]) as $right
| if $left == $right then true else empty end;
|
http://rosettacode.org/wiki/Accumulator_factory | Accumulator factory | A problem posed by Paul Graham is that of creating a function that takes a single (numeric) argument and which returns another function that is an accumulator. The returned accumulator function in turn also takes a single numeric argument, and returns the sum of all the numeric values passed in so far to that accumulator (including the initial value passed when the accumulator was created).
Rules
The detailed rules are at http://paulgraham.com/accgensub.html and are reproduced here for simplicity (with additions in small italic text).
Before you submit an example, make sure the function
Takes a number n and returns a function (lets call it g), that takes a number i, and returns n incremented by the accumulation of i from every call of function g(i).
Although these exact function and parameter names need not be used
Works for any numeric type-- i.e. can take both ints and floats and returns functions that can take both ints and floats. (It is not enough simply to convert all input to floats. An accumulator that has only seen integers must return integers.) (i.e., if the language doesn't allow for numeric polymorphism, you have to use overloading or something like that)
Generates functions that return the sum of every number ever passed to them, not just the most recent. (This requires a piece of state to hold the accumulated value, which in turn means that pure functional languages can't be used for this task.)
Returns a real function, meaning something that you can use wherever you could use a function you had defined in the ordinary way in the text of your program. (Follow your language's conventions here.)
Doesn't store the accumulated value or the returned functions in a way that could cause them to be inadvertently modified by other code. (No global variables or other such things.)
E.g. if after the example, you added the following code (in a made-up language) where the factory function is called foo:
x = foo(1);
x(5);
foo(3);
print x(2.3);
It should print 8.3. (There is no need to print the form of the accumulator function returned by foo(3); it's not part of the task at all.)
Task
Create a function that implements the described rules.
It need not handle any special error cases not described above. The simplest way to implement the task as described is typically to use a closure, providing the language supports them.
Where it is not possible to hold exactly to the constraints above, describe the deviations.
| #Ceylon | Ceylon | shared void run() {
Integer|Float accumulator
(variable Integer|Float n)
(Integer|Float i)
=> switch (i)
case (is Integer)
(n = n.plusInteger(i))
case (is Float)
(n = i + (switch(prev = n)
case (is Float) prev
case (is Integer) prev.float));
value x = accumulator(1);
print(x(5));
print(accumulator(3));
print(x(2.3));
} |
http://rosettacode.org/wiki/Accumulator_factory | Accumulator factory | A problem posed by Paul Graham is that of creating a function that takes a single (numeric) argument and which returns another function that is an accumulator. The returned accumulator function in turn also takes a single numeric argument, and returns the sum of all the numeric values passed in so far to that accumulator (including the initial value passed when the accumulator was created).
Rules
The detailed rules are at http://paulgraham.com/accgensub.html and are reproduced here for simplicity (with additions in small italic text).
Before you submit an example, make sure the function
Takes a number n and returns a function (lets call it g), that takes a number i, and returns n incremented by the accumulation of i from every call of function g(i).
Although these exact function and parameter names need not be used
Works for any numeric type-- i.e. can take both ints and floats and returns functions that can take both ints and floats. (It is not enough simply to convert all input to floats. An accumulator that has only seen integers must return integers.) (i.e., if the language doesn't allow for numeric polymorphism, you have to use overloading or something like that)
Generates functions that return the sum of every number ever passed to them, not just the most recent. (This requires a piece of state to hold the accumulated value, which in turn means that pure functional languages can't be used for this task.)
Returns a real function, meaning something that you can use wherever you could use a function you had defined in the ordinary way in the text of your program. (Follow your language's conventions here.)
Doesn't store the accumulated value or the returned functions in a way that could cause them to be inadvertently modified by other code. (No global variables or other such things.)
E.g. if after the example, you added the following code (in a made-up language) where the factory function is called foo:
x = foo(1);
x(5);
foo(3);
print x(2.3);
It should print 8.3. (There is no need to print the form of the accumulator function returned by foo(3); it's not part of the task at all.)
Task
Create a function that implements the described rules.
It need not handle any special error cases not described above. The simplest way to implement the task as described is typically to use a closure, providing the language supports them.
Where it is not possible to hold exactly to the constraints above, describe the deviations.
| #Clay | Clay | acc(n) {
return (m) => {
n = n + m;
return n;
};
}
main() {
var x = acc(1.0);
x(5);
acc(3);
println(x(2.3)); // Prints “8.300000000000001”.
} |
http://rosettacode.org/wiki/Ackermann_function | Ackermann function | The Ackermann function is a classic example of a recursive function, notable especially because it is not a primitive recursive function. It grows very quickly in value, as does the size of its call tree.
The Ackermann function is usually defined as follows:
A
(
m
,
n
)
=
{
n
+
1
if
m
=
0
A
(
m
−
1
,
1
)
if
m
>
0
and
n
=
0
A
(
m
−
1
,
A
(
m
,
n
−
1
)
)
if
m
>
0
and
n
>
0.
{\displaystyle A(m,n)={\begin{cases}n+1&{\mbox{if }}m=0\\A(m-1,1)&{\mbox{if }}m>0{\mbox{ and }}n=0\\A(m-1,A(m,n-1))&{\mbox{if }}m>0{\mbox{ and }}n>0.\end{cases}}}
Its arguments are never negative and it always terminates.
Task
Write a function which returns the value of
A
(
m
,
n
)
{\displaystyle A(m,n)}
. Arbitrary precision is preferred (since the function grows so quickly), but not required.
See also
Conway chained arrow notation for the Ackermann function.
| #8080_Assembly | 8080 Assembly | org 100h
jmp demo
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; ACK(M,N); DE=M, HL=N, return value in HL.
ack: mov a,d ; M=0?
ora e
jnz ackm
inx h ; If so, N+1.
ret
ackm: mov a,h ; N=0?
ora l
jnz ackmn
lxi h,1 ; If so, N=1,
dcx d ; N-=1,
jmp ack ; A(M,N) - tail recursion
ackmn: push d ; M>0 and N>0: store M on the stack
dcx h ; N-=1
call ack ; N = ACK(M,N-1)
pop d ; Restore previous M
dcx d ; M-=1
jmp ack ; A(M,N) - tail recursion
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; Print table of ack(m,n)
MMAX: equ 4 ; Size of table to print. Note that math is done in
NMAX: equ 9 ; 16 bits.
demo: lhld 6 ; Put stack pointer at top of available memory
sphl
lxi b,0 ; let B,C hold 8-bit M and N.
acknum: xra a ; Set high bit of M and N to zero
mov d,a ; DE = B (M)
mov e,b
mov h,a ; HL = C (N)
mov l,c
call ack ; HL = ack(DE,HL)
call prhl ; Print the number
inr c ; N += 1
mvi a,NMAX ; Time for next line?
cmp c
jnz acknum ; If not, print next number
push b ; Otherwise, save BC
mvi c,9 ; Print newline
lxi d,nl
call 5
pop b ; Restore BC
mvi c,0 ; Set N to 0
inr b ; M += 1
mvi a,MMAX ; Time to stop?
cmp b
jnz acknum ; If not, print next number
rst 0
;;; Print HL as ASCII number.
prhl: push h ; Save all registers
push d
push b
lxi b,pnum ; Store pointer to num string on stack
push b
lxi b,-10 ; Divisor
prdgt: lxi d,-1
prdgtl: inx d ; Divide by 10 through trial subtraction
dad b
jc prdgtl
mvi a,'0'+10
add l ; L = remainder - 10
pop h ; Get pointer from stack
dcx h ; Store digit
mov m,a
push h ; Put pointer back on stack
xchg ; Put quotient in HL
mov a,h ; Check if zero
ora l
jnz prdgt ; If not, next digit
pop d ; Get pointer and put in DE
mvi c,9 ; CP/M print string
call 5
pop b ; Restore registers
pop d
pop h
ret
db '*****' ; Placeholder for number
pnum: db 9,'$'
nl: db 13,10,'$' |
http://rosettacode.org/wiki/Abundant,_deficient_and_perfect_number_classifications | Abundant, deficient and perfect number classifications | These define three classifications of positive integers based on their proper divisors.
Let P(n) be the sum of the proper divisors of n where the proper divisors are all positive divisors of n other than n itself.
if P(n) < n then n is classed as deficient (OEIS A005100).
if P(n) == n then n is classed as perfect (OEIS A000396).
if P(n) > n then n is classed as abundant (OEIS A005101).
Example
6 has proper divisors of 1, 2, and 3.
1 + 2 + 3 = 6, so 6 is classed as a perfect number.
Task
Calculate how many of the integers 1 to 20,000 (inclusive) are in each of the three classes.
Show the results here.
Related tasks
Aliquot sequence classifications. (The whole series from which this task is a subset.)
Proper divisors
Amicable pairs
| #ALGOL_68 | ALGOL 68 | BEGIN # classify the numbers 1 : 20 000 as abudant, deficient or perfect #
INT abundant count := 0;
INT deficient count := 0;
INT perfect count := 0;
INT abundant example := 0;
INT deficient example := 0;
INT perfect example := 0;
INT max number = 20 000;
# construct a table of the proper divisor sums #
[ 1 : max number ]INT pds;
pds[ 1 ] := 0;
FOR i FROM 2 TO UPB pds DO pds[ i ] := 1 OD;
FOR i FROM 2 TO UPB pds DO
FOR j FROM i + i BY i TO UPB pds DO pds[ j ] +:= i OD
OD;
# classify the numbers #
FOR n TO max number DO
IF INT pd sum = pds[ n ];
pd sum < n
THEN
# have a deficient number #
deficient count +:= 1;
deficient example := n
ELIF pd sum = n
THEN
# have a perfect number #
perfect count +:= 1;
perfect example := n
ELSE # pd sum > n #
# have an abundant number #
abundant count +:= 1;
abundant example := n
FI
OD;
# displays the classification, count and example #
PROC show result = ( STRING classification, INT count, example )VOID:
print( ( "There are "
, whole( count, -8 )
, " "
, classification
, " numbers up to "
, whole( max number, 0 )
, " e.g.: "
, whole( example, 0 )
, newline
)
);
# show how many of each type of number there are and an example #
show result( "abundant ", abundant count, abundant example );
show result( "deficient", deficient count, deficient example );
show result( "perfect ", perfect count, perfect example )
END |
http://rosettacode.org/wiki/Align_columns | Align columns | Given a text file of many lines, where fields within a line
are delineated by a single 'dollar' character, write a program
that aligns each column of fields by ensuring that words in each
column are separated by at least one space.
Further, allow for each word in a column to be either left
justified, right justified, or center justified within its column.
Use the following text to test your programs:
Given$a$text$file$of$many$lines,$where$fields$within$a$line$
are$delineated$by$a$single$'dollar'$character,$write$a$program
that$aligns$each$column$of$fields$by$ensuring$that$words$in$each$
column$are$separated$by$at$least$one$space.
Further,$allow$for$each$word$in$a$column$to$be$either$left$
justified,$right$justified,$or$center$justified$within$its$column.
Note that:
The example input texts lines may, or may not, have trailing dollar characters.
All columns should share the same alignment.
Consecutive space characters produced adjacent to the end of lines are insignificant for the purposes of the task.
Output text will be viewed in a mono-spaced font on a plain text editor or basic terminal.
The minimum space between columns should be computed from the text and not hard-coded.
It is not a requirement to add separating characters between or around columns.
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
| #Arturo | Arturo | text: {
Given$a$text$file$of$many$lines,$where$fields$within$a$line$
are$delineated$by$a$single$'dollar'$character,$write$a$program
that$aligns$each$column$of$fields$by$ensuring$that$words$in$each$
column$are$separated$by$at$least$one$space.
Further,$allow$for$each$word$in$a$column$to$be$either$left$
justified,$right$justified,$or$center$justified$within$its$column.
}
output: map split.lines text => [split.by:"$"]
loop output 'line [
loop line 'word -> prints pad word 12
print ""
] |
http://rosettacode.org/wiki/Active_object | Active object | In object-oriented programming an object is active when its state depends on clock. Usually an active object encapsulates a task that updates the object's state. To the outer world the object looks like a normal object with methods that can be called from outside. Implementation of such methods must have a certain synchronization mechanism with the encapsulated task in order to prevent object's state corruption.
A typical instance of an active object is an animation widget. The widget state changes with the time, while as an object it has all properties of a normal widget.
The task
Implement an active integrator object. The object has an input and output. The input can be set using the method Input. The input is a function of time. The output can be queried using the method Output. The object integrates its input over the time and the result becomes the object's output. So if the input is K(t) and the output is S, the object state S is changed to S + (K(t1) + K(t0)) * (t1 - t0) / 2, i.e. it integrates K using the trapeze method. Initially K is constant 0 and S is 0.
In order to test the object:
set its input to sin (2π f t), where the frequency f=0.5Hz. The phase is irrelevant.
wait 2s
set the input to constant 0
wait 0.5s
Verify that now the object's output is approximately 0 (the sine has the period of 2s). The accuracy of the result will depend on the OS scheduler time slicing and the accuracy of the clock.
| #F.23 | F# | open System
open System.Threading
// current time in seconds
let now() = float( DateTime.Now.Ticks / 10000L ) / 1000.0
type Integrator( intervalMs ) as x =
let mutable k = fun _ -> 0.0 // function to integrate
let mutable s = 0.0 // current value
let mutable t0 = now() // last time s was updated
let mutable running = true // still running?
do x.ScheduleNextUpdate()
member x.Input(f) = k <- f
member x.Output() = s
member x.Stop() = running <- false
member private x.Update() =
let t1 = now()
s <- s + (k t0 + k t1) * (t1 - t0) / 2.0
t0 <- t1
x.ScheduleNextUpdate()
member private x.ScheduleNextUpdate() =
if running then
async { do! Async.Sleep( intervalMs )
x.Update()
}
|> Async.Start
let i = new Integrator(10)
i.Input( fun t -> Math.Sin (2.0 * Math.PI * 0.5 * t) )
Thread.Sleep(2000)
i.Input( fun _ -> 0.0 )
Thread.Sleep(500)
printfn "%f" (i.Output())
i.Stop() |
http://rosettacode.org/wiki/Aliquot_sequence_classifications | Aliquot sequence classifications | An aliquot sequence of a positive integer K is defined recursively as the first member
being K and subsequent members being the sum of the Proper divisors of the previous term.
If the terms eventually reach 0 then the series for K is said to terminate.
There are several classifications for non termination:
If the second term is K then all future terms are also K and so the sequence repeats from the first term with period 1 and K is called perfect.
If the third term would be repeating K then the sequence repeats with period 2 and K is called amicable.
If the Nth term would be repeating K for the first time, with N > 3 then the sequence repeats with period N - 1 and K is called sociable.
Perfect, amicable and sociable numbers eventually repeat the original number K; there are other repetitions...
Some K have a sequence that eventually forms a periodic repetition of period 1 but of a number other than K, for example 95 which forms the sequence 95, 25, 6, 6, 6, ... such K are called aspiring.
K that have a sequence that eventually forms a periodic repetition of period >= 2 but of a number other than K, for example 562 which forms the sequence 562, 284, 220, 284, 220, ... such K are called cyclic.
And finally:
Some K form aliquot sequences that are not known to be either terminating or periodic; these K are to be called non-terminating.
For the purposes of this task, K is to be classed as non-terminating if it has not been otherwise classed after generating 16 terms or if any term of the sequence is greater than 2**47 = 140,737,488,355,328.
Task
Create routine(s) to generate the aliquot sequence of a positive integer enough to classify it according to the classifications given above.
Use it to display the classification and sequences of the numbers one to ten inclusive.
Use it to show the classification and sequences of the following integers, in order:
11, 12, 28, 496, 220, 1184, 12496, 1264460, 790, 909, 562, 1064, 1488, and optionally 15355717786080.
Show all output on this page.
Related tasks
Abundant, deficient and perfect number classifications. (Classifications from only the first two members of the whole sequence).
Proper divisors
Amicable pairs
| #Julia | Julia |
function aliquotclassifier{T<:Integer}(n::T)
a = T[n]
b = divisorsum(a[end])
len = 1
while len < 17 && !(b in a) && 0 < b && b < 2^47+1
push!(a, b)
b = divisorsum(a[end])
len += 1
end
if b in a
1 < len || return ("Perfect", a)
if b == a[1]
2 < len || return ("Amicable", a)
return ("Sociable", a)
elseif b == a[end]
return ("Aspiring", a)
else
return ("Cyclic", push!(a, b))
end
end
push!(a, b)
b != 0 || return ("Terminating", a)
return ("Non-terminating", a)
end
|
http://rosettacode.org/wiki/Add_a_variable_to_a_class_instance_at_runtime | Add a variable to a class instance at runtime | Demonstrate how to dynamically add variables to an object (a class instance) at runtime.
This is useful when the methods/variables of an instance are based on a data file that isn't available until runtime. Hal Fulton gives an example of creating an OO CSV parser at An Exercise in Metaprogramming with Ruby. This is referred to as "monkeypatching" by Pythonistas and some others.
| #Ruby | Ruby | class Empty
end
e = Empty.new
class << e
attr_accessor :foo
end
e.foo = 1
puts e.foo # output: "1"
f = Empty.new
f.foo = 1 # raises NoMethodError
|
http://rosettacode.org/wiki/Add_a_variable_to_a_class_instance_at_runtime | Add a variable to a class instance at runtime | Demonstrate how to dynamically add variables to an object (a class instance) at runtime.
This is useful when the methods/variables of an instance are based on a data file that isn't available until runtime. Hal Fulton gives an example of creating an OO CSV parser at An Exercise in Metaprogramming with Ruby. This is referred to as "monkeypatching" by Pythonistas and some others.
| #Scala | Scala | import language.dynamics
import scala.collection.mutable.HashMap
class A extends Dynamic {
private val map = new HashMap[String, Any]
def selectDynamic(name: String): Any = {
return map(name)
}
def updateDynamic(name:String)(value: Any) = {
map(name) = value
}
} |
http://rosettacode.org/wiki/Add_a_variable_to_a_class_instance_at_runtime | Add a variable to a class instance at runtime | Demonstrate how to dynamically add variables to an object (a class instance) at runtime.
This is useful when the methods/variables of an instance are based on a data file that isn't available until runtime. Hal Fulton gives an example of creating an OO CSV parser at An Exercise in Metaprogramming with Ruby. This is referred to as "monkeypatching" by Pythonistas and some others.
| #Sidef | Sidef | class Empty{};
var e = Empty(); # create a new class instance
e{:foo} = 42; # add variable 'foo'
say e{:foo}; # print the value of 'foo' |
http://rosettacode.org/wiki/Address_of_a_variable | Address of a variable |
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
Task
Demonstrate how to get the address of a variable and how to set the address of a variable.
| #RapidQ | RapidQ |
Dim TheAddress as long
Dim SecVar as byte
Dim MyVar as byte
MyVar = 10
'Get the address of MyVar
TheAddress = varptr(MyVar)
'Set a new value on the address
MEMSET(TheAddress, 102, SizeOf(byte))
'Myvar is now = 102
showmessage "MyVar = " + str$(MyVar)
'...or copy from one address to another using:
MEMCPY(VarPtr(SecVar), TheAddress, SizeOf(byte))
'SecVar is now also = 102
showmessage "SecVar = " + str$(SecVar)
|
http://rosettacode.org/wiki/Address_of_a_variable | Address of a variable |
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
Task
Demonstrate how to get the address of a variable and how to set the address of a variable.
| #Retro | Retro | 'a var
&a |
http://rosettacode.org/wiki/Address_of_a_variable | Address of a variable |
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
Task
Demonstrate how to get the address of a variable and how to set the address of a variable.
| #REXX | REXX | zzz = storage(xxx) |
http://rosettacode.org/wiki/Address_of_a_variable | Address of a variable |
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
Task
Demonstrate how to get the address of a variable and how to set the address of a variable.
| #Ruby | Ruby | >foo = Object.new # => #<Object:0x10ae32000>
>id = foo.object_id # => 2238812160
>"%x" % (id << 1) # => "10ae32000"
|
http://rosettacode.org/wiki/AKS_test_for_primes | AKS test for primes | The AKS algorithm for testing whether a number is prime is a polynomial-time algorithm based on an elementary theorem about Pascal triangles.
The theorem on which the test is based can be stated as follows:
a number
p
{\displaystyle p}
is prime if and only if all the coefficients of the polynomial expansion of
(
x
−
1
)
p
−
(
x
p
−
1
)
{\displaystyle (x-1)^{p}-(x^{p}-1)}
are divisible by
p
{\displaystyle p}
.
Example
Using
p
=
3
{\displaystyle p=3}
:
(x-1)^3 - (x^3 - 1)
= (x^3 - 3x^2 + 3x - 1) - (x^3 - 1)
= -3x^2 + 3x
And all the coefficients are divisible by 3, so 3 is prime.
Note:
This task is not the AKS primality test. It is an inefficient exponential time algorithm discovered in the late 1600s and used as an introductory lemma in the AKS derivation.
Task
Create a function/subroutine/method that given
p
{\displaystyle p}
generates the coefficients of the expanded polynomial representation of
(
x
−
1
)
p
{\displaystyle (x-1)^{p}}
.
Use the function to show here the polynomial expansions of
(
x
−
1
)
p
{\displaystyle (x-1)^{p}}
for
p
{\displaystyle p}
in the range 0 to at least 7, inclusive.
Use the previous function in creating another function that when given
p
{\displaystyle p}
returns whether
p
{\displaystyle p}
is prime using the theorem.
Use your test to generate a list of all primes under 35.
As a stretch goal, generate all primes under 50 (needs integers larger than 31-bit).
References
Agrawal-Kayal-Saxena (AKS) primality test (Wikipedia)
Fool-Proof Test for Primes - Numberphile (Video). The accuracy of this video is disputed -- at best it is an oversimplification.
| #Factor | Factor | USING: combinators formatting io kernel make math math.parser
math.polynomials prettyprint sequences ;
IN: rosetta-code.aks-test
! Polynomials are represented by the math.polynomials vocabulary
! as sequences with the highest exponent on the right. Hence
! { -1 1 } represents x - 1.
: (x-1)^ ( n -- seq ) { -1 1 } swap p^ ;
: choose-exp ( n -- str )
{ { 0 [ "" ] } { 1 [ "x" ] } [ "x^%d" sprintf ] } case ;
: choose-coeff ( n -- str )
[ dup neg? [ neg "- " ] [ "+ " ] if % # ] "" make ;
: terms ( coeffs-seq -- terms-seq )
[ [ choose-coeff ] [ choose-exp append ] bi* ] map-index ;
: (.p) ( n -- str ) (x-1)^ terms <reversed> " " join 3 tail ;
: .p ( n -- ) dup zero? [ drop "1" ] [ (.p) ] if print ;
: show-poly ( n -- ) [ "(x-1)^%d = " printf ] [ .p ] bi ;
: part1 ( -- ) 8 <iota> [ show-poly ] each ;
: (prime?) ( n -- ? )
(x-1)^ rest but-last dup first [ mod 0 = not ] curry find
nip not ;
: prime? ( n -- ? ) dup 2 < [ drop f ] [ (prime?) ] if ;
: part2 ( -- )
"Primes up to 50 via AKS:" print
50 <iota> [ prime? ] filter . ;
: aks-test ( -- ) part1 nl part2 ;
MAIN: aks-test |
http://rosettacode.org/wiki/Additive_primes | Additive primes | Definitions
In mathematics, additive primes are prime numbers for which the sum of their decimal digits are also primes.
Task
Write a program to determine (and show here) all additive primes less than 500.
Optionally, show the number of additive primes.
Also see
the OEIS entry: A046704 additive primes.
the prime-numbers entry: additive primes.
the geeks for geeks entry: additive prime number.
the prime-numbers fandom: additive primes.
| #langur | langur | val .isPrime = f .i == 2 or .i > 2 and not any f(.x) .i div .x, pseries 2 to .i ^/ 2
val .sumDigits = f fold f{+}, s2n toString .i
writeln "Additive primes less than 500:"
var .count = 0
for .i in [2] ~ series(3..500, 2) {
if .isPrime(.i) and .isPrime(.sumDigits(.i)) {
write $"\.i:3; "
.count += 1
if .count div 10: writeln()
}
}
writeln $"\n\n\.count; additive primes found.\n"
|
http://rosettacode.org/wiki/Additive_primes | Additive primes | Definitions
In mathematics, additive primes are prime numbers for which the sum of their decimal digits are also primes.
Task
Write a program to determine (and show here) all additive primes less than 500.
Optionally, show the number of additive primes.
Also see
the OEIS entry: A046704 additive primes.
the prime-numbers entry: additive primes.
the geeks for geeks entry: additive prime number.
the prime-numbers fandom: additive primes.
| #Lua | Lua | function sumdigits(n)
local sum = 0
while n > 0 do
sum = sum + n % 10
n = math.floor(n/10)
end
return sum
end
primegen:generate(nil, 500)
aprimes = primegen:filter(function(n) return primegen.tbd(sumdigits(n)) end)
print(table.concat(aprimes, " "))
print("Count:", #aprimes) |
http://rosettacode.org/wiki/Almost_prime | Almost prime | A k-Almost-prime is a natural number
n
{\displaystyle n}
that is the product of
k
{\displaystyle k}
(possibly identical) primes.
Example
1-almost-primes, where
k
=
1
{\displaystyle k=1}
, are the prime numbers themselves.
2-almost-primes, where
k
=
2
{\displaystyle k=2}
, are the semiprimes.
Task
Write a function/method/subroutine/... that generates k-almost primes and use it to create a table here of the first ten members of k-Almost primes for
1
<=
K
<=
5
{\displaystyle 1<=K<=5}
.
Related tasks
Semiprime
Category:Prime Numbers
| #Kotlin | Kotlin | fun Int.k_prime(x: Int): Boolean {
var n = x
var f = 0
var p = 2
while (f < this && p * p <= n) {
while (0 == n % p) { n /= p; f++ }
p++
}
return f + (if (n > 1) 1 else 0) == this
}
fun Int.primes(n : Int) : List<Int> {
var i = 2
var list = mutableListOf<Int>()
while (list.size < n) {
if (k_prime(i)) list.add(i)
i++
}
return list
}
fun main(args: Array<String>) {
for (k in 1..5)
println("k = $k: " + k.primes(10))
} |
http://rosettacode.org/wiki/Anagrams | Anagrams | When two or more words are composed of the same characters, but in a different order, they are called anagrams.
Task[edit]
Using the word list at http://wiki.puzzlers.org/pub/wordlists/unixdict.txt,
find the sets of words that share the same characters that contain the most words in them.
Related tasks
Word plays
Ordered words
Palindrome detection
Semordnilap
Anagrams
Anagrams/Deranged anagrams
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
| #Eiffel | Eiffel |
class
ANAGRAMS
create
make
feature
make
-- Set of Anagrams, containing most words.
local
count: INTEGER
do
read_wordlist
across
words as wo
loop
if wo.item.count > count then
count := wo.item.count
end
end
across
words as wo
loop
if wo.item.count = count then
across
wo.item as list
loop
io.put_string (list.item + "%T")
end
io.new_line
end
end
end
original_list: STRING = "unixdict.txt"
feature {NONE}
read_wordlist
-- Preprocessed wordlist for finding Anagrams.
local
l_file: PLAIN_TEXT_FILE
sorted: STRING
empty_list: LINKED_LIST [STRING]
do
create l_file.make_open_read_write (original_list)
l_file.read_stream (l_file.count)
wordlist := l_file.last_string.split ('%N')
l_file.close
create words.make (wordlist.count)
across
wordlist as w
loop
create empty_list.make
sorted := sort_letters (w.item)
words.put (empty_list, sorted)
if attached words.at (sorted) as ana then
ana.extend (w.item)
end
end
end
wordlist: LIST [STRING]
sort_letters (word: STRING): STRING
--Sorted in alphabetical order.
local
letters: SORTED_TWO_WAY_LIST [STRING]
do
create letters.make
create Result.make_empty
across
1 |..| word.count as i
loop
letters.extend (word.at (i.item).out)
end
across
letters as s
loop
Result.append (s.item)
end
end
words: HASH_TABLE [LINKED_LIST [STRING], STRING]
end
|
http://rosettacode.org/wiki/Angle_difference_between_two_bearings | Angle difference between two bearings | Finding the angle between two bearings is often confusing.[1]
Task
Find the angle which is the result of the subtraction b2 - b1, where b1 and b2 are the bearings.
Input bearings are expressed in the range -180 to +180 degrees.
The result is also expressed in the range -180 to +180 degrees.
Compute the angle for the following pairs:
20 degrees (b1) and 45 degrees (b2)
-45 and 45
-85 and 90
-95 and 90
-45 and 125
-45 and 145
29.4803 and -88.6381
-78.3251 and -159.036
Optional extra
Allow the input bearings to be any (finite) value.
Test cases
-70099.74233810938 and 29840.67437876723
-165313.6666297357 and 33693.9894517456
1174.8380510598456 and -154146.66490124757
60175.77306795546 and 42213.07192354373
| #REXX | REXX | /*REXX pgm calculates difference between two angles (in degrees), normalizes the result.*/
numeric digits 25 /*use enough dec. digits for angles*/
call show 20, 45 /*display angular difference (deg).*/
call show -45, 45 /* " " " " */
call show -85, 90 /* " " " " */
call show -95, 90 /* " " " " */
call show -45, 125 /* " " " " */
call show 45, 145 /* " " " " */
call show 29.4803, -88.6361 /* " " " " */
call show -78.3251, -159.036 /* " " " " */
call show -70099.74233810938, 29840.67437876723 /* " " " " */
call show -165313.6666297357, 33693.9894517456 /* " " " " */
call show 1174.8380510598456, -154146.66490124757 /* " " " " */
call show 60175.773067955546, 42213.07192354373 /* " " " " */
exit /*stick a fork in it, we're done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
show: parse arg a,b; d=digits(); $='º' /*obtain the 2 angles (are in degrees).*/
x=format( ( ( ((b-a) // 360) + 540) // 360) - 180, 4, d) /*compute and format. */
if pos(., x)\==0 then x=strip( strip(x, 'T', 0), "T", .) /*strip trailing chaff.*/
say center(a || $, d) '─' center(b || $, d) " ────► " x || $
return /* [↑] display the angular difference.*/ |
http://rosettacode.org/wiki/Anagrams/Deranged_anagrams | Anagrams/Deranged anagrams | Two or more words are said to be anagrams if they have the same characters, but in a different order.
By analogy with derangements we define a deranged anagram as two words with the same characters, but in which the same character does not appear in the same position in both words.
Task[edit]
Use the word list at unixdict to find and display the longest deranged anagram.
Related tasks
Permutations/Derangements
Best shuffle
Word plays
Ordered words
Palindrome detection
Semordnilap
Anagrams
Anagrams/Deranged anagrams
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
| #Run_BASIC | Run BASIC | a$ = httpGet$("http://www.puzzlers.org/pub/wordlists/unixdict.txt")
dim theWord$(30000)
dim ssWord$(30000)
c10$ = chr$(10)
i = 1
while instr(a$,c10$,i) <> 0
j = instr(a$,c10$,i)
ln = j - i
again = 1
sWord$ = mid$(a$,i,j-i)
n = n + 1
theWord$(n) = sWord$
while again = 1
again = 0
for kk = 1 to len(sWord$) - 1
if mid$(sWord$,kk,1) > mid$(sWord$,kk +1,1) then
sWord$ = left$(sWord$,kk-1);mid$(sWord$,kk+1,1);mid$(sWord$,kk,1);mid$(sWord$,kk+2)
again = 1
end if
next kk
wend
ssWord$(n) = sWord$
i = j + 1
wend
for i = 1 to n
if len(theWord$(i)) > maxLen then
for j = 1 to n
if ssWord$(i) = ssWord$(j) and i <> j then
cnt = 0
for k = 1 to len(theWord$(i))
if mid$(theWord$(i),k,1) = mid$(theWord$(j),k,1) then cnt = cnt + 1
next k
if cnt = 0 then
maxLen = len(theWord$(i))
maxPtrI = i
maxPtrJ = j
end if
end if
next j
end if
next i
print maxLen;" ";theWord$(maxPtrI);" => ";theWord$(maxPtrJ)
end |
http://rosettacode.org/wiki/Anonymous_recursion | Anonymous recursion | While implementing a recursive function, it often happens that we must resort to a separate helper function to handle the actual recursion.
This is usually the case when directly calling the current function would waste too many resources (stack space, execution time), causing unwanted side-effects, and/or the function doesn't have the right arguments and/or return values.
So we end up inventing some silly name like foo2 or foo_helper. I have always found it painful to come up with a proper name, and see some disadvantages:
You have to think up a name, which then pollutes the namespace
Function is created which is called from nowhere else
The program flow in the source code is interrupted
Some languages allow you to embed recursion directly in-place. This might work via a label, a local gosub instruction, or some special keyword.
Anonymous recursion can also be accomplished using the Y combinator.
Task
If possible, demonstrate this by writing the recursive version of the fibonacci function (see Fibonacci sequence) which checks for a negative argument before doing the actual recursion.
| #Phix | Phix | without js -- (no class yet)
class Fib
private function fib_i(integer n)
return iff(n<2?n:this.fib_i(n-1)+this.fib_i(n-2))
end function
public function fib(integer n)
if n<0 then throw("constraint error") end if
return this.fib_i(n)
end function
end class
Fib f = new()
function fib_i(integer i)
return sprintf("this is not the fib_i(%d) you are looking for\n",i)
end function
?f.fib(10)
--?f.fib_i(10) -- illegal
?fib_i(10)
|
http://rosettacode.org/wiki/Amicable_pairs | Amicable pairs | Two integers
N
{\displaystyle N}
and
M
{\displaystyle M}
are said to be amicable pairs if
N
≠
M
{\displaystyle N\neq M}
and the sum of the proper divisors of
N
{\displaystyle N}
(
s
u
m
(
p
r
o
p
D
i
v
s
(
N
)
)
{\displaystyle \mathrm {sum} (\mathrm {propDivs} (N))}
)
=
M
{\displaystyle =M}
as well as
s
u
m
(
p
r
o
p
D
i
v
s
(
M
)
)
=
N
{\displaystyle \mathrm {sum} (\mathrm {propDivs} (M))=N}
.
Example
1184 and 1210 are an amicable pair, with proper divisors:
1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592 and
1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605 respectively.
Task
Calculate and show here the Amicable pairs below 20,000; (there are eight).
Related tasks
Proper divisors
Abundant, deficient and perfect number classifications
Aliquot sequence classifications and its amicable classification.
| #Pascal | Pascal | Chasing Chains of Sums of Factors of Numbers.
Perfect!! 6,
Perfect!! 28,
Amicable! 220,284,
Perfect!! 496,
Amicable! 1184,1210,
Amicable! 2620,2924,
Amicable! 5020,5564,
Amicable! 6232,6368,
Perfect!! 8128,
Amicable! 10744,10856,
Amicable! 12285,14595,
Sociable: 12496,14288,15472,14536,14264,
Sociable: 14316,19116,31704,47616,83328,177792,295488,629072,589786,294896,358336,418904,366556,274924,275444,243760,376736,381028,285778,152990,122410,97946,48976,45946,22976,22744,19916,17716,
Amicable! 17296,18416,
|
http://rosettacode.org/wiki/Animate_a_pendulum | Animate a pendulum |
One good way of making an animation is by simulating a physical system and illustrating the variables in that system using a dynamically changing graphical display.
The classic such physical system is a simple gravity pendulum.
Task
Create a simple physical model of a pendulum and animate it.
| #Raku | Raku | use SDL2::Raw;
use Cairo;
my $width = 1000;
my $height = 400;
SDL_Init(VIDEO);
my $window = SDL_CreateWindow(
'Pendulum - Raku',
SDL_WINDOWPOS_CENTERED_MASK,
SDL_WINDOWPOS_CENTERED_MASK,
$width, $height, RESIZABLE
);
my $render = SDL_CreateRenderer($window, -1, ACCELERATED +| PRESENTVSYNC);
my $bob = Cairo::Image.create( Cairo::FORMAT_ARGB32, 32, 32 );
given Cairo::Context.new($bob) {
my Cairo::Pattern::Gradient::Radial $sphere .=
create(13.3, 12.8, 3.2, 12.8, 12.8, 32);
$sphere.add_color_stop_rgba(0, 1, 1, .698, 1);
$sphere.add_color_stop_rgba(1, .623, .669, .144, 1);
.pattern($sphere);
.arc(16, 16, 15, 0, 2 * pi);
.fill;
$sphere.destroy;
}
my $bob_texture = SDL_CreateTexture(
$render, %PIXELFORMAT<ARGB8888>,
STATIC, 32, 32
);
SDL_UpdateTexture(
$bob_texture,
SDL_Rect.new(:x(0), :y(0), :w(32), :h(32)),
$bob.data, $bob.stride // 32
);
SDL_SetTextureBlendMode($bob_texture, 1);
SDL_SetRenderDrawBlendMode($render, 1);
my $event = SDL_Event.new;
my $now = now; # time
my $Θ = -π/3; # start angle
my $ppi = 500; # scale
my $g = -9.81; # accelaration of gravity
my $ax = $width/2; # anchor x
my $ay = 25; # anchor y
my $len = $height - 75; # 'rope' length
my $vel; # velocity
my $dt; # delta time
main: loop {
while SDL_PollEvent($event) {
my $casted_event = SDL_CastEvent($event);
given $casted_event {
when *.type == QUIT { last main }
when *.type == WINDOWEVENT {
if .event == 5 {
$width = .data1;
$height = .data2;
$ax = $width/2;
$len = $height - 75;
}
}
}
}
$dt = now - $now;
$now = now;
$vel += $g / $len * sin($Θ) * $ppi * $dt;
$Θ += $vel * $dt;
my $bx = $ax + sin($Θ) * $len;
my $by = $ay + cos($Θ) * $len;
SDL_SetRenderDrawColor($render, 255, 255, 255, 255);
SDL_RenderDrawLine($render, |($ax, $ay, $bx, $by)».round);
SDL_RenderCopy( $render, $bob_texture, Nil,
SDL_Rect.new($bx - 16, $by - 16, 32, 32)
);
SDL_RenderPresent($render);
SDL_SetRenderDrawColor($render, 0, 0, 0, 0);
SDL_RenderClear($render);
}
SDL_Quit(); |
http://rosettacode.org/wiki/Amb | Amb | Define and give an example of the Amb operator.
The Amb operator (short for "ambiguous") expresses nondeterminism. This doesn't refer to randomness (as in "nondeterministic universe") but is closely related to the term as it is used in automata theory ("non-deterministic finite automaton").
The Amb operator takes a variable number of expressions (or values if that's simpler in the language) and yields a correct one which will satisfy a constraint in some future computation, thereby avoiding failure.
Problems whose solution the Amb operator naturally expresses can be approached with other tools, such as explicit nested iterations over data sets, or with pattern matching. By contrast, the Amb operator appears integrated into the language. Invocations of Amb are not wrapped in any visible loops or other search patterns; they appear to be independent.
Essentially Amb(x, y, z) splits the computation into three possible futures: a future in which the value x is yielded, a future in which the value y is yielded and a future in which the value z is yielded. The future which leads to a successful subsequent computation is chosen. The other "parallel universes" somehow go away. Amb called with no arguments fails.
For simplicity, one of the domain values usable with Amb may denote failure, if that is convenient. For instance, it is convenient if a Boolean false denotes failure, so that Amb(false) fails, and thus constraints can be expressed using Boolean expressions like Amb(x * y == 8) which unless x and y add to four.
A pseudo-code program which satisfies this constraint might look like:
let x = Amb(1, 2, 3)
let y = Amb(7, 6, 4, 5)
Amb(x * y = 8)
print x, y
The output is 2 4 because Amb(1, 2, 3) correctly chooses the future in which x has value 2, Amb(7, 6, 4, 5) chooses 4 and consequently Amb(x * y = 8) produces a success.
Alternatively, failure could be represented using strictly Amb():
unless x * y = 8 do Amb()
Or else Amb could take the form of two operators or functions: one for producing values and one for enforcing constraints:
let x = Ambsel(1, 2, 3)
let y = Ambsel(4, 5, 6)
Ambassert(x * y = 8)
print x, y
where Ambassert behaves like Amb() if the Boolean expression is false, otherwise it allows the future computation to take place, without yielding any value.
The task is to somehow implement Amb, and demonstrate it with a program which chooses one word from each of the following four sets of character strings to generate a four-word sentence:
"the" "that" "a"
"frog" "elephant" "thing"
"walked" "treaded" "grows"
"slowly" "quickly"
The constraint to be satisfied is that the last character of each word (other than the last) is the same as the first character of its successor.
The only successful sentence is "that thing grows slowly"; other combinations do not satisfy the constraint and thus fail.
The goal of this task isn't to simply process the four lists of words with explicit, deterministic program flow such as nested iteration, to trivially demonstrate the correct output. The goal is to implement the Amb operator, or a facsimile thereof that is possible within the language limitations.
| #Julia | Julia | # This is a general purpose AMB function that takes a two-argument failure function and
# arbitrary number of iterable objects and returns the first solution found as an array
# this function is in essence an iterative backtracking solver
function amb(failure, itrs...)
n = length(itrs)
if n == 1 return end
states = Vector(n)
values = Vector(n)
# starting point, we put down the first value from the first iterable object
states[1] = start(itrs[1])
values[1], states[1] = next(itrs[1], states[1])
i = 1
# main solver loop
while true
# test for failure
if i > 1 && failure(values[i-1], values[i])
# loop for generating a new value upon failure
# in fact this would be way more readable using goto, but Julia doesn't seem to have that :(
while true
# if we failed, we must generate a new value, but first we must check whether there is any
if done(itrs[i], states[i])
# backtracking step with sanity check in case we ran out of values from the current generator
if i == 1
return
else
i -= 1
continue
end
else
# if there is indeed a new value, generate it
values[i], states[i] = next(itrs[i], states[i])
break
end
end
else
# no failure branch
# if solution is ready (i.e. all generators are used) just return it
if i == n return values end
# else start up the next generator
i += 1
states[i] = start(itrs[i])
values[i], states[i] = next(itrs[i], states[i])
end
end
end
# Call our generic AMB function according to the task description and
# form the solution sentence from the returned array of words
amb((s1,s2) -> s1[end] != s2[1], # failure function
["the", "that", "a"],
["frog", "elephant", "thing"],
["walked", "treaded", "grows"],
["slowly", "quickly"]) |>
x -> join(x, " ") |>
println
|
http://rosettacode.org/wiki/Accumulator_factory | Accumulator factory | A problem posed by Paul Graham is that of creating a function that takes a single (numeric) argument and which returns another function that is an accumulator. The returned accumulator function in turn also takes a single numeric argument, and returns the sum of all the numeric values passed in so far to that accumulator (including the initial value passed when the accumulator was created).
Rules
The detailed rules are at http://paulgraham.com/accgensub.html and are reproduced here for simplicity (with additions in small italic text).
Before you submit an example, make sure the function
Takes a number n and returns a function (lets call it g), that takes a number i, and returns n incremented by the accumulation of i from every call of function g(i).
Although these exact function and parameter names need not be used
Works for any numeric type-- i.e. can take both ints and floats and returns functions that can take both ints and floats. (It is not enough simply to convert all input to floats. An accumulator that has only seen integers must return integers.) (i.e., if the language doesn't allow for numeric polymorphism, you have to use overloading or something like that)
Generates functions that return the sum of every number ever passed to them, not just the most recent. (This requires a piece of state to hold the accumulated value, which in turn means that pure functional languages can't be used for this task.)
Returns a real function, meaning something that you can use wherever you could use a function you had defined in the ordinary way in the text of your program. (Follow your language's conventions here.)
Doesn't store the accumulated value or the returned functions in a way that could cause them to be inadvertently modified by other code. (No global variables or other such things.)
E.g. if after the example, you added the following code (in a made-up language) where the factory function is called foo:
x = foo(1);
x(5);
foo(3);
print x(2.3);
It should print 8.3. (There is no need to print the form of the accumulator function returned by foo(3); it's not part of the task at all.)
Task
Create a function that implements the described rules.
It need not handle any special error cases not described above. The simplest way to implement the task as described is typically to use a closure, providing the language supports them.
Where it is not possible to hold exactly to the constraints above, describe the deviations.
| #Clojure | Clojure | (defn accum [n]
(let [acc (atom n)]
(fn [m] (swap! acc + m)))) |
http://rosettacode.org/wiki/Accumulator_factory | Accumulator factory | A problem posed by Paul Graham is that of creating a function that takes a single (numeric) argument and which returns another function that is an accumulator. The returned accumulator function in turn also takes a single numeric argument, and returns the sum of all the numeric values passed in so far to that accumulator (including the initial value passed when the accumulator was created).
Rules
The detailed rules are at http://paulgraham.com/accgensub.html and are reproduced here for simplicity (with additions in small italic text).
Before you submit an example, make sure the function
Takes a number n and returns a function (lets call it g), that takes a number i, and returns n incremented by the accumulation of i from every call of function g(i).
Although these exact function and parameter names need not be used
Works for any numeric type-- i.e. can take both ints and floats and returns functions that can take both ints and floats. (It is not enough simply to convert all input to floats. An accumulator that has only seen integers must return integers.) (i.e., if the language doesn't allow for numeric polymorphism, you have to use overloading or something like that)
Generates functions that return the sum of every number ever passed to them, not just the most recent. (This requires a piece of state to hold the accumulated value, which in turn means that pure functional languages can't be used for this task.)
Returns a real function, meaning something that you can use wherever you could use a function you had defined in the ordinary way in the text of your program. (Follow your language's conventions here.)
Doesn't store the accumulated value or the returned functions in a way that could cause them to be inadvertently modified by other code. (No global variables or other such things.)
E.g. if after the example, you added the following code (in a made-up language) where the factory function is called foo:
x = foo(1);
x(5);
foo(3);
print x(2.3);
It should print 8.3. (There is no need to print the form of the accumulator function returned by foo(3); it's not part of the task at all.)
Task
Create a function that implements the described rules.
It need not handle any special error cases not described above. The simplest way to implement the task as described is typically to use a closure, providing the language supports them.
Where it is not possible to hold exactly to the constraints above, describe the deviations.
| #CoffeeScript | CoffeeScript | accumulator = (sum) ->
(n) -> sum += n
f = accumulator(1)
console.log f(5)
console.log f(2.3) |
http://rosettacode.org/wiki/Ackermann_function | Ackermann function | The Ackermann function is a classic example of a recursive function, notable especially because it is not a primitive recursive function. It grows very quickly in value, as does the size of its call tree.
The Ackermann function is usually defined as follows:
A
(
m
,
n
)
=
{
n
+
1
if
m
=
0
A
(
m
−
1
,
1
)
if
m
>
0
and
n
=
0
A
(
m
−
1
,
A
(
m
,
n
−
1
)
)
if
m
>
0
and
n
>
0.
{\displaystyle A(m,n)={\begin{cases}n+1&{\mbox{if }}m=0\\A(m-1,1)&{\mbox{if }}m>0{\mbox{ and }}n=0\\A(m-1,A(m,n-1))&{\mbox{if }}m>0{\mbox{ and }}n>0.\end{cases}}}
Its arguments are never negative and it always terminates.
Task
Write a function which returns the value of
A
(
m
,
n
)
{\displaystyle A(m,n)}
. Arbitrary precision is preferred (since the function grows so quickly), but not required.
See also
Conway chained arrow notation for the Ackermann function.
| #8086_Assembly | 8086 Assembly | cpu 8086
bits 16
org 100h
section .text
jmp demo
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; ACK(M,N); DX=M, AX=N, return value in AX.
ack: and dx,dx ; N=0?
jnz .m
inc ax ; If so, return N+1
ret
.m: and ax,ax ; M=0?
jnz .mn
mov ax,1 ; If so, N=1,
dec dx ; M -= 1
jmp ack ; ACK(M-1,1) - tail recursion
.mn: push dx ; Keep M on the stack
dec ax ; N-=1
call ack ; N = ACK(M,N-1)
pop dx ; Restore M
dec dx ; M -= 1
jmp ack ; ACK(M-1,ACK(M,N-1)) - tail recursion
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; Print table of ack(m,n)
MMAX: equ 4 ; Size of table to print. Noe that math is done
NMAX: equ 9 ; in 16 bits.
demo: xor si,si ; Let SI hold M,
xor di,di ; and DI hold N.
acknum: mov dx,si ; Calculate ack(M,N)
mov ax,di
call ack
call prax ; Print number
inc di ; N += 1
cmp di,NMAX ; Row done?
jb acknum ; If not, print next number on row
xor di,di ; Otherwise, N=0,
inc si ; M += 1
mov dx,nl ; Print newline
call prstr
cmp si,MMAX ; Done?
jb acknum ; If not, start next row
ret ; Otherwise, stop.
;;; Print AX as ASCII number.
prax: mov bx,pnum ; Pointer to number string
mov cx,10 ; Divisor
.dgt: xor dx,dx ; Divide AX by ten
div cx
add dl,'0' ; DX holds remainder - add ASCII 0
dec bx ; Move pointer backwards
mov [bx],dl ; Save digit in string
and ax,ax ; Are we done yet?
jnz .dgt ; If not, next digit
mov dx,bx ; Tell DOS to print the string
prstr: mov ah,9
int 21h
ret
section .data
db '*****' ; Placeholder for ASCII number
pnum: db 9,'$'
nl: db 13,10,'$' |
http://rosettacode.org/wiki/Abundant,_deficient_and_perfect_number_classifications | Abundant, deficient and perfect number classifications | These define three classifications of positive integers based on their proper divisors.
Let P(n) be the sum of the proper divisors of n where the proper divisors are all positive divisors of n other than n itself.
if P(n) < n then n is classed as deficient (OEIS A005100).
if P(n) == n then n is classed as perfect (OEIS A000396).
if P(n) > n then n is classed as abundant (OEIS A005101).
Example
6 has proper divisors of 1, 2, and 3.
1 + 2 + 3 = 6, so 6 is classed as a perfect number.
Task
Calculate how many of the integers 1 to 20,000 (inclusive) are in each of the three classes.
Show the results here.
Related tasks
Aliquot sequence classifications. (The whole series from which this task is a subset.)
Proper divisors
Amicable pairs
| #ALGOL_W | ALGOL W | begin % count abundant, perfect and deficient numbers up to 20 000 %
integer MAX_NUMBER;
MAX_NUMBER := 20000;
begin
integer array pds ( 1 :: MAX_NUMBER );
integer aCount, dCount, pCount, dSum;
% construct a table of proper divisor sums %
pds( 1 ) := 0;
for i := 2 until MAX_NUMBER do pds( i ) := 1;
for i := 2 until MAX_NUMBER do begin
for j := i + i step i until MAX_NUMBER do pds( j ) := pds( j ) + i
end for_i ;
aCount := dCount := pCOunt := 0;
for i := 1 until 20000 do begin
dSum := pds( i );
if dSum > i then aCount := aCount + 1
else if dSum < i then dCount := dCOunt + 1
else % dSum = i % pCount := pCount + 1
end for_i ;
write( "Abundant numbers up to 20 000: ", aCount );
write( "Perfect numbers up to 20 000: ", pCount );
write( "Deficient numbers up to 20 000: ", dCount )
end
end. |
http://rosettacode.org/wiki/Align_columns | Align columns | Given a text file of many lines, where fields within a line
are delineated by a single 'dollar' character, write a program
that aligns each column of fields by ensuring that words in each
column are separated by at least one space.
Further, allow for each word in a column to be either left
justified, right justified, or center justified within its column.
Use the following text to test your programs:
Given$a$text$file$of$many$lines,$where$fields$within$a$line$
are$delineated$by$a$single$'dollar'$character,$write$a$program
that$aligns$each$column$of$fields$by$ensuring$that$words$in$each$
column$are$separated$by$at$least$one$space.
Further,$allow$for$each$word$in$a$column$to$be$either$left$
justified,$right$justified,$or$center$justified$within$its$column.
Note that:
The example input texts lines may, or may not, have trailing dollar characters.
All columns should share the same alignment.
Consecutive space characters produced adjacent to the end of lines are insignificant for the purposes of the task.
Output text will be viewed in a mono-spaced font on a plain text editor or basic terminal.
The minimum space between columns should be computed from the text and not hard-coded.
It is not a requirement to add separating characters between or around columns.
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
| #AutoHotkey | AutoHotkey | Alignment := "L" ; Options: L, R, C
Text =
( LTrim
Given$a$text$file$of$many$lines,$where$fields$within$a$line$
are$delineated$by$a$single$'dollar'$character,$write$a$program
that$aligns$each$column$of$fields$by$ensuring$that$words$in$each$
column$are$separated$by$at$least$one$space.
Further,$allow$for$each$word$in$a$column$to$be$either$left$
justified,$right$justified,$or$center$justified$within$its$column.
)
Loop, Parse, Text ; calculate column's width
If A_LoopField in $,`n
If (N > W)
W := N, N := 0
Else
N := 0
Else
++N
Width := ++W
Loop, Parse, Text, `n ; process each line
{
Words := StrSplit(A_LoopField, "$")
For i, Word in Words ; process each word
Line .= Align(Word, Alignment, Width)
Result .= RTrim(Line) . "`n"
Line := ""
}
Clipboard := Result ; present results
MsgBox, The results are in the Clipboard
Align(Pal, How, Width) { ; function for alignment
Length := StrLen(Pal)
If (How = "L")
Return Pal . Spc(Width - Length)
Else If (How = "R")
Return Spc(Width - Length) . Pal
Else If (How = "C")
Return Spc((Width - Length)//2) . Pal . Spc(Width - Length - (Width - Length)//2)
}
Spc(Number) { ; function to concatenate space characters
Loop, %Number%
Ret .= A_Space
Return Ret
}
|
http://rosettacode.org/wiki/Active_object | Active object | In object-oriented programming an object is active when its state depends on clock. Usually an active object encapsulates a task that updates the object's state. To the outer world the object looks like a normal object with methods that can be called from outside. Implementation of such methods must have a certain synchronization mechanism with the encapsulated task in order to prevent object's state corruption.
A typical instance of an active object is an animation widget. The widget state changes with the time, while as an object it has all properties of a normal widget.
The task
Implement an active integrator object. The object has an input and output. The input can be set using the method Input. The input is a function of time. The output can be queried using the method Output. The object integrates its input over the time and the result becomes the object's output. So if the input is K(t) and the output is S, the object state S is changed to S + (K(t1) + K(t0)) * (t1 - t0) / 2, i.e. it integrates K using the trapeze method. Initially K is constant 0 and S is 0.
In order to test the object:
set its input to sin (2π f t), where the frequency f=0.5Hz. The phase is irrelevant.
wait 2s
set the input to constant 0
wait 0.5s
Verify that now the object's output is approximately 0 (the sine has the period of 2s). The accuracy of the result will depend on the OS scheduler time slicing and the accuracy of the clock.
| #Factor | Factor | USING: accessors alarms calendar combinators kernel locals math
math.constants math.functions prettyprint system threads ;
IN: rosettacode.active
TUPLE: active-object alarm function state previous-time ;
: apply-stack-effect ( quot -- quot' )
[ call( x -- x ) ] curry ; inline
: nano-to-seconds ( -- seconds ) nano-count 9 10^ / ;
: object-times ( active-object -- t1 t2 )
[ previous-time>> ]
[ nano-to-seconds [ >>previous-time drop ] keep ] bi ;
:: adding-function ( t1 t2 active-object -- function )
t2 t1 active-object function>> apply-stack-effect bi@ +
t2 t1 - * 2 / [ + ] curry ;
: integrate ( active-object -- )
[ object-times ]
[ adding-function ]
[ swap apply-stack-effect change-state drop ] tri ;
: <active-object> ( -- object )
active-object new
0 >>state
nano-to-seconds >>previous-time
[ drop 0 ] >>function
dup [ integrate ] curry 1 nanoseconds every >>alarm ;
: destroy ( active-object -- ) alarm>> cancel-alarm ;
: input ( object quot -- object ) >>function ;
: output ( object -- val ) state>> ;
: active-test ( -- )
<active-object>
[ 2 pi 0.5 * * * sin ] input
2 seconds sleep
[ drop 0 ] input
0.5 seconds sleep
[ output . ] [ destroy ] bi ;
MAIN: active-test |
http://rosettacode.org/wiki/Active_object | Active object | In object-oriented programming an object is active when its state depends on clock. Usually an active object encapsulates a task that updates the object's state. To the outer world the object looks like a normal object with methods that can be called from outside. Implementation of such methods must have a certain synchronization mechanism with the encapsulated task in order to prevent object's state corruption.
A typical instance of an active object is an animation widget. The widget state changes with the time, while as an object it has all properties of a normal widget.
The task
Implement an active integrator object. The object has an input and output. The input can be set using the method Input. The input is a function of time. The output can be queried using the method Output. The object integrates its input over the time and the result becomes the object's output. So if the input is K(t) and the output is S, the object state S is changed to S + (K(t1) + K(t0)) * (t1 - t0) / 2, i.e. it integrates K using the trapeze method. Initially K is constant 0 and S is 0.
In order to test the object:
set its input to sin (2π f t), where the frequency f=0.5Hz. The phase is irrelevant.
wait 2s
set the input to constant 0
wait 0.5s
Verify that now the object's output is approximately 0 (the sine has the period of 2s). The accuracy of the result will depend on the OS scheduler time slicing and the accuracy of the clock.
| #FBSL | FBSL | #APPTYPE CONSOLE
#INCLUDE <Include\Windows.inc>
DIM Entity AS NEW Integrator(): SLEEP(2000) ' respawn and do the job
Entity.Relax(): SLEEP(500) ' get some rest
PRINT ">>> ", Entity.Yield(): DELETE Entity ' report and die
PAUSE
' ------------- End Program Code -------------
#DEFINE SpawnMutex CreateMutex(NULL, FALSE, "mutex")
#DEFINE LockMutex WaitForSingleObject(mutex, INFINITE)
#DEFINE UnlockMutex ReleaseMutex(mutex)
#DEFINE KillMutex CloseHandle(mutex)
CLASS Integrator
PRIVATE:
TYPE LARGE_INTEGER
lowPart AS INTEGER
highPart AS INTEGER
END TYPE
DIM dfreq AS DOUBLE, dlast AS DOUBLE, dnow AS DOUBLE, llint AS LARGE_INTEGER
DIM dret0 AS DOUBLE, dret1 AS DOUBLE, mutex AS INTEGER, sum AS DOUBLE, thread AS INTEGER
' --------------------------------------------
SUB INITIALIZE()
mutex = SpawnMutex
QueryPerformanceFrequency(@llint)
dfreq = LargeInt2Double(llint)
QueryPerformanceCounter(@llint)
dlast = LargeInt2Double(llint) / dfreq
thread = FBSLTHREAD(ADDRESSOF Sampler)
FBSLTHREADRESUME(thread)
END SUB
SUB TERMINATE()
' nothing special
END SUB
' --------------------------------------------
SUB Sampler()
DO
LockMutex
SLEEP(5)
QueryPerformanceCounter(@llint)
dnow = LargeInt2Double(llint) / dfreq
dret0 = Task(dlast): dret1 = Task(dnow)
sum = sum + (dret1 + dret0) * (dnow - dlast) / 2
dlast = dnow
UnlockMutex
LOOP
END SUB
FUNCTION LargeInt2Double(obj AS VARIANT) AS DOUBLE
STATIC ret
ret = obj.highPart
IF obj.highPart < 0 THEN ret = ret + (2 ^ 32)
ret = ret * 2 ^ 32
ret = ret + obj.lowPart
IF obj.lowPart < 0 THEN ret = ret + (2 ^ 32)
RETURN ret
END FUNCTION
PUBLIC:
METHOD Relax()
LockMutex
ADDRESSOF Task = ADDRESSOF Idle
UnlockMutex
END METHOD
METHOD Yield() AS DOUBLE
LockMutex
Yield = sum
FBSLTHREADKILL(thread)
UnlockMutex
KillMutex
END METHOD
END CLASS
FUNCTION Idle(BYVAL t AS DOUBLE) AS DOUBLE
RETURN 0.0
END FUNCTION
FUNCTION Task(BYVAL t AS DOUBLE) AS DOUBLE
RETURN SIN(2 * PI * 0.5 * t)
END FUNCTION |
http://rosettacode.org/wiki/Aliquot_sequence_classifications | Aliquot sequence classifications | An aliquot sequence of a positive integer K is defined recursively as the first member
being K and subsequent members being the sum of the Proper divisors of the previous term.
If the terms eventually reach 0 then the series for K is said to terminate.
There are several classifications for non termination:
If the second term is K then all future terms are also K and so the sequence repeats from the first term with period 1 and K is called perfect.
If the third term would be repeating K then the sequence repeats with period 2 and K is called amicable.
If the Nth term would be repeating K for the first time, with N > 3 then the sequence repeats with period N - 1 and K is called sociable.
Perfect, amicable and sociable numbers eventually repeat the original number K; there are other repetitions...
Some K have a sequence that eventually forms a periodic repetition of period 1 but of a number other than K, for example 95 which forms the sequence 95, 25, 6, 6, 6, ... such K are called aspiring.
K that have a sequence that eventually forms a periodic repetition of period >= 2 but of a number other than K, for example 562 which forms the sequence 562, 284, 220, 284, 220, ... such K are called cyclic.
And finally:
Some K form aliquot sequences that are not known to be either terminating or periodic; these K are to be called non-terminating.
For the purposes of this task, K is to be classed as non-terminating if it has not been otherwise classed after generating 16 terms or if any term of the sequence is greater than 2**47 = 140,737,488,355,328.
Task
Create routine(s) to generate the aliquot sequence of a positive integer enough to classify it according to the classifications given above.
Use it to display the classification and sequences of the numbers one to ten inclusive.
Use it to show the classification and sequences of the following integers, in order:
11, 12, 28, 496, 220, 1184, 12496, 1264460, 790, 909, 562, 1064, 1488, and optionally 15355717786080.
Show all output on this page.
Related tasks
Abundant, deficient and perfect number classifications. (Classifications from only the first two members of the whole sequence).
Proper divisors
Amicable pairs
| #Kotlin | Kotlin | // version 1.1.3
data class Classification(val sequence: List<Long>, val aliquot: String)
const val THRESHOLD = 1L shl 47
fun sumProperDivisors(n: Long): Long {
if (n < 2L) return 0L
val sqrt = Math.sqrt(n.toDouble()).toLong()
var sum = 1L + (2L..sqrt)
.filter { n % it == 0L }
.map { it + n / it }
.sum()
if (sqrt * sqrt == n) sum -= sqrt
return sum
}
fun classifySequence(k: Long): Classification {
require(k > 0)
var last = k
val seq = mutableListOf(k)
while (true) {
last = sumProperDivisors(last)
seq.add(last)
val n = seq.size
val aliquot = when {
last == 0L -> "Terminating"
n == 2 && last == k -> "Perfect"
n == 3 && last == k -> "Amicable"
n >= 4 && last == k -> "Sociable[${n - 1}]"
last == seq[n - 2] -> "Aspiring"
last in seq.slice(1..n - 3) -> "Cyclic[${n - 1 - seq.indexOf(last)}]"
n == 16 || last > THRESHOLD -> "Non-Terminating"
else -> ""
}
if (aliquot != "") return Classification(seq, aliquot)
}
}
fun main(args: Array<String>) {
println("Aliqot classifications - periods for Sociable/Cyclic in square brackets:\n")
for (k in 1L..10) {
val (seq, aliquot) = classifySequence(k)
println("${"%2d".format(k)}: ${aliquot.padEnd(15)} $seq")
}
val la = longArrayOf(
11, 12, 28, 496, 220, 1184, 12496, 1264460, 790, 909, 562, 1064, 1488
)
println()
for (k in la) {
val (seq, aliquot) = classifySequence(k)
println("${"%7d".format(k)}: ${aliquot.padEnd(15)} $seq")
}
println()
val k = 15355717786080L
val (seq, aliquot) = classifySequence(k)
println("$k: ${aliquot.padEnd(15)} $seq")
} |
http://rosettacode.org/wiki/Add_a_variable_to_a_class_instance_at_runtime | Add a variable to a class instance at runtime | Demonstrate how to dynamically add variables to an object (a class instance) at runtime.
This is useful when the methods/variables of an instance are based on a data file that isn't available until runtime. Hal Fulton gives an example of creating an OO CSV parser at An Exercise in Metaprogramming with Ruby. This is referred to as "monkeypatching" by Pythonistas and some others.
| #Slate | Slate | define: #Empty -> Cloneable clone.
define: #e -> Empty clone.
e addSlotNamed: #foo valued: 1. |
http://rosettacode.org/wiki/Add_a_variable_to_a_class_instance_at_runtime | Add a variable to a class instance at runtime | Demonstrate how to dynamically add variables to an object (a class instance) at runtime.
This is useful when the methods/variables of an instance are based on a data file that isn't available until runtime. Hal Fulton gives an example of creating an OO CSV parser at An Exercise in Metaprogramming with Ruby. This is referred to as "monkeypatching" by Pythonistas and some others.
| #Smalltalk | Smalltalk | |addSlot p|
addSlot :=
[:obj :slotName |
|anonCls newObj|
anonCls := obj class
subclass:(obj class name,'+') asSymbol
instanceVariableNames:slotName
classVariableNames:''
poolDictionaries:'' category:nil
inEnvironment:nil.
anonCls compile:('%1 ^ %1' bindWith:slotName).
anonCls compile:('%1:v %1 := v' bindWith:slotName).
newObj := anonCls cloneFrom:obj.
obj become:newObj.
]. |
http://rosettacode.org/wiki/Add_a_variable_to_a_class_instance_at_runtime | Add a variable to a class instance at runtime | Demonstrate how to dynamically add variables to an object (a class instance) at runtime.
This is useful when the methods/variables of an instance are based on a data file that isn't available until runtime. Hal Fulton gives an example of creating an OO CSV parser at An Exercise in Metaprogramming with Ruby. This is referred to as "monkeypatching" by Pythonistas and some others.
| #Swift | Swift | import Foundation
let fooKey = UnsafeMutablePointer<UInt8>.alloc(1)
class MyClass { }
let e = MyClass()
// set
objc_setAssociatedObject(e, fooKey, 1, .OBJC_ASSOCIATION_RETAIN)
// get
if let associatedObject = objc_getAssociatedObject(e, fooKey) {
print("associated object: \(associatedObject)")
} else {
print("no associated object")
} |
http://rosettacode.org/wiki/Add_a_variable_to_a_class_instance_at_runtime | Add a variable to a class instance at runtime | Demonstrate how to dynamically add variables to an object (a class instance) at runtime.
This is useful when the methods/variables of an instance are based on a data file that isn't available until runtime. Hal Fulton gives an example of creating an OO CSV parser at An Exercise in Metaprogramming with Ruby. This is referred to as "monkeypatching" by Pythonistas and some others.
| #Tcl | Tcl | % package require TclOO
% oo::class create summation {
constructor {} {
variable v 0
}
method add x {
variable v
incr v $x
}
method value {{var v}} {
variable $var
return [set $var]
}
destructor {
variable v
puts "Ended with value $v"
}
}
::summation
% set s [summation new]
% # Do the monkey patch!
% set [info object namespace $s]::time now
now
% # Prove it's really part of the object...
% $s value time
now
% |
http://rosettacode.org/wiki/Address_of_a_variable | Address of a variable |
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
Task
Demonstrate how to get the address of a variable and how to set the address of a variable.
| #Rust | Rust | let v1 = vec![vec![1,2,3]; 10];
println!("Original address: {:p}", &v1);
let mut v2;
// Override rust protections on reading from uninitialized memory
unsafe {v2 = mem::uninitialized();}
let addr = &mut v2 as *mut _;
// ptr::write() though it takes v1 by value, v1s destructor is not run when it goes out of
// scope, which is good since then we'd have a vector of free'd vectors
unsafe {ptr::write(addr, v1)}
println!("New address: {:p}", &v2); |
http://rosettacode.org/wiki/Address_of_a_variable | Address of a variable |
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
Task
Demonstrate how to get the address of a variable and how to set the address of a variable.
| #Scala | Scala | var n = 42;
say Sys.refaddr(\n); # prints the address of the variable
say Sys.refaddr(n); # prints the address of the object at which the variable points to |
http://rosettacode.org/wiki/Address_of_a_variable | Address of a variable |
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
Task
Demonstrate how to get the address of a variable and how to set the address of a variable.
| #Sidef | Sidef | var n = 42;
say Sys.refaddr(\n); # prints the address of the variable
say Sys.refaddr(n); # prints the address of the object at which the variable points to |
http://rosettacode.org/wiki/Address_of_a_variable | Address of a variable |
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
Task
Demonstrate how to get the address of a variable and how to set the address of a variable.
| #Smalltalk | Smalltalk | |p|
p := Point x:10 y:20.
ObjectMemory addressOf:p.
ObjectMemory collectGarbage.
ObjectMemory addressOf:p "may return another value" |
http://rosettacode.org/wiki/AKS_test_for_primes | AKS test for primes | The AKS algorithm for testing whether a number is prime is a polynomial-time algorithm based on an elementary theorem about Pascal triangles.
The theorem on which the test is based can be stated as follows:
a number
p
{\displaystyle p}
is prime if and only if all the coefficients of the polynomial expansion of
(
x
−
1
)
p
−
(
x
p
−
1
)
{\displaystyle (x-1)^{p}-(x^{p}-1)}
are divisible by
p
{\displaystyle p}
.
Example
Using
p
=
3
{\displaystyle p=3}
:
(x-1)^3 - (x^3 - 1)
= (x^3 - 3x^2 + 3x - 1) - (x^3 - 1)
= -3x^2 + 3x
And all the coefficients are divisible by 3, so 3 is prime.
Note:
This task is not the AKS primality test. It is an inefficient exponential time algorithm discovered in the late 1600s and used as an introductory lemma in the AKS derivation.
Task
Create a function/subroutine/method that given
p
{\displaystyle p}
generates the coefficients of the expanded polynomial representation of
(
x
−
1
)
p
{\displaystyle (x-1)^{p}}
.
Use the function to show here the polynomial expansions of
(
x
−
1
)
p
{\displaystyle (x-1)^{p}}
for
p
{\displaystyle p}
in the range 0 to at least 7, inclusive.
Use the previous function in creating another function that when given
p
{\displaystyle p}
returns whether
p
{\displaystyle p}
is prime using the theorem.
Use your test to generate a list of all primes under 35.
As a stretch goal, generate all primes under 50 (needs integers larger than 31-bit).
References
Agrawal-Kayal-Saxena (AKS) primality test (Wikipedia)
Fool-Proof Test for Primes - Numberphile (Video). The accuracy of this video is disputed -- at best it is an oversimplification.
| #Forth | Forth | : coeffs ( u -- nu ... n0 ) \ coefficients of (x-1)^u
1 swap 1+ dup 1 ?do over over i - i */ negate swap loop drop ;
: prime? ( u -- f )
dup 2 < if drop false exit then
dup >r coeffs 1+
\ if not prime, this loop consumes at most half the coefficients, otherwise all
begin dup 1 <> while
r@ mod 0= while
repeat then rdrop
dup 1 = >r
begin 1 = until
r> ;
: .monom ( u1 u2 -- )
dup 0> if [char] + emit then 0 .r ?dup if ." x^" . else space then ;
: .poly ( u -- )
dup >r coeffs 0 r> 1+ 0 ?do
tuck swap .monom 1+
loop ;
: main
11 0 ?do i . ." : " i .poly cr loop cr
50 1 ?do i prime? if i . then loop
cr ; |
http://rosettacode.org/wiki/Additive_primes | Additive primes | Definitions
In mathematics, additive primes are prime numbers for which the sum of their decimal digits are also primes.
Task
Write a program to determine (and show here) all additive primes less than 500.
Optionally, show the number of additive primes.
Also see
the OEIS entry: A046704 additive primes.
the prime-numbers entry: additive primes.
the geeks for geeks entry: additive prime number.
the prime-numbers fandom: additive primes.
| #Mathematica.2FWolfram_Language | Mathematica/Wolfram Language | ClearAll[AdditivePrimeQ]
AdditivePrimeQ[n_Integer] := PrimeQ[n] \[And] PrimeQ[Total[IntegerDigits[n]]]
Select[Range[500], AdditivePrimeQ] |
http://rosettacode.org/wiki/Additive_primes | Additive primes | Definitions
In mathematics, additive primes are prime numbers for which the sum of their decimal digits are also primes.
Task
Write a program to determine (and show here) all additive primes less than 500.
Optionally, show the number of additive primes.
Also see
the OEIS entry: A046704 additive primes.
the prime-numbers entry: additive primes.
the geeks for geeks entry: additive prime number.
the prime-numbers fandom: additive primes.
| #Modula-2 | Modula-2 | MODULE AdditivePrimes;
FROM InOut IMPORT WriteString, WriteCard, WriteLn;
CONST
Max = 500;
VAR
N: CARDINAL;
Count: CARDINAL;
Prime: ARRAY [2..Max] OF BOOLEAN;
PROCEDURE DigitSum(n: CARDINAL): CARDINAL;
BEGIN
IF n < 10 THEN
RETURN n;
ELSE
RETURN (n MOD 10) + DigitSum(n DIV 10);
END;
END DigitSum;
PROCEDURE Sieve;
VAR i, j, max2: CARDINAL;
BEGIN
FOR i := 2 TO Max DO
Prime[i] := TRUE;
END;
FOR i := 2 TO Max DIV 2 DO
IF Prime[i] THEN;
j := i*2;
WHILE j <= Max DO
Prime[j] := FALSE;
j := j + i;
END;
END;
END;
END Sieve;
BEGIN
Count := 0;
Sieve();
FOR N := 2 TO Max DO
IF Prime[N] AND Prime[DigitSum(N)] THEN
WriteCard(N, 4);
Count := Count + 1;
IF Count MOD 10 = 0 THEN WriteLn(); END;
END;
END;
WriteLn();
WriteString('There are '); WriteCard(Count,0);
WriteString(' additive primes less than '); WriteCard(Max,0);
WriteString('.');
WriteLn();
END AdditivePrimes. |
http://rosettacode.org/wiki/Almost_prime | Almost prime | A k-Almost-prime is a natural number
n
{\displaystyle n}
that is the product of
k
{\displaystyle k}
(possibly identical) primes.
Example
1-almost-primes, where
k
=
1
{\displaystyle k=1}
, are the prime numbers themselves.
2-almost-primes, where
k
=
2
{\displaystyle k=2}
, are the semiprimes.
Task
Write a function/method/subroutine/... that generates k-almost primes and use it to create a table here of the first ten members of k-Almost primes for
1
<=
K
<=
5
{\displaystyle 1<=K<=5}
.
Related tasks
Semiprime
Category:Prime Numbers
| #Liberty_BASIC | Liberty BASIC |
' Almost prime
for k = 1 to 5
print "k = "; k; ":";
i = 2
c = 0
while c < 10
if kPrime(i, k) then
print " "; using("###", i);
c = c + 1
end if
i = i + 1
wend
print
next k
end
function kPrime(n, k)
f = 0
for i = 2 to n
while n mod i = 0
if f = k then kPrime = 0: exit function
f = f + 1
n = int(n / i)
wend
next i
kPrime = abs(f = k)
end function
|
http://rosettacode.org/wiki/Anagrams | Anagrams | When two or more words are composed of the same characters, but in a different order, they are called anagrams.
Task[edit]
Using the word list at http://wiki.puzzlers.org/pub/wordlists/unixdict.txt,
find the sets of words that share the same characters that contain the most words in them.
Related tasks
Word plays
Ordered words
Palindrome detection
Semordnilap
Anagrams
Anagrams/Deranged anagrams
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
| #Ela | Ela | open monad io list string
groupon f x y = f x == f y
lines = split "\n" << replace "\n\n" "\n" << replace "\r" "\n"
main = do
fh <- readFile "c:\\test\\unixdict.txt" OpenMode
f <- readLines fh
closeFile fh
let words = lines f
let wix = groupBy (groupon fst) << sort $ zip (map sort words) words
let mxl = maximum $ map length wix
mapM_ (putLn << map snd) << filter ((==mxl) << length) $ wix |
http://rosettacode.org/wiki/Angle_difference_between_two_bearings | Angle difference between two bearings | Finding the angle between two bearings is often confusing.[1]
Task
Find the angle which is the result of the subtraction b2 - b1, where b1 and b2 are the bearings.
Input bearings are expressed in the range -180 to +180 degrees.
The result is also expressed in the range -180 to +180 degrees.
Compute the angle for the following pairs:
20 degrees (b1) and 45 degrees (b2)
-45 and 45
-85 and 90
-95 and 90
-45 and 125
-45 and 145
29.4803 and -88.6381
-78.3251 and -159.036
Optional extra
Allow the input bearings to be any (finite) value.
Test cases
-70099.74233810938 and 29840.67437876723
-165313.6666297357 and 33693.9894517456
1174.8380510598456 and -154146.66490124757
60175.77306795546 and 42213.07192354373
| #Ring | Ring |
# Project : Angle difference between two bearings
decimals(4)
see "Input in -180 to +180 range:" + nl
see getDifference(20.0, 45.0) + nl
see getDifference(-45.0, 45.0) + nl
see getDifference(-85.0, 90.0) + nl
see getDifference(-95.0, 90.0) + nl
see getDifference(-45.0, 125.0) + nl
see getDifference(-45.0, 145.0) + nl
see getDifference(-45.0, 125.0) + nl
see getDifference(-45.0, 145.0) + nl
see getDifference(29.4803, -88.6381) + nl
see getDifference(-78.3251, -159.036) + nl
func getDifference(b1, b2)
r = (b2 - b1) % 360.0
if r >= 180.0
r = r - 360.0
end
return r
|
http://rosettacode.org/wiki/Angle_difference_between_two_bearings | Angle difference between two bearings | Finding the angle between two bearings is often confusing.[1]
Task
Find the angle which is the result of the subtraction b2 - b1, where b1 and b2 are the bearings.
Input bearings are expressed in the range -180 to +180 degrees.
The result is also expressed in the range -180 to +180 degrees.
Compute the angle for the following pairs:
20 degrees (b1) and 45 degrees (b2)
-45 and 45
-85 and 90
-95 and 90
-45 and 125
-45 and 145
29.4803 and -88.6381
-78.3251 and -159.036
Optional extra
Allow the input bearings to be any (finite) value.
Test cases
-70099.74233810938 and 29840.67437876723
-165313.6666297357 and 33693.9894517456
1174.8380510598456 and -154146.66490124757
60175.77306795546 and 42213.07192354373
| #Ruby | Ruby | def getDifference(b1, b2)
r = (b2 - b1) % 360.0
# Ruby modulus has same sign as divisor, which is positive here,
# so no need to consider negative case
if r >= 180.0
r -= 360.0
end
return r
end
if __FILE__ == $PROGRAM_NAME
puts "Input in -180 to +180 range"
puts getDifference(20.0, 45.0)
puts getDifference(-45.0, 45.0)
puts getDifference(-85.0, 90.0)
puts getDifference(-95.0, 90.0)
puts getDifference(-45.0, 125.0)
puts getDifference(-45.0, 145.0)
puts getDifference(-45.0, 125.0)
puts getDifference(-45.0, 145.0)
puts getDifference(29.4803, -88.6381)
puts getDifference(-78.3251, -159.036)
puts "Input in wider range"
puts getDifference(-70099.74233810938, 29840.67437876723)
puts getDifference(-165313.6666297357, 33693.9894517456)
puts getDifference(1174.8380510598456, -154146.66490124757)
puts getDifference(60175.77306795546, 42213.07192354373)
end |
http://rosettacode.org/wiki/Anagrams/Deranged_anagrams | Anagrams/Deranged anagrams | Two or more words are said to be anagrams if they have the same characters, but in a different order.
By analogy with derangements we define a deranged anagram as two words with the same characters, but in which the same character does not appear in the same position in both words.
Task[edit]
Use the word list at unixdict to find and display the longest deranged anagram.
Related tasks
Permutations/Derangements
Best shuffle
Word plays
Ordered words
Palindrome detection
Semordnilap
Anagrams
Anagrams/Deranged anagrams
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
| #Rust | Rust | //! Deranged anagrams
use std::cmp::Ordering;
use std::collections::HashMap;
use std::fs::File;
use std::io;
use std::io::BufReader;
use std::io::BufRead;
use std::usize::MAX;
/// Get words from unix dictionary file
pub fn get_words() -> Result<Vec<String>, io::Error> {
let mut words = vec!();
// open file
let f = File::open("data/unixdict.txt")?;
// read line by line
let reader = BufReader::new(&f);
for line in reader.lines() {
words.push(line?)
}
Ok(words)
}
/// Get the longest deranged anagram in the given list of word if any
pub fn longest_deranged(v: &mut Vec<String>) -> Option<(String,String)>{
// sort by length descending then by alphabetical order
v.sort_by(|s1, s2| {
let mut c = s2.len().cmp(&s1.len());
if c == Ordering::Equal {
c = s1.cmp(s2);
}
c
});
// keep all strings keyed by sorted characters (since anagrams have the same list of sorted characters)
let mut signatures : HashMap<Vec<char>, Vec<&String>> = HashMap::new();
// save on memory by only keeping in the map strings of the current processed length
let mut previous_length = MAX;
for s in v {
// length change, clear the map
if s.len()<previous_length {
signatures.clear();
previous_length = s.len();
}
// generate key as sorted characters
let mut sorted_chars = s.chars().collect::<Vec<char>>();
sorted_chars.sort();
let anagrams = signatures.entry(sorted_chars).or_insert(vec!());
// find if any anagram (string with the same sorted character vector) is deranged
if let Some(a) = anagrams.iter().filter(|anagram| is_deranged(anagram, s)).next(){
return Some(((*a).clone(), s.clone()));
}
anagrams.push(s);
}
None
}
/// check if two strings do NOT have the same character in the same position
pub fn is_deranged(s1: &String, s2: &String) -> bool {
// we zip the character iterators and check we find no position with the same two characters
s1.chars().zip(s2.chars()).filter(|(a,b)| a == b).next().is_none()
}
/// an example main method printing the results
fn main() {
let r = get_words();
match r {
Ok(mut v) => {
let od = longest_deranged(&mut v);
match od {
None => println!("No deranged anagrams found!"),
Some((s1,s2)) => println!("{} {}",s1,s2),
}
},
Err(e) => panic!("Could not read words: {}",e)
}
} |
http://rosettacode.org/wiki/Anonymous_recursion | Anonymous recursion | While implementing a recursive function, it often happens that we must resort to a separate helper function to handle the actual recursion.
This is usually the case when directly calling the current function would waste too many resources (stack space, execution time), causing unwanted side-effects, and/or the function doesn't have the right arguments and/or return values.
So we end up inventing some silly name like foo2 or foo_helper. I have always found it painful to come up with a proper name, and see some disadvantages:
You have to think up a name, which then pollutes the namespace
Function is created which is called from nowhere else
The program flow in the source code is interrupted
Some languages allow you to embed recursion directly in-place. This might work via a label, a local gosub instruction, or some special keyword.
Anonymous recursion can also be accomplished using the Y combinator.
Task
If possible, demonstrate this by writing the recursive version of the fibonacci function (see Fibonacci sequence) which checks for a negative argument before doing the actual recursion.
| #PHP | PHP | <?php
function fib($n) {
if ($n < 0)
throw new Exception('Negative numbers not allowed');
$f = function($n) { // This function must be called using call_user_func() only
if ($n < 2)
return 1;
else {
$g = debug_backtrace()[1]['args'][0];
return call_user_func($g, $n-1) + call_user_func($g, $n-2);
}
};
return call_user_func($f, $n);
}
echo fib(8), "\n";
?> |
http://rosettacode.org/wiki/Amicable_pairs | Amicable pairs | Two integers
N
{\displaystyle N}
and
M
{\displaystyle M}
are said to be amicable pairs if
N
≠
M
{\displaystyle N\neq M}
and the sum of the proper divisors of
N
{\displaystyle N}
(
s
u
m
(
p
r
o
p
D
i
v
s
(
N
)
)
{\displaystyle \mathrm {sum} (\mathrm {propDivs} (N))}
)
=
M
{\displaystyle =M}
as well as
s
u
m
(
p
r
o
p
D
i
v
s
(
M
)
)
=
N
{\displaystyle \mathrm {sum} (\mathrm {propDivs} (M))=N}
.
Example
1184 and 1210 are an amicable pair, with proper divisors:
1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592 and
1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605 respectively.
Task
Calculate and show here the Amicable pairs below 20,000; (there are eight).
Related tasks
Proper divisors
Abundant, deficient and perfect number classifications
Aliquot sequence classifications and its amicable classification.
| #Perl | Perl | use ntheory qw/divisor_sum/;
for my $x (1..20000) {
my $y = divisor_sum($x)-$x;
say "$x $y" if $y > $x && $x == divisor_sum($y)-$y;
} |
http://rosettacode.org/wiki/Animate_a_pendulum | Animate a pendulum |
One good way of making an animation is by simulating a physical system and illustrating the variables in that system using a dynamically changing graphical display.
The classic such physical system is a simple gravity pendulum.
Task
Create a simple physical model of a pendulum and animate it.
| #REXX | REXX | /*REXX program displays the (x, y) coördinates (at the end of a swinging pendulum). */
parse arg cycles Plength theta . /*obtain optional argument from the CL.*/
if cycles=='' | cycles=="," then cycles= 60 /*Not specified? Then use the default.*/
if pLength=='' | pLength=="," then pLength= 10 /* " " " " " " */
if theta=='' | theta=="," then theta= 30 /* " " " " " " */
theta= theta / 180 * pi() /* 'cause that's the way Ada did it. */
was= time('R') /*obtain the current elapsed time (was)*/
g= -9.81 /*gravitation constant (for earth). */
speed= 0 /*velocity of the pendulum, now resting*/
do cycles; call delay 1/20 /*swing the pendulum a number of times.*/
now= time('E') /*obtain the current time (in seconds).*/
duration= now - was /*calculate duration since last cycle. */
acceleration= g / pLength * sin(theta) /*compute the pendulum acceleration. */
x= sin(theta) * pLength /*calculate X coördinate of pendulum.*/
y= cos(theta) * pLength /* " Y " " */
speed= speed + acceleration * duration /*calculate " speed " " */
theta= theta + speed * duration /* " " angle " " */
was= now /*save the elapsed time as it was then.*/
say right('X: ',20) fmt(x) right("Y: ", 10) fmt(y)
end /*cycles*/
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
fmt: procedure; parse arg z; return left('', z>=0)format(z, , digits() - 1) /*align#*/
pi: pi= 3.1415926535897932384626433832795028841971693993751058209749445923078; return pi
r2r: return arg(1) // (pi() * 2) /*normalize radians ──► a unit circle. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
cos: procedure; parse arg x; x=r2r(x); numeric fuzz min(6,digits()-3); z=1; _=1; x=x*x
p=z; do k=2 by 2; _=-_*x/(k*(k-1)); z=z+_; if z=p then leave; p=z; end; return z
/*──────────────────────────────────────────────────────────────────────────────────────*/
sin: procedure; parse arg x; x=r2r(x); _=x; numeric fuzz min(5, max(1,digits()-3)); q=x*x
z=x; do k=2 by 2 until p=z; p= z; _= -_*q/(k*k+k); z= z+_; end; return z |
http://rosettacode.org/wiki/Amb | Amb | Define and give an example of the Amb operator.
The Amb operator (short for "ambiguous") expresses nondeterminism. This doesn't refer to randomness (as in "nondeterministic universe") but is closely related to the term as it is used in automata theory ("non-deterministic finite automaton").
The Amb operator takes a variable number of expressions (or values if that's simpler in the language) and yields a correct one which will satisfy a constraint in some future computation, thereby avoiding failure.
Problems whose solution the Amb operator naturally expresses can be approached with other tools, such as explicit nested iterations over data sets, or with pattern matching. By contrast, the Amb operator appears integrated into the language. Invocations of Amb are not wrapped in any visible loops or other search patterns; they appear to be independent.
Essentially Amb(x, y, z) splits the computation into three possible futures: a future in which the value x is yielded, a future in which the value y is yielded and a future in which the value z is yielded. The future which leads to a successful subsequent computation is chosen. The other "parallel universes" somehow go away. Amb called with no arguments fails.
For simplicity, one of the domain values usable with Amb may denote failure, if that is convenient. For instance, it is convenient if a Boolean false denotes failure, so that Amb(false) fails, and thus constraints can be expressed using Boolean expressions like Amb(x * y == 8) which unless x and y add to four.
A pseudo-code program which satisfies this constraint might look like:
let x = Amb(1, 2, 3)
let y = Amb(7, 6, 4, 5)
Amb(x * y = 8)
print x, y
The output is 2 4 because Amb(1, 2, 3) correctly chooses the future in which x has value 2, Amb(7, 6, 4, 5) chooses 4 and consequently Amb(x * y = 8) produces a success.
Alternatively, failure could be represented using strictly Amb():
unless x * y = 8 do Amb()
Or else Amb could take the form of two operators or functions: one for producing values and one for enforcing constraints:
let x = Ambsel(1, 2, 3)
let y = Ambsel(4, 5, 6)
Ambassert(x * y = 8)
print x, y
where Ambassert behaves like Amb() if the Boolean expression is false, otherwise it allows the future computation to take place, without yielding any value.
The task is to somehow implement Amb, and demonstrate it with a program which chooses one word from each of the following four sets of character strings to generate a four-word sentence:
"the" "that" "a"
"frog" "elephant" "thing"
"walked" "treaded" "grows"
"slowly" "quickly"
The constraint to be satisfied is that the last character of each word (other than the last) is the same as the first character of its successor.
The only successful sentence is "that thing grows slowly"; other combinations do not satisfy the constraint and thus fail.
The goal of this task isn't to simply process the four lists of words with explicit, deterministic program flow such as nested iteration, to trivially demonstrate the correct output. The goal is to implement the Amb operator, or a facsimile thereof that is possible within the language limitations.
| #Kotlin | Kotlin | // version 1.2.41
import kotlin.coroutines.experimental.*
import kotlin.coroutines.experimental.intrinsics.*
fun main(args: Array<String>) = amb {
val a = amb("the", "that", "a")
val b = amb("frog", "elephant", "thing")
val c = amb("walked", "treaded", "grows")
val d = amb("slowly", "quickly")
if (a[a.lastIndex] != b[0]) amb()
if (b[b.lastIndex] != c[0]) amb()
if (c[c.lastIndex] != d[0]) amb()
println(listOf(a, b, c, d))
val x = amb(1, 2, 3)
val y = amb(7, 6, 4, 5)
if (x * y != 8) amb()
println(listOf(x, y))
}
class AmbException(): Exception("Refusing to execute")
data class AmbPair<T>(val cont: Continuation<T>, val valuesLeft: MutableList<T>)
@RestrictsSuspension
class AmbEnvironment {
val ambList = mutableListOf<AmbPair<*>>()
suspend fun <T> amb(value: T, vararg rest: T): T = suspendCoroutineOrReturn { cont ->
if (rest.size > 0) {
ambList.add(AmbPair(clone(cont), mutableListOf(*rest)))
}
value
}
suspend fun amb(): Nothing = suspendCoroutine<Nothing> { }
}
@Suppress("UNCHECKED_CAST")
fun <R> amb(block: suspend AmbEnvironment.() -> R): R {
var result: R? = null
var toThrow: Throwable? = null
val dist = AmbEnvironment()
block.startCoroutine(receiver = dist, completion = object : Continuation<R> {
override val context: CoroutineContext get() = EmptyCoroutineContext
override fun resume(value: R) { result = value }
override fun resumeWithException(exception: Throwable) { toThrow = exception }
})
while (result == null && toThrow == null && !dist.ambList.isEmpty()) {
val last = dist.ambList.run { this[lastIndex] }
if (last.valuesLeft.size == 1) {
dist.ambList.removeAt(dist.ambList.lastIndex)
last.apply {
(cont as Continuation<Any?>).resume(valuesLeft[0])
}
} else {
val value = last.valuesLeft.removeAt(last.valuesLeft.lastIndex)
(clone(last.cont) as Continuation<Any?>).resume(value)
}
}
if (toThrow != null)
{
throw toThrow!!
}
else if (result != null)
{
return result!!
}
else
{
throw AmbException()
}
}
val UNSAFE = Class.forName("sun.misc.Unsafe")
.getDeclaredField("theUnsafe")
.apply { isAccessible = true }
.get(null) as sun.misc.Unsafe
@Suppress("UNCHECKED_CAST")
fun <T: Any> clone(obj: T): T {
val clazz = obj::class.java
val copy = UNSAFE.allocateInstance(clazz) as T
copyDeclaredFields(obj, copy, clazz)
return copy
}
tailrec fun <T> copyDeclaredFields(obj: T, copy: T, clazz: Class<out T>) {
for (field in clazz.declaredFields) {
field.isAccessible = true
val v = field.get(obj)
field.set(copy, if (v === obj) copy else v)
}
val superclass = clazz.superclass
if (superclass != null) copyDeclaredFields(obj, copy, superclass)
} |
http://rosettacode.org/wiki/Accumulator_factory | Accumulator factory | A problem posed by Paul Graham is that of creating a function that takes a single (numeric) argument and which returns another function that is an accumulator. The returned accumulator function in turn also takes a single numeric argument, and returns the sum of all the numeric values passed in so far to that accumulator (including the initial value passed when the accumulator was created).
Rules
The detailed rules are at http://paulgraham.com/accgensub.html and are reproduced here for simplicity (with additions in small italic text).
Before you submit an example, make sure the function
Takes a number n and returns a function (lets call it g), that takes a number i, and returns n incremented by the accumulation of i from every call of function g(i).
Although these exact function and parameter names need not be used
Works for any numeric type-- i.e. can take both ints and floats and returns functions that can take both ints and floats. (It is not enough simply to convert all input to floats. An accumulator that has only seen integers must return integers.) (i.e., if the language doesn't allow for numeric polymorphism, you have to use overloading or something like that)
Generates functions that return the sum of every number ever passed to them, not just the most recent. (This requires a piece of state to hold the accumulated value, which in turn means that pure functional languages can't be used for this task.)
Returns a real function, meaning something that you can use wherever you could use a function you had defined in the ordinary way in the text of your program. (Follow your language's conventions here.)
Doesn't store the accumulated value or the returned functions in a way that could cause them to be inadvertently modified by other code. (No global variables or other such things.)
E.g. if after the example, you added the following code (in a made-up language) where the factory function is called foo:
x = foo(1);
x(5);
foo(3);
print x(2.3);
It should print 8.3. (There is no need to print the form of the accumulator function returned by foo(3); it's not part of the task at all.)
Task
Create a function that implements the described rules.
It need not handle any special error cases not described above. The simplest way to implement the task as described is typically to use a closure, providing the language supports them.
Where it is not possible to hold exactly to the constraints above, describe the deviations.
| #Common_Lisp | Common Lisp | (defun accumulator (sum)
(lambda (n)
(incf sum n))) |
http://rosettacode.org/wiki/Accumulator_factory | Accumulator factory | A problem posed by Paul Graham is that of creating a function that takes a single (numeric) argument and which returns another function that is an accumulator. The returned accumulator function in turn also takes a single numeric argument, and returns the sum of all the numeric values passed in so far to that accumulator (including the initial value passed when the accumulator was created).
Rules
The detailed rules are at http://paulgraham.com/accgensub.html and are reproduced here for simplicity (with additions in small italic text).
Before you submit an example, make sure the function
Takes a number n and returns a function (lets call it g), that takes a number i, and returns n incremented by the accumulation of i from every call of function g(i).
Although these exact function and parameter names need not be used
Works for any numeric type-- i.e. can take both ints and floats and returns functions that can take both ints and floats. (It is not enough simply to convert all input to floats. An accumulator that has only seen integers must return integers.) (i.e., if the language doesn't allow for numeric polymorphism, you have to use overloading or something like that)
Generates functions that return the sum of every number ever passed to them, not just the most recent. (This requires a piece of state to hold the accumulated value, which in turn means that pure functional languages can't be used for this task.)
Returns a real function, meaning something that you can use wherever you could use a function you had defined in the ordinary way in the text of your program. (Follow your language's conventions here.)
Doesn't store the accumulated value or the returned functions in a way that could cause them to be inadvertently modified by other code. (No global variables or other such things.)
E.g. if after the example, you added the following code (in a made-up language) where the factory function is called foo:
x = foo(1);
x(5);
foo(3);
print x(2.3);
It should print 8.3. (There is no need to print the form of the accumulator function returned by foo(3); it's not part of the task at all.)
Task
Create a function that implements the described rules.
It need not handle any special error cases not described above. The simplest way to implement the task as described is typically to use a closure, providing the language supports them.
Where it is not possible to hold exactly to the constraints above, describe the deviations.
| #Crystal | Crystal |
# Make types a bit easier with an alias
alias Num = Int32 | Int64 | Float32 | Float64
def accumulator(sum : Num)
# This proc is very similar to a Ruby lambda
->(n : Num){ sum += n }
end
x = accumulator(5)
puts x.call(5) #=> 10
puts x.call(10) #=> 20
puts x.call(2.4) #=> 22.4
|
http://rosettacode.org/wiki/Ackermann_function | Ackermann function | The Ackermann function is a classic example of a recursive function, notable especially because it is not a primitive recursive function. It grows very quickly in value, as does the size of its call tree.
The Ackermann function is usually defined as follows:
A
(
m
,
n
)
=
{
n
+
1
if
m
=
0
A
(
m
−
1
,
1
)
if
m
>
0
and
n
=
0
A
(
m
−
1
,
A
(
m
,
n
−
1
)
)
if
m
>
0
and
n
>
0.
{\displaystyle A(m,n)={\begin{cases}n+1&{\mbox{if }}m=0\\A(m-1,1)&{\mbox{if }}m>0{\mbox{ and }}n=0\\A(m-1,A(m,n-1))&{\mbox{if }}m>0{\mbox{ and }}n>0.\end{cases}}}
Its arguments are never negative and it always terminates.
Task
Write a function which returns the value of
A
(
m
,
n
)
{\displaystyle A(m,n)}
. Arbitrary precision is preferred (since the function grows so quickly), but not required.
See also
Conway chained arrow notation for the Ackermann function.
| #8th | 8th |
\ Ackermann function, illustrating use of "memoization".
\ Memoization is a technique whereby intermediate computed values are stored
\ away against later need. It is particularly valuable when calculating those
\ values is time or resource intensive, as with the Ackermann function.
\ make the stack much bigger so this can complete!
100000 stack-size
\ This is where memoized values are stored:
{} var, dict
\ Simple accessor words
: dict! \ "key" val --
dict @ -rot m:! drop ;
: dict@ \ "key" -- val
dict @ swap m:@ nip ;
defer: ack1
\ We just jam the string representation of the two numbers together for a key:
: makeKey \ m n -- m n key
2dup >s swap >s s:+ ;
: ack2 \ m n -- A
makeKey dup
dict@ null?
if \ can't find key in dict
\ m n key null
drop \ m n key
-rot \ key m n
ack1 \ key A
tuck \ A key A
dict! \ A
else \ found value
\ m n key value
>r drop 2drop r>
then ;
: ack \ m n -- A
over not
if
nip n:1+
else
dup not
if
drop n:1- 1 ack2
else
over swap n:1- ack2
swap n:1- swap ack2
then
then ;
' ack is ack1
: ackOf \ m n --
2dup
"Ack(" . swap . ", " . . ") = " . ack . cr ;
0 0 ackOf
0 4 ackOf
1 0 ackOf
1 1 ackOf
2 1 ackOf
2 2 ackOf
3 1 ackOf
3 3 ackOf
4 0 ackOf
\ this last requires a very large data stack. So start 8th with a parameter '-k 100000'
4 1 ackOf
bye |
http://rosettacode.org/wiki/Abundant,_deficient_and_perfect_number_classifications | Abundant, deficient and perfect number classifications | These define three classifications of positive integers based on their proper divisors.
Let P(n) be the sum of the proper divisors of n where the proper divisors are all positive divisors of n other than n itself.
if P(n) < n then n is classed as deficient (OEIS A005100).
if P(n) == n then n is classed as perfect (OEIS A000396).
if P(n) > n then n is classed as abundant (OEIS A005101).
Example
6 has proper divisors of 1, 2, and 3.
1 + 2 + 3 = 6, so 6 is classed as a perfect number.
Task
Calculate how many of the integers 1 to 20,000 (inclusive) are in each of the three classes.
Show the results here.
Related tasks
Aliquot sequence classifications. (The whole series from which this task is a subset.)
Proper divisors
Amicable pairs
| #AppleScript | AppleScript | on aliquotSum(n)
if (n < 2) then return 0
set sum to 1
set sqrt to n ^ 0.5
set limit to sqrt div 1
if (limit = sqrt) then
set sum to sum + limit
set limit to limit - 1
end if
repeat with i from 2 to limit
if (n mod i is 0) then set sum to sum + i + n div i
end repeat
return sum
end aliquotSum
on task()
set {deficient, perfect, abundant} to {0, 0, 0}
repeat with n from 1 to 20000
set s to aliquotSum(n)
if (s < n) then
set deficient to deficient + 1
else if (s > n) then
set abundant to abundant + 1
else
set perfect to perfect + 1
end if
end repeat
return {deficient:deficient, perfect:perfect, abundant:abundant}
end task
task() |
http://rosettacode.org/wiki/Align_columns | Align columns | Given a text file of many lines, where fields within a line
are delineated by a single 'dollar' character, write a program
that aligns each column of fields by ensuring that words in each
column are separated by at least one space.
Further, allow for each word in a column to be either left
justified, right justified, or center justified within its column.
Use the following text to test your programs:
Given$a$text$file$of$many$lines,$where$fields$within$a$line$
are$delineated$by$a$single$'dollar'$character,$write$a$program
that$aligns$each$column$of$fields$by$ensuring$that$words$in$each$
column$are$separated$by$at$least$one$space.
Further,$allow$for$each$word$in$a$column$to$be$either$left$
justified,$right$justified,$or$center$justified$within$its$column.
Note that:
The example input texts lines may, or may not, have trailing dollar characters.
All columns should share the same alignment.
Consecutive space characters produced adjacent to the end of lines are insignificant for the purposes of the task.
Output text will be viewed in a mono-spaced font on a plain text editor or basic terminal.
The minimum space between columns should be computed from the text and not hard-coded.
It is not a requirement to add separating characters between or around columns.
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
| #AutoIt | AutoIt |
; == If the given text is in an file, it will read with:
#include <File.au3>
Global $aRead
_FileReadToArray($sPath, $aRead) ; == $aRead[0] includes count of lines, every line stored in one item (without linebreak)
; == For example we get the same result with StringSplit()
Global $sText = _
"Given$a$text$file$of$many$lines,$where$fields$within$a$line$" & @CRLF & _
"are$delineated$by$a$single$'dollar'$character,$write$a$program" & @CRLF & _
"that$aligns$each$column$of$fields$by$ensuring$that$words$in$each$" & @CRLF & _
"column$are$separated$by$at$least$one$space." & @CRLF & _
"Further,$allow$for$each$word$in$a$column$to$be$either$left$" & @CRLF & _
"justified,$right$justified,$or$center$justified$within$its$column." & @CRLF
$aRead = StringSplit($sText, @CRLF, 1)
; == strip leading and trailing "$" and trailing spaces, count remaining "$" to get max column number
Global $iMaxColumn = 0, $iLines = 0
For $i = 1 To $aRead[0]
If $aRead[$i] = '' Then ContinueLoop ; skip empty lines
$iLines += 1
$aRead[$i] = StringRegExpReplace(StringRegExpReplace(StringRegExpReplace($aRead[$i], '^\$', ''), '\$$', ''), '\s*$', '')
StringReplace($aRead[$i], '$', '$')
If @extended +1 > $iMaxColumn Then $iMaxColumn = @extended +1
Next
; == build array to store all fields and length of every item
Global $aFields[$iLines][$iMaxColumn +1][2]
; == and store the max. length of item in columns
Global $aColLen[$iMaxColumn]
; == fill the array
Global $aSplitLine
$iLines = 0
For $i = 1 To $aRead[0]
If $aRead[$i] = '' Then ContinueLoop ; skip empty lines
$iMaxColLen = 0
$aSplitLine = StringSplit($aRead[$i], '$')
For $j = 1 To $aSplitLine[0]
$aFields[$iLines][$j-1][0] = $aSplitLine[$j]
$aFields[$iLines][$j-1][1] = StringLen($aSplitLine[$j])
If $aFields[$iLines][$j-1][1] > $aColLen[$j-1] Then $aColLen[$j-1] = $aFields[$iLines][$j-1][1]
Next
$iLines += 1
Next
; == let the user select the alignment for every column
$sAlign = InputBox('Column alignment', 'There are ' & $iMaxColumn & ' columns.' & @LF & '0 = left 1 = center 2 = right' & @LF & _
'Input alignment for all columns without delimiters.' & @LF & 'Let it empty, to align all left.')
If $sAlign = '' Then
For $i = 1 To $iMaxColumn
$sAlign &= '0'
Next
EndIf
Global $aAlignment = StringSplit($sAlign, '', 2)
; == output all to console
Global $sLineOut
For $i = 0 To UBound($aFields) -1
$sLineOut = ''
For $j = 0 To $iMaxColumn -1
If $aFields[$i][$j][0] = '' Then ContinueLoop
$sLineOut &= _GetAligned($aFields[$i][$j][0], $aFields[$i][$j][1], $aAlignment[$j], $aColLen[$j])
Next
ConsoleWrite(StringTrimRight($sLineOut, 1) & @LF)
Next
Func _GetAligned($_sString, $_iLen, $_iAlign, $_iMaxLen)
Local $sSpace = ''
For $i = 1 To $_iMaxLen
$sSpace &= ' '
Next
Switch $_iAlign
Case 0
Return $_sString & StringLeft($sSpace, $_iMaxLen - $_iLen +1)
Case 1
Local $iLenLeft = Int(($_iMaxLen - $_iLen)/2)
Local $iLenRight = $_iMaxLen - $iLenLeft - $_iLen
Return StringLeft($sSpace, $iLenLeft) & $_sString & StringLeft($sSpace, $iLenRight) & ' '
Case 2
Return StringLeft($sSpace, $_iMaxLen - $_iLen) & $_sString & ' '
EndSwitch
EndFunc ;==>_GetAligned
|
http://rosettacode.org/wiki/Active_object | Active object | In object-oriented programming an object is active when its state depends on clock. Usually an active object encapsulates a task that updates the object's state. To the outer world the object looks like a normal object with methods that can be called from outside. Implementation of such methods must have a certain synchronization mechanism with the encapsulated task in order to prevent object's state corruption.
A typical instance of an active object is an animation widget. The widget state changes with the time, while as an object it has all properties of a normal widget.
The task
Implement an active integrator object. The object has an input and output. The input can be set using the method Input. The input is a function of time. The output can be queried using the method Output. The object integrates its input over the time and the result becomes the object's output. So if the input is K(t) and the output is S, the object state S is changed to S + (K(t1) + K(t0)) * (t1 - t0) / 2, i.e. it integrates K using the trapeze method. Initially K is constant 0 and S is 0.
In order to test the object:
set its input to sin (2π f t), where the frequency f=0.5Hz. The phase is irrelevant.
wait 2s
set the input to constant 0
wait 0.5s
Verify that now the object's output is approximately 0 (the sine has the period of 2s). The accuracy of the result will depend on the OS scheduler time slicing and the accuracy of the clock.
| #FreeBASIC | FreeBASIC | #define twopi 6.2831853071795864769252867665590057684
dim shared as double S = 0 'set up the state as a global variable
dim shared as double t0, t1, ta
function sine( x as double, f as double ) as double
return sin(twopi*f*x)
end function
function zero( x as double, f as double ) as double
return 0
end function
sub integrate( K as function(as double, as double) as double, f as double )
'represent input as pointers to functions
t1 = timer
s += (K(t1,f) + K(t0,f))*(t1-t0)/2.0
t0 = t1
end sub
t0 = timer
ta = timer
while timer-ta <= 2.5
if timer-ta <= 2 then integrate( @sine, 0.5 ) else integrate( @zero, 0 )
wend
print S
|
http://rosettacode.org/wiki/Active_object | Active object | In object-oriented programming an object is active when its state depends on clock. Usually an active object encapsulates a task that updates the object's state. To the outer world the object looks like a normal object with methods that can be called from outside. Implementation of such methods must have a certain synchronization mechanism with the encapsulated task in order to prevent object's state corruption.
A typical instance of an active object is an animation widget. The widget state changes with the time, while as an object it has all properties of a normal widget.
The task
Implement an active integrator object. The object has an input and output. The input can be set using the method Input. The input is a function of time. The output can be queried using the method Output. The object integrates its input over the time and the result becomes the object's output. So if the input is K(t) and the output is S, the object state S is changed to S + (K(t1) + K(t0)) * (t1 - t0) / 2, i.e. it integrates K using the trapeze method. Initially K is constant 0 and S is 0.
In order to test the object:
set its input to sin (2π f t), where the frequency f=0.5Hz. The phase is irrelevant.
wait 2s
set the input to constant 0
wait 0.5s
Verify that now the object's output is approximately 0 (the sine has the period of 2s). The accuracy of the result will depend on the OS scheduler time slicing and the accuracy of the clock.
| #Go | Go | package main
import (
"fmt"
"math"
"time"
)
// type for input function, k.
// input is duration since an arbitrary start time t0.
type tFunc func(time.Duration) float64
// active integrator object. state variables are not here, but in
// function aif, started as a goroutine in the constructor.
type aio struct {
iCh chan tFunc // channel for setting input function
oCh chan chan float64 // channel for requesting output
}
// constructor
func newAio() *aio {
var a aio
a.iCh = make(chan tFunc)
a.oCh = make(chan chan float64)
go aif(&a)
return &a
}
// input method required by task description. in practice, this method is
// unnecessary; you would just put that single channel send statement in
// your code wherever you wanted to set the input function.
func (a aio) input(f tFunc) {
a.iCh <- f
}
// output method required by task description. in practice, this method too
// would not likely be best. instead any client interested in the value would
// likely make a return channel sCh once, and then reuse it as needed.
func (a aio) output() float64 {
sCh := make(chan float64)
a.oCh <- sCh
return <-sCh
}
// integration function that returns constant 0
func zeroFunc(time.Duration) float64 { return 0 }
// goroutine serializes access to integrated function k and state variable s
func aif(a *aio) {
var k tFunc = zeroFunc // integration function
s := 0. // "object state" initialized to 0
t0 := time.Now() // initial time
k0 := k(0) // initial sample value
t1 := t0 // t1, k1 used for trapezoid formula
k1 := k0
tk := time.Tick(10 * time.Millisecond) // 10 ms -> 100 Hz
for {
select {
case t2 := <-tk: // timer tick event
k2 := k(t2.Sub(t0)) // new sample value
s += (k1 + k2) * .5 * t2.Sub(t1).Seconds() // trapezoid formula
t1, k1 = t2, k2 // save time and value
case k = <-a.iCh: // input method event: function change
case sCh := <-a.oCh: // output method event: sample object state
sCh <- s
}
}
}
func main() {
a := newAio() // create object
a.input(func(t time.Duration) float64 { // 1. set input to sin function
return math.Sin(t.Seconds() * math.Pi)
})
time.Sleep(2 * time.Second) // 2. sleep 2 sec
a.input(zeroFunc) // 3. set input to zero function
time.Sleep(time.Second / 2) // 4. sleep .5 sec
fmt.Println(a.output()) // output should be near zero
} |
http://rosettacode.org/wiki/Aliquot_sequence_classifications | Aliquot sequence classifications | An aliquot sequence of a positive integer K is defined recursively as the first member
being K and subsequent members being the sum of the Proper divisors of the previous term.
If the terms eventually reach 0 then the series for K is said to terminate.
There are several classifications for non termination:
If the second term is K then all future terms are also K and so the sequence repeats from the first term with period 1 and K is called perfect.
If the third term would be repeating K then the sequence repeats with period 2 and K is called amicable.
If the Nth term would be repeating K for the first time, with N > 3 then the sequence repeats with period N - 1 and K is called sociable.
Perfect, amicable and sociable numbers eventually repeat the original number K; there are other repetitions...
Some K have a sequence that eventually forms a periodic repetition of period 1 but of a number other than K, for example 95 which forms the sequence 95, 25, 6, 6, 6, ... such K are called aspiring.
K that have a sequence that eventually forms a periodic repetition of period >= 2 but of a number other than K, for example 562 which forms the sequence 562, 284, 220, 284, 220, ... such K are called cyclic.
And finally:
Some K form aliquot sequences that are not known to be either terminating or periodic; these K are to be called non-terminating.
For the purposes of this task, K is to be classed as non-terminating if it has not been otherwise classed after generating 16 terms or if any term of the sequence is greater than 2**47 = 140,737,488,355,328.
Task
Create routine(s) to generate the aliquot sequence of a positive integer enough to classify it according to the classifications given above.
Use it to display the classification and sequences of the numbers one to ten inclusive.
Use it to show the classification and sequences of the following integers, in order:
11, 12, 28, 496, 220, 1184, 12496, 1264460, 790, 909, 562, 1064, 1488, and optionally 15355717786080.
Show all output on this page.
Related tasks
Abundant, deficient and perfect number classifications. (Classifications from only the first two members of the whole sequence).
Proper divisors
Amicable pairs
| #Liberty_BASIC | Liberty BASIC |
print "ROSETTA CODE - Aliquot sequence classifications"
[Start]
input "Enter an integer: "; K
K=abs(int(K)): if K=0 then goto [Quit]
call PrintAS K
goto [Start]
[Quit]
print "Program complete."
end
sub PrintAS K
Length=52
dim Aseq(Length)
n=K: class=0
for element=2 to Length
Aseq(element)=PDtotal(n)
print Aseq(element); " ";
select case
case Aseq(element)=0
print " terminating": class=1: exit for
case Aseq(element)=K and element=2
print " perfect": class=2: exit for
case Aseq(element)=K and element=3
print " amicable": class=3: exit for
case Aseq(element)=K and element>3
print " sociable": class=4: exit for
case Aseq(element)<>K and Aseq(element-1)=Aseq(element)
print " aspiring": class=5: exit for
case Aseq(element)<>K and Aseq(element-2)= Aseq(element)
print " cyclic": class=6: exit for
end select
n=Aseq(element)
if n>priorn then priorn=n: inc=inc+1 else inc=0: priorn=0
if inc=11 or n>30000000 then exit for
next element
if class=0 then print " non-terminating"
end sub
function PDtotal(n)
for y=2 to n
if (n mod y)=0 then PDtotal=PDtotal+(n/y)
next
end function
|
http://rosettacode.org/wiki/Add_a_variable_to_a_class_instance_at_runtime | Add a variable to a class instance at runtime | Demonstrate how to dynamically add variables to an object (a class instance) at runtime.
This is useful when the methods/variables of an instance are based on a data file that isn't available until runtime. Hal Fulton gives an example of creating an OO CSV parser at An Exercise in Metaprogramming with Ruby. This is referred to as "monkeypatching" by Pythonistas and some others.
| #Wren | Wren | import "io" for Stdin, Stdout
class Birds {
construct new(userFields) {
_userFields = userFields
}
userFields { _userFields }
}
var userFields = {}
System.print("Enter three fields to add to the Birds class:")
for (i in 0..2) {
System.write("\n name : ")
Stdout.flush()
var name = Stdin.readLine()
System.write(" value: ")
Stdout.flush()
var value = Num.fromString(Stdin.readLine())
userFields[name] = value
}
var birds = Birds.new(userFields)
System.print("\nYour fields are:\n")
for (kv in birds.userFields) {
System.print(" %(kv.key) = %(kv.value)")
} |
http://rosettacode.org/wiki/Add_a_variable_to_a_class_instance_at_runtime | Add a variable to a class instance at runtime | Demonstrate how to dynamically add variables to an object (a class instance) at runtime.
This is useful when the methods/variables of an instance are based on a data file that isn't available until runtime. Hal Fulton gives an example of creating an OO CSV parser at An Exercise in Metaprogramming with Ruby. This is referred to as "monkeypatching" by Pythonistas and some others.
| #XBS | XBS | set Object = {}
Object.Hello = "World";
log(Object.Hello); |
http://rosettacode.org/wiki/Address_of_a_variable | Address of a variable |
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
Task
Demonstrate how to get the address of a variable and how to set the address of a variable.
| #Stata | Stata | a = 1
&a
function f(x) {
return(x+1)
}
&f() |
http://rosettacode.org/wiki/Address_of_a_variable | Address of a variable |
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
Task
Demonstrate how to get the address of a variable and how to set the address of a variable.
| #Swift | Swift |
class MyClass { }
func printAddress<T>(of pointer: UnsafePointer<T>) {
print(pointer)
}
func test() {
var x = 42
var y = 3.14
var z = "foo"
var obj = MyClass()
// Use a pointer to a variable on the stack and print its address.
withUnsafePointer(to: &x) { print($0) }
withUnsafePointer(to: &y) { print($0) }
withUnsafePointer(to: &z) { print($0) }
withUnsafePointer(to: &obj) { print($0) }
// Alternately:
printAddress(of: &x)
printAddress(of: &y)
printAddress(of: &z)
printAddress(of: &obj)
// Printing the address of an object that an object reference points to.
print(Unmanaged.passUnretained(obj).toOpaque())
}
test()
|
http://rosettacode.org/wiki/Address_of_a_variable | Address of a variable |
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
Task
Demonstrate how to get the address of a variable and how to set the address of a variable.
| #Tcl | Tcl | package require critcl
# This code assumes an ILP32 architecture, like classic x86 or VAX.
critcl::cproc peek {int addr} int {
union {
int i;
int *a;
} u;
u.i = addr;
return *u.a;
}
critcl::cproc poke {int addr int value} void {
union {
int i;
int *a;
} u;
u.i = addr;
*u.a = value;
}
package provide poker 1.0 |
http://rosettacode.org/wiki/Address_of_a_variable | Address of a variable |
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
Task
Demonstrate how to get the address of a variable and how to set the address of a variable.
| #Toka | Toka | variable foo
foo .
|
http://rosettacode.org/wiki/AKS_test_for_primes | AKS test for primes | The AKS algorithm for testing whether a number is prime is a polynomial-time algorithm based on an elementary theorem about Pascal triangles.
The theorem on which the test is based can be stated as follows:
a number
p
{\displaystyle p}
is prime if and only if all the coefficients of the polynomial expansion of
(
x
−
1
)
p
−
(
x
p
−
1
)
{\displaystyle (x-1)^{p}-(x^{p}-1)}
are divisible by
p
{\displaystyle p}
.
Example
Using
p
=
3
{\displaystyle p=3}
:
(x-1)^3 - (x^3 - 1)
= (x^3 - 3x^2 + 3x - 1) - (x^3 - 1)
= -3x^2 + 3x
And all the coefficients are divisible by 3, so 3 is prime.
Note:
This task is not the AKS primality test. It is an inefficient exponential time algorithm discovered in the late 1600s and used as an introductory lemma in the AKS derivation.
Task
Create a function/subroutine/method that given
p
{\displaystyle p}
generates the coefficients of the expanded polynomial representation of
(
x
−
1
)
p
{\displaystyle (x-1)^{p}}
.
Use the function to show here the polynomial expansions of
(
x
−
1
)
p
{\displaystyle (x-1)^{p}}
for
p
{\displaystyle p}
in the range 0 to at least 7, inclusive.
Use the previous function in creating another function that when given
p
{\displaystyle p}
returns whether
p
{\displaystyle p}
is prime using the theorem.
Use your test to generate a list of all primes under 35.
As a stretch goal, generate all primes under 50 (needs integers larger than 31-bit).
References
Agrawal-Kayal-Saxena (AKS) primality test (Wikipedia)
Fool-Proof Test for Primes - Numberphile (Video). The accuracy of this video is disputed -- at best it is an oversimplification.
| #Fortran | Fortran |
program aks
implicit none
! Coefficients of polynomial expansion
integer(kind=16), dimension(:), allocatable :: coeffs
integer(kind=16) :: n
! Character variable for I/O
character(len=40) :: tmp
! Point #2
do n = 0, 7
write(tmp, *) n
call polynomial_expansion(n, coeffs)
write(*, fmt='(A)', advance='no') '(x - 1)^'//trim(adjustl(tmp))//' ='
call print_polynom(coeffs)
end do
! Point #4
do n = 2, 35
if (is_prime(n)) write(*, '(I4)', advance='no') n
end do
write(*, *)
! Point #5
do n = 2, 124
if (is_prime(n)) write(*, '(I4)', advance='no') n
end do
write(*, *)
if (allocated(coeffs)) deallocate(coeffs)
contains
! Calculate coefficients of (x - 1)^n using binomial theorem
subroutine polynomial_expansion(n, coeffs)
integer(kind=16), intent(in) :: n
integer(kind=16), dimension(:), allocatable, intent(out) :: coeffs
integer(kind=16) :: i, j
if (allocated(coeffs)) deallocate(coeffs)
allocate(coeffs(n + 1))
do i = 1, n + 1
coeffs(i) = binomial(n, i - 1)*(-1)**(n - i - 1)
end do
end subroutine
! Calculate binomial coefficient using recurrent relation, as calculation
! using factorial overflows too quickly.
function binomial(n, k) result (res)
integer(kind=16), intent(in) :: n, k
integer(kind=16) :: res
integer(kind=16) :: i
if (k == 0) then
res = 1
return
end if
res = 1
do i = 0, k - 1
res = res*(n - i)/(i + 1)
end do
end function
! Outputs polynomial with given coefficients
subroutine print_polynom(coeffs)
integer(kind=16), dimension(:), allocatable, intent(in) :: coeffs
integer(kind=4) :: i, p
character(len=40) :: cbuf, pbuf
logical(kind=1) :: non_zero
if (.not. allocated(coeffs)) return
non_zero = .false.
do i = 1, size(coeffs)
if (coeffs(i) .eq. 0) cycle
p = i - 1
write(cbuf, '(I40)') abs(coeffs(i))
write(pbuf, '(I40)') p
if (non_zero) then
if (coeffs(i) .gt. 0) then
write(*, fmt='(A)', advance='no') ' + '
else
write(*, fmt='(A)', advance='no') ' - '
endif
else
if (coeffs(i) .gt. 0) then
write(*, fmt='(A)', advance='no') ' '
else
write(*, fmt='(A)', advance='no') ' - '
endif
endif
if (p .eq. 0) then
write(*, fmt='(A)', advance='no') trim(adjustl(cbuf))
elseif (p .eq. 1) then
if (coeffs(i) .eq. 1) then
write(*, fmt='(A)', advance='no') 'x'
else
write(*, fmt='(A)', advance='no') trim(adjustl(cbuf))//'x'
end if
else
if (coeffs(i) .eq. 1) then
write(*, fmt='(A)', advance='no') 'x^'//trim(adjustl(pbuf))
else
write(*, fmt='(A)', advance='no') &
trim(adjustl(cbuf))//'x^'//trim(adjustl(pbuf))
end if
end if
non_zero = .true.
end do
write(*, *)
end subroutine
! Test if n is prime using AKS test. Point #3.
function is_prime(n) result (res)
integer(kind=16), intent (in) :: n
logical(kind=1) :: res
integer(kind=16), dimension(:), allocatable :: coeffs
integer(kind=16) :: i
call polynomial_expansion(n, coeffs)
coeffs(1) = coeffs(1) + 1
coeffs(n + 1) = coeffs(n + 1) - 1
res = .true.
do i = 1, n + 1
res = res .and. (mod(coeffs(i), n) == 0)
end do
if (allocated(coeffs)) deallocate(coeffs)
end function
end program aks
|
http://rosettacode.org/wiki/Additive_primes | Additive primes | Definitions
In mathematics, additive primes are prime numbers for which the sum of their decimal digits are also primes.
Task
Write a program to determine (and show here) all additive primes less than 500.
Optionally, show the number of additive primes.
Also see
the OEIS entry: A046704 additive primes.
the prime-numbers entry: additive primes.
the geeks for geeks entry: additive prime number.
the prime-numbers fandom: additive primes.
| #Nim | Nim | import math, strutils
const N = 499
# Sieve of Erathostenes.
var composite: array[2..N, bool] # Initialized to false, ie. prime.
for n in 2..sqrt(N.toFloat).int:
if not composite[n]:
for k in countup(n * n, N, n):
composite[k] = true
func digitSum(n: Positive): Natural =
## Compute sum of digits.
var n = n.int
while n != 0:
result += n mod 10
n = n div 10
echo "Additive primes less than 500:"
var count = 0
for n in 2..N:
if not composite[n] and not composite[digitSum(n)]:
inc count
stdout.write ($n).align(3)
stdout.write if count mod 10 == 0: '\n' else: ' '
echo()
echo "\nNumber of additive primes found: ", count |
http://rosettacode.org/wiki/Additive_primes | Additive primes | Definitions
In mathematics, additive primes are prime numbers for which the sum of their decimal digits are also primes.
Task
Write a program to determine (and show here) all additive primes less than 500.
Optionally, show the number of additive primes.
Also see
the OEIS entry: A046704 additive primes.
the prime-numbers entry: additive primes.
the geeks for geeks entry: additive prime number.
the prime-numbers fandom: additive primes.
| #Pari.2FGP | Pari/GP | hasPrimeDigitsum(n)=isprime(sumdigits(n)); \\ see A028834 in the OEIS
v1 = select(isprime, select(hasPrimeDigitsum, [1..499]));
v2 = select(hasPrimeDigitsum, select(isprime, [1..499]));
v3 = select(hasPrimeDigitsum, primes([1, 499]));
s=0; forprime(p=2,499, if(hasPrimeDigitsum(p), s++)); s;
[#v1, #v2, #v3, s] |
http://rosettacode.org/wiki/Almost_prime | Almost prime | A k-Almost-prime is a natural number
n
{\displaystyle n}
that is the product of
k
{\displaystyle k}
(possibly identical) primes.
Example
1-almost-primes, where
k
=
1
{\displaystyle k=1}
, are the prime numbers themselves.
2-almost-primes, where
k
=
2
{\displaystyle k=2}
, are the semiprimes.
Task
Write a function/method/subroutine/... that generates k-almost primes and use it to create a table here of the first ten members of k-Almost primes for
1
<=
K
<=
5
{\displaystyle 1<=K<=5}
.
Related tasks
Semiprime
Category:Prime Numbers
| #Lua | Lua | -- Returns boolean indicating whether n is k-almost prime
function almostPrime (n, k)
local divisor, count = 2, 0
while count < k + 1 and n ~= 1 do
if n % divisor == 0 then
n = n / divisor
count = count + 1
else
divisor = divisor + 1
end
end
return count == k
end
-- Generates table containing first ten k-almost primes for given k
function kList (k)
local n, kTab = 2^k, {}
while #kTab < 10 do
if almostPrime(n, k) then
table.insert(kTab, n)
end
n = n + 1
end
return kTab
end
-- Main procedure, displays results from five calls to kList()
for k = 1, 5 do
io.write("k=" .. k .. ": ")
for _, v in pairs(kList(k)) do
io.write(v .. ", ")
end
print("...")
end |
http://rosettacode.org/wiki/Anagrams | Anagrams | When two or more words are composed of the same characters, but in a different order, they are called anagrams.
Task[edit]
Using the word list at http://wiki.puzzlers.org/pub/wordlists/unixdict.txt,
find the sets of words that share the same characters that contain the most words in them.
Related tasks
Word plays
Ordered words
Palindrome detection
Semordnilap
Anagrams
Anagrams/Deranged anagrams
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
| #Elena | Elena | import system'routines;
import system'calendar;
import system'io;
import system'collections;
import extensions;
import extensions'routines;
import extensions'text;
extension op
{
string normalized()
= self.toArray().ascendant().summarize(new StringWriter());
}
public program()
{
var start := now;
auto dictionary := new Map<string,object>();
File.assign("unixdict.txt").forEachLine:(word)
{
var key := word.normalized();
var item := dictionary[key];
if (nil == item)
{
item := new ArrayList();
dictionary[key] := item
};
item.append:word
};
dictionary.Values
.sort:(former,later => former.Item2.Length > later.Item2.Length )
.top:20
.forEach:(pair){ console.printLine(pair.Item2) };
var end := now;
var diff := end - start;
console.printLine("Time elapsed in msec:",diff.Milliseconds);
console.readChar()
} |
http://rosettacode.org/wiki/Angle_difference_between_two_bearings | Angle difference between two bearings | Finding the angle between two bearings is often confusing.[1]
Task
Find the angle which is the result of the subtraction b2 - b1, where b1 and b2 are the bearings.
Input bearings are expressed in the range -180 to +180 degrees.
The result is also expressed in the range -180 to +180 degrees.
Compute the angle for the following pairs:
20 degrees (b1) and 45 degrees (b2)
-45 and 45
-85 and 90
-95 and 90
-45 and 125
-45 and 145
29.4803 and -88.6381
-78.3251 and -159.036
Optional extra
Allow the input bearings to be any (finite) value.
Test cases
-70099.74233810938 and 29840.67437876723
-165313.6666297357 and 33693.9894517456
1174.8380510598456 and -154146.66490124757
60175.77306795546 and 42213.07192354373
| #Run_BASIC | Run BASIC | sub getDifference b1, b2
r = (b2 - b1) mod 360
if r >= 180 then r = r - 360
print r
end sub
print "Input in -180 to +180 range:"
call getDifference 20, 45
call getDifference -45, 45
call getDifference -85, 90
call getDifference -95, 90
call getDifference -45, 125
call getDifference -45, 145
call getDifference -45, 125
call getDifference -45, 145
call getDifference 29.4803, -88.6381
call getDifference -78.3251, -159.036
print "Input in wider range:"
call getDifference -70099.74233810938, 29840.67437876723
call getDifference -165313.6666297357, 33693.9894517456
call getDifference 1174.8380510598456, -154146.66490124757 |
http://rosettacode.org/wiki/Angle_difference_between_two_bearings | Angle difference between two bearings | Finding the angle between two bearings is often confusing.[1]
Task
Find the angle which is the result of the subtraction b2 - b1, where b1 and b2 are the bearings.
Input bearings are expressed in the range -180 to +180 degrees.
The result is also expressed in the range -180 to +180 degrees.
Compute the angle for the following pairs:
20 degrees (b1) and 45 degrees (b2)
-45 and 45
-85 and 90
-95 and 90
-45 and 125
-45 and 145
29.4803 and -88.6381
-78.3251 and -159.036
Optional extra
Allow the input bearings to be any (finite) value.
Test cases
-70099.74233810938 and 29840.67437876723
-165313.6666297357 and 33693.9894517456
1174.8380510598456 and -154146.66490124757
60175.77306795546 and 42213.07192354373
| #Rust | Rust |
/// Calculate difference between two bearings, in -180 to 180 degrees range
pub fn angle_difference(bearing1: f64, bearing2: f64) -> f64 {
let diff = (bearing2 - bearing1) % 360.0;
if diff < -180.0 {
360.0 + diff
} else if diff > 180.0 {
-360.0 + diff
} else {
diff
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_angle_difference() {
assert_eq!(25.00, angle_difference(20.00, 45.00));
assert_eq!(90.00, angle_difference(-45.00, 45.00));
assert_eq!(175.00, angle_difference(-85.00, 90.00));
assert_eq!(-175.00, angle_difference(-95.00, 90.00));
assert_eq!(170.00, angle_difference(-45.00, 125.00));
assert_eq!(-170.00, angle_difference(-45.00, 145.00));
approx_eq(-118.1184, angle_difference(29.4803, -88.6381));
approx_eq(-80.7109, angle_difference(-78.3251 , -159.036));
approx_eq(-139.5832, angle_difference(-70099.74233810938, 29840.67437876723));
approx_eq(-72.3439, angle_difference(-165313.6666297357, 33693.9894517456));
approx_eq(-161.5029, angle_difference(1174.8380510598456, -154146.66490124757));
approx_eq(37.2988, angle_difference(60175.77306795546, 42213.07192354373));
}
// approximate equality on floats.
// see also https://crates.io/crates/float-cmp
fn approx_eq(f1: f64, f2: f64) {
assert!((f2-f1).abs() < 0.0001, "{} != {}", f1, f2)
}
}
|
http://rosettacode.org/wiki/Anagrams/Deranged_anagrams | Anagrams/Deranged anagrams | Two or more words are said to be anagrams if they have the same characters, but in a different order.
By analogy with derangements we define a deranged anagram as two words with the same characters, but in which the same character does not appear in the same position in both words.
Task[edit]
Use the word list at unixdict to find and display the longest deranged anagram.
Related tasks
Permutations/Derangements
Best shuffle
Word plays
Ordered words
Palindrome detection
Semordnilap
Anagrams
Anagrams/Deranged anagrams
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
| #Scala | Scala | object DerangedAnagrams {
/** Returns a map of anagrams keyed by the sorted characters */
def groupAnagrams(words: Iterable[String]): Map[String, Set[String]] =
words.foldLeft (Map[String, Set[String]]()) { (map, word) =>
val sorted = word.sorted
val entry = map.getOrElse(sorted, Set.empty)
map + (sorted -> (entry + word))
}
/* Returns true if the pair of strings has no positions with the same
* characters */
def isDeranged(ss: (String, String)): Boolean =
ss._1 zip ss._2 forall { case (c1, c2) => c1 != c2 }
/* Returns pairwise combination of all Strings in the argument Iterable */
def pairWords(as: Iterable[String]): Iterable[(String, String)] =
if (as.size < 2) Seq() else (as.tail map (as.head -> _)) ++ pairWords(as.tail)
/* Returns the contents of the argument URL as an Iterable[String], each
* String is one line in the file */
def readLines(url: String): Iterable[String] =
io.Source.fromURL(url).getLines().toIterable
val wordsURL = "http://www.puzzlers.org/pub/wordlists/unixdict.txt"
def main(args: Array[String]): Unit = {
val anagramMap = groupAnagrams(readLines(wordsURL))
val derangedPairs = anagramMap.values flatMap (pairWords) filter (isDeranged)
val (w1, w2) = derangedPairs maxBy (pair => pair._1.length)
println("Longest deranged pair: "+w1+" and "+w2)
}
} |
http://rosettacode.org/wiki/Anonymous_recursion | Anonymous recursion | While implementing a recursive function, it often happens that we must resort to a separate helper function to handle the actual recursion.
This is usually the case when directly calling the current function would waste too many resources (stack space, execution time), causing unwanted side-effects, and/or the function doesn't have the right arguments and/or return values.
So we end up inventing some silly name like foo2 or foo_helper. I have always found it painful to come up with a proper name, and see some disadvantages:
You have to think up a name, which then pollutes the namespace
Function is created which is called from nowhere else
The program flow in the source code is interrupted
Some languages allow you to embed recursion directly in-place. This might work via a label, a local gosub instruction, or some special keyword.
Anonymous recursion can also be accomplished using the Y combinator.
Task
If possible, demonstrate this by writing the recursive version of the fibonacci function (see Fibonacci sequence) which checks for a negative argument before doing the actual recursion.
| #PicoLisp | PicoLisp | (de fibo (N)
(if (lt0 N)
(quit "Illegal argument" N) )
(recur (N)
(if (> 2 N)
1
(+ (recurse (dec N)) (recurse (- N 2))) ) ) ) |
http://rosettacode.org/wiki/Amicable_pairs | Amicable pairs | Two integers
N
{\displaystyle N}
and
M
{\displaystyle M}
are said to be amicable pairs if
N
≠
M
{\displaystyle N\neq M}
and the sum of the proper divisors of
N
{\displaystyle N}
(
s
u
m
(
p
r
o
p
D
i
v
s
(
N
)
)
{\displaystyle \mathrm {sum} (\mathrm {propDivs} (N))}
)
=
M
{\displaystyle =M}
as well as
s
u
m
(
p
r
o
p
D
i
v
s
(
M
)
)
=
N
{\displaystyle \mathrm {sum} (\mathrm {propDivs} (M))=N}
.
Example
1184 and 1210 are an amicable pair, with proper divisors:
1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592 and
1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605 respectively.
Task
Calculate and show here the Amicable pairs below 20,000; (there are eight).
Related tasks
Proper divisors
Abundant, deficient and perfect number classifications
Aliquot sequence classifications and its amicable classification.
| #Phix | Phix | integer n
for m=1 to 20000 do
n = sum(factors(m,-1))
if m<n and m=sum(factors(n,-1)) then ?{m,n} end if
end for
|
http://rosettacode.org/wiki/Animate_a_pendulum | Animate a pendulum |
One good way of making an animation is by simulating a physical system and illustrating the variables in that system using a dynamically changing graphical display.
The classic such physical system is a simple gravity pendulum.
Task
Create a simple physical model of a pendulum and animate it.
| #Ring | Ring |
# Project : Animate a pendulum
load "guilib.ring"
load "stdlib.ring"
CounterMan = 1
paint = null
pi = 22/7
theta = pi/180*40
g = 9.81
l = 0.50
speed = 0
new qapp
{
win1 = new qwidget() {
setwindowtitle("Animate a pendulum")
setgeometry(100,100,800,600)
label1 = new qlabel(win1) {
setgeometry(10,10,800,600)
settext("")
}
new qpushbutton(win1) {
setgeometry(150,500,100,30)
settext("draw")
setclickevent("draw()")
}
TimerMan = new qtimer(win1)
{
setinterval(1000)
settimeoutevent("draw()")
start()
}
show()
}
exec()
}
func draw
p1 = new qpicture()
color = new qcolor() {
setrgb(0,0,255,255)
}
pen = new qpen() {
setcolor(color)
setwidth(1)
}
paint = new qpainter() {
begin(p1)
setpen(pen)
ptime()
endpaint()
}
label1 { setpicture(p1) show() }
return
func ptime()
TimerMan.start()
pPlaySleep()
sleep(0.1)
CounterMan++
if CounterMan = 20
TimerMan.stop()
ok
func pPlaySleep()
pendulum(theta, l)
pendulum(theta, l)
accel = - g * sin(theta) / l / 100
speed = speed + accel / 100
theta = theta + speed
func pendulum(a, l)
pivotx = 640
pivoty = 800
bobx = pivotx + l * 1000 * sin(a)
boby = pivoty - l * 1000 * cos(a)
paint.drawline(pivotx, pivoty, bobx, boby)
paint.drawellipse(bobx + 24 * sin(a), boby - 24 * cos(a), 24, 24)
|
http://rosettacode.org/wiki/Amb | Amb | Define and give an example of the Amb operator.
The Amb operator (short for "ambiguous") expresses nondeterminism. This doesn't refer to randomness (as in "nondeterministic universe") but is closely related to the term as it is used in automata theory ("non-deterministic finite automaton").
The Amb operator takes a variable number of expressions (or values if that's simpler in the language) and yields a correct one which will satisfy a constraint in some future computation, thereby avoiding failure.
Problems whose solution the Amb operator naturally expresses can be approached with other tools, such as explicit nested iterations over data sets, or with pattern matching. By contrast, the Amb operator appears integrated into the language. Invocations of Amb are not wrapped in any visible loops or other search patterns; they appear to be independent.
Essentially Amb(x, y, z) splits the computation into three possible futures: a future in which the value x is yielded, a future in which the value y is yielded and a future in which the value z is yielded. The future which leads to a successful subsequent computation is chosen. The other "parallel universes" somehow go away. Amb called with no arguments fails.
For simplicity, one of the domain values usable with Amb may denote failure, if that is convenient. For instance, it is convenient if a Boolean false denotes failure, so that Amb(false) fails, and thus constraints can be expressed using Boolean expressions like Amb(x * y == 8) which unless x and y add to four.
A pseudo-code program which satisfies this constraint might look like:
let x = Amb(1, 2, 3)
let y = Amb(7, 6, 4, 5)
Amb(x * y = 8)
print x, y
The output is 2 4 because Amb(1, 2, 3) correctly chooses the future in which x has value 2, Amb(7, 6, 4, 5) chooses 4 and consequently Amb(x * y = 8) produces a success.
Alternatively, failure could be represented using strictly Amb():
unless x * y = 8 do Amb()
Or else Amb could take the form of two operators or functions: one for producing values and one for enforcing constraints:
let x = Ambsel(1, 2, 3)
let y = Ambsel(4, 5, 6)
Ambassert(x * y = 8)
print x, y
where Ambassert behaves like Amb() if the Boolean expression is false, otherwise it allows the future computation to take place, without yielding any value.
The task is to somehow implement Amb, and demonstrate it with a program which chooses one word from each of the following four sets of character strings to generate a four-word sentence:
"the" "that" "a"
"frog" "elephant" "thing"
"walked" "treaded" "grows"
"slowly" "quickly"
The constraint to be satisfied is that the last character of each word (other than the last) is the same as the first character of its successor.
The only successful sentence is "that thing grows slowly"; other combinations do not satisfy the constraint and thus fail.
The goal of this task isn't to simply process the four lists of words with explicit, deterministic program flow such as nested iteration, to trivially demonstrate the correct output. The goal is to implement the Amb operator, or a facsimile thereof that is possible within the language limitations.
| #langur | langur | val .wordsets = [
w/the that a/,
w/frog elephant thing/,
w/walked treaded grows/,
w/slowly quickly/,
]
val .alljoin = f(.words) for[=true] .i of len(.words)-1 {
if last(.words[.i]) != first(.words[.i+1]): break = false
}
# .amb expects 2 or more arguments
val .amb = f(...[2 to -1] .words) if(.alljoin(.words): join " ", .words)
writeln join "\n", where(mapX(.amb, .wordsets...)) |
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