Permutations: Difference between revisions

 

=={{header|11l}}==

L

print(a)

I !a.next_permutation()

 

{{out}}

=={{header|360 Assembly}}==

{{trans|Liberty BASIC}}

PERMUTE CSECT

USING PERMUTE,R15 set base register

PG DC CL80' ' buffer

YREGS

{{out}}

<pre style="height:40ex;overflow:scroll">

=={{header|AArch64 Assembly}}==

{{works with|as|Raspberry Pi 3B version Buster 64 bits}}

/* ARM assembly AARCH64 Raspberry PI 3B */

/* program permutation64.s */

.include "../includeARM64.inc"

 

<pre>

Value : +1

</pre>

=={{header|ABAP}}==

lv_number type i,

lt_numbers type table of i.

modify iv_set index lv_perm from lv_temp_2.

modify iv_set index lv_len from lv_temp.

{{out}}

<pre>

 

=={{header|Action!}}==

BYTE i

 

 

RMARGIN=oldRMARGIN ;restore right margin on the screen

{{out}}

[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Permutations.png Screenshot from Atari 8-bit computer]

===The generic package Generic_Perm===

When given N, this package defines the Element and Permutation types and exports procedures to set a permutation P to the first one, and to change P into the next one:

N: positive;

package Generic_Perm is

procedure Set_To_First(P: out Permutation; Is_Last: out Boolean);

procedure Go_To_Next(P: in out Permutation; Is_Last: out Boolean);

 

Here is the implementation of the package:

 

end Go_To_Next;

 

===The procedure Print_Perms===

procedure Print_Perms is

when Constraint_Error

=> TIO.Put_Line ("*** Error: enter one numerical argument n with n >= 1");

 

{{out}}

 

=={{header|Aime}}==

f1(record r, ...)

{

 

0;

{{Out}}

<pre>aime permutations -a Aaa Bb C

{{works with|ALGOL 68G|Any - tested with release [http://sourceforge.net/projects/algol68/files/algol68g/algol68g-2.6 algol68g-2.6].}}

{{wont work with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release [http://sourceforge.net/projects/algol68/files/algol68toc/algol68toc-1.8.8d/algol68toc-1.8-8d.fc9.i386.rpm/download 1.8-8d] - due to extensive use of '''format'''[ted] ''transput''.}}

 

COMMENT REQUIRED BY "prelude_permutations.a68"

);

# -*- coding: utf-8 -*- #

 

# OD #))

<pre>

(1, 22, 333, 44444)

=={{header|Amazing Hopper}}==

{{trans|AWK}}

/* hopper-JAMBO - a flavour of Amazing Hopper! */

 

Set(c), [ leng ] Cput(lista)

Return

{{out}}

<pre>

=={{header|APL}}==

For Dyalog APL(assumes index origin ⎕IO←1):

⍝ Builtin version, takes a vector:

⎕CY'dfns'

dpmat←{1=⍵:,⊂,0 ⋄ (⊃,/)¨(⍳⍵)⌽¨⊂(⊂(!⍵-1)⍴⍵-1),⍨∇⍵-1}

perms2←{↓⍵[1+⍉↑dpmat ≢⍵]}

 

<pre>

 

Recursively, in terms of concatMap and delete:

 

-- permutations :: [a] -> [[a]]

missing value

end if

{{Out}}

<pre>{{"aardvarks", "eat", "ants"}, {"aardvarks", "ants", "eat"},

{{trans|Pseudocode}}

(Fast recursive Heap's algorithm)

--> Heaps's algorithm (Permutation by interchanging pairs)

if n = 1 then

DoPermutations(SourceList, SourceList's length)

--> result (value of Permlist)

 

===Non-recursive===

As a right fold (which turns out to be significantly faster than recurse + delete):

 

-- permutations :: [a] -> [[a]]

{}

end if

{{Out}}

<pre>{{1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {1, 3, 2}, {3, 1, 2}, {3, 2, 1}}</pre>

 

===Recursive again===

 

-- <https://www.cs.princeton.edu/~rs/talks/perms.pdf>

 

on allPermutations(theList)

script o

on prmt(l)

end tell

end repeat

else

end tell

end repeat

end if

end tell

end repeat

set p to p + 6

end prmt

if (o's r < 3) then

else

copy theList to o's workList

end repeat

o's prmt(1)

end if

end allPermutations

 

 

{{output}}

 

=={{header|ARM Assembly}}==

{{works with|as|Raspberry Pi}}

/* ARM assembly Raspberry PI */

/* program permutation.s */

/***************************************************/

.include "../affichage.inc"

<pre>

Value : +1

</pre>

=={{header|Arturo}}==

{{out}}

 

=={{header|AutoHotkey}}==

from the forum topic http://www.autohotkey.com/forum/viewtopic.php?t=77959

StringCaseSense On

 

o := A_LoopField o

return o

{{out}}

<pre style="height:40ex;overflow:scroll">Hello

===Alternate Version===

Alternate version to produce numerical permutations of combinations.

;1..n = range, or delimited list, or string to parse

; to process with a different min index, pass a delimited list, e.g. "0`n1`n2"

. P(n,k-1,opt,delim,str . A_LoopField . delim)

Return s

{{out}}

<pre style="height:40ex;overflow:scroll">---------------------------

permute.ahk

OK

---------------------------</pre>

<pre style="height:40ex;overflow:scroll">---------------------------

permute.ahk

OK

---------------------------</pre>

<pre style="height:40ex;overflow:scroll">---------------------------

permute.ahk

OK

---------------------------</pre>

<pre style="height:40ex;overflow:scroll">---------------------------

permute.ahk

 

=={{header|AWK}}==

# syntax: GAWK -f PERMUTATIONS.AWK [-v sep=x] [word]

#

arr[leng-1] = c

}

<p>sample command:</p>

GAWK -f PERMUTATIONS.AWK Gwen

</pre>

 

{{trans|Liberty BASIC}}

n = 4 : cont = 0

dim a(n)

end if

until i = 0

 

The procedure PROC_NextPermutation() will give the next lexicographic permutation of an integer array.

List%() = 1, 2, 3, 4

FOR perm% = 1 TO 24

last -= 1

ENDWHILE

'''Output:'''

<pre>

4 3 1 2

4 3 2 1

</pre>

 

=={{header|Bracmat}}==

= prefix List result original A Z

. !arg:(?.)

& !result

)

Output:

<pre> (a 2 ] u+z.)

===version 1===

Non-recursive algorithm to generate all permutations. It prints objects in lexicographical order.

#include <stdio.h>

int main (int argc, char *argv[]) {

}

}

 

===version 2===

Non-recursive algorithm to generate all permutations. It prints them from right to left.

 

#include <stdio.h>

}

 

 

===version 3===

See [[wp:Permutation#Systematic_generation_of_all_permutations|lexicographic generation]] of permutations.

#include <stdlib.h>

 

return 0;

}

 

===version 4===

See [[wp:Permutation#Systematic_generation_of_all_permutations|lexicographic generation]] of permutations.

#include <stdlib.h>

 

return 0;

}

 

=={{header|C sharp|C#}}==

Recursive Linq

{{works with|C sharp|C#|7}}

{

public static IEnumerable<IEnumerable<T>> Permutations<T>(this IEnumerable<T> values) where T : IComparable<T>

return values.SelectMany(v => Permutations(values.Where(x => x.CompareTo(v) != 0)), (v, p) => p.Prepend(v));

}

Usage

A recursive Iterator. Runs under C#2 (VS2005), i.e. no `var`, no lambdas,...

{

public static System.Collections.Generic.IEnumerable<T[]> AllFor(T[] array)

}

}

Usage:

{

class Program

}

}

 

 

 

Recursive version

class Permutations

{

}

}

 

Alternate recursive version

 

using System;

class Permutations

}

}

 

=={{header|C++}}==

The C++ standard library provides for this in the form of <code>std::next_permutation</code> and <code>std::prev_permutation</code>.

#include <string>

#include <vector>

 

return 0;

{{out}}

<pre>

In an REPL:

 

user=> (require 'clojure.contrib.combinatorics)

nil

user=> (clojure.contrib.combinatorics/permutations [1 2 3])

 

===Explicit===

Replacing the call to the combinatorics library function by its real implementation.

(defn- iter-perm [v]

(let [len (count v),

(println (permutations [1 2 3]))

 

 

=={{header|CoffeeScript}}==

# removed from it.

arrayExcept = (arr, idx) ->

# Flatten the array before returning it.

This implementation utilises the fact that the permutations of an array could be defined recursively, with the fixed point being the permutations of an empty array.

{{out|Usage}}

1,2,3

1,3,2

2,3,1

3,1,2

 

=={{header|Common Lisp}}==

(if list

(mapcan #'(lambda (x)

'(()))) ; else

 

{{out}}

<pre>((A B Z) (A Z B) (B A Z) (B Z A) (Z A B) (Z B A))</pre>

Lexicographic next permutation:

(declare (type (simple-array * (*)) vec))

(macrolet ((el (i) `(aref vec ,i))

;;; test code

(loop for a = "1234" then (next-perm a #'char<) while a do

Recursive implementation of Heap's algorithm:

(let ((permutations nil))

(labels ((permute (seq k)

(permute seq (1- k)))))))

(permute seq (length seq))

 

=={{header|Crystal}}==

{{out}}

<pre>[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]</pre>

=={{header|Curry}}==

 

insert :: a -> [a] -> [a]

insert x xs = x : xs

permutation [] = []

permutation (x:xs) = insert x $ permutation xs

 

=={{header|D}}==

===Simple Eager version===

Compile with -version=permutations1_main to see the output.

T[][] result;

 

writefln("%(%s\n%)", [1, 2, 3].permutations);

}

{{out}}

<pre>[1, 2, 3]

===Fast Lazy Version===

Compiled with <code>-version=permutations2_main</code> produces its output.

 

struct Permutations(bool doCopy=true, T) if (isMutable!T) {

[B(1), B(2), B(3)].permutations!false.writeln;

}

 

===Standard Version===

import std.stdio, std.algorithm;

 

items.writeln;

while (items.nextPermutation);

 

=={{header|Delphi}}==

 

{$APPTYPE CONSOLE}

if Length(S) > 0 then Writeln(S);

Readln;

{{out}}

<pre>

2341 1342 2143 1243 3124 3214 2314

1324 2134 1234

</pre>

 

(2) Return the next permutation in lexicographic order, or set a flag to indicate there are no more permutations.

The algorithm for (2) is the same as in the Wikipedia article "Permutation".

[Permutations task for Rosetta Code.]

[EDSAC program, Initial Orders 2.]

PF [enter with acc = 0]

[end]

{{out}}

<pre>

 

=={{header|Eiffel}}==

class

APPLICATION

end

 

{{out}}

<pre>

=={{header|Elixir}}==

{{trans|Erlang}}

def permute([]), do: [[]]

def permute(list) do

end

 

 

{{out}}

=={{header|Erlang}}==

Shortest form:

-export([permute/1]).

 

permute([]) -> [[]];

Y-combinator (for shell):

More efficient zipper implementation:

 

-export([permute/1]).

 

prepend(_, [], T, R, Acc) -> zipper(T, R, Acc); % continue in zipper

Demonstration (escript):

{{out}}

<pre>[[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]</pre>

=={{header|Euphoria}}==

{{trans|PureBasic}}

object x

while first < last do

end if

puts(1, s & '\t')

{{out}}

<pre>abcd abdc acbd acdb adbc adcb bacd badc bcad bcda

 

=={{header|F Sharp|F#}}==

let rec insert left x right = seq {

match right with

|> Seq.iter (fun x -> printf "%A\n" x)

0

 

<pre>

 

Translation of Haskell "insertion-based approach" (last version)

let permutations xs =

let rec insert x = function

| head :: tail -> (x :: (head :: tail)) :: (List.map (fun l -> head :: l) (insert x tail))

List.fold (fun s e -> List.collect (insert e) s) [[]] xs

 

=={{header|Factor}}==

 

=={{header|Fortran}}==

 

implicit none

end subroutine generate

 

{{out}}

<pre> 1 2 3

The values need to be "swapped back" after the recursive call.

 

implicit none

integer :: n, i

end if

end subroutine

 

 

Here below is the speed test for a couple of algorithms of permutation. We can add more algorithms into this frame-work. When they work in the same circumstance, we can see which is the fastest one.

 

 

implicit none

 

!=====

 

An example of performance:

Here is an alternate, iterative version in Fortran 77.

{{trans|Ada}}

integer n,i,a

logical nextp

a(j)=t

nextp=.true.

 

=== Ratfor 77 ===

See [[#RATFOR|RATFOR]].

 

=={{header|Frink}}==

Frink's array class has built-in methods <CODE>permute[]</CODE> and <CODE>lexicographicPermute[]</CODE> which permute the elements of an array in reflected Gray code order and lexicographic order respectively.

 

{{out}}

4 3 2 1

</pre>

 

=={{header|GAP}}==

compute the images of 1 .. n by p. As an alternative, List(SymmetricGroup(n)) would yield the permutations as GAP ''Permutation'' objects,

which would probably be more manageable in later computations.

perms(4);

[ [ 1, 2, 3, 4 ], [ 4, 2, 3, 1 ], [ 2, 4, 3, 1 ], [ 3, 2, 4, 1 ], [ 1, 4, 3, 2 ], [ 4, 1, 3, 2 ], [ 2, 1, 3, 4 ],

[ 3, 1, 4, 2 ], [ 1, 3, 4, 2 ], [ 4, 3, 1, 2 ], [ 2, 3, 1, 4 ], [ 3, 4, 1, 2 ], [ 1, 2, 4, 3 ], [ 4, 2, 1, 3 ],

[ 2, 4, 1, 3 ], [ 3, 2, 1, 4 ], [ 1, 4, 2, 3 ], [ 4, 1, 2, 3 ], [ 2, 1, 4, 3 ], [ 3, 1, 2, 4 ], [ 1, 3, 2, 4 ],

GAP has also built-in functions to get permutations

Arrangements([1 .. 4], 4);

# All permutations of 1 .. 4

Here is an implementation using a function to compute next permutation in lexicographic order:

local i, j, k, n, t;

n := Length(a);

[ [ 1, 2, 3 ], [ 1, 3, 2 ],

[ 2, 1, 3 ], [ 2, 3, 1 ],

 

=={{header|Glee}}==

$$ #s monadic: number of elements in s

$$ ,, monadic: expose with space-lf separators

 

'Hello' 123 7.9 '•'=>s;

 

Result:

Hello 123 • 7.9

Hello 7.9 123 •

• 123 7.9 Hello

• 7.9 Hello 123

 

=={{header|GNU make}}==

Recursive on unique elements

 

#delimiter should not occur inside elements

delimiter=;

delimiter_separated_output=$(call permutations,a b c d)

$(info $(delimiter_separated_output))

 

{{out}}

=== recursive ===

 

 

import "fmt"

}

rc(len(s))

{{out}}

<pre>[1 2 3]

=== non-recursive, lexicographical order ===

 

 

import "fmt"

fmt.Println(a)

}

 

{{out}}

=={{header|Groovy}}==

Solution:

Test:

def permutations = makePermutations(list)

assert permutations.size() == (1..<(list.size()+1)).inject(1) { prod, i -> prod*i }

{{out}}

<pre style="height:30ex;overflow:scroll;">[Young, Crosby, Stills, Nash]

 

=={{header|Haskell}}==

 

 

A simple implementation, that assumes elements are unique and support equality:

 

permutations :: Eq a => [a] -> [[a]]

permutations [] = [[]]

 

A slightly more efficient implementation that doesn't have the above restrictions:

permutations [] = [[]]

permutations xs = [ y:zs | (y,ys) <- select xs, zs <- permutations ys]

where select [] = []

 

The above are all selection-based approaches. The following is an insertion-based approach:

permutations = foldr (concatMap . insertEverywhere) [[]]

where insertEverywhere :: a -> [a] -> [[a]]

insertEverywhere x [] = [[x]]

 

A serialized version:

{{Trans|Mathematica}}

 

permutations :: [a] -> [[a]]

 

main :: IO ()

{{Out}}

<pre>[[1,2,3],[2,3,1],[3,1,2],[2,1,3],[1,3,2],[3,2,1]]</pre>

 

=={{header|Icon}} and {{header|Unicon}}==

every p := permute(A) do every writes((!p||" ")|"\n")

end

if *A <= 1 then return A

suspend [(A[1]<->A[i := 1 to *A])] ||| permute(A[2:0])

{{out}}

<pre>->permute Aardvarks eat ants

ants Aardvarks eat

-></pre>

 

=={{header|J}}==

{{out|Example use}}

0 1

1 0

random text some

text some random

 

=={{header|Java}}==

Using the code of Michael Gilleland.

private int[] array;

private int firstNum;

}

 

{{out}}

<pre>

 

Following needs: [[User:Margusmartsepp/Contributions/Java/Utils.java|Utils.java]]

public static void main(String[] args) {

System.out.println(Utils.Permutations(Utils.mRange(1, 3)));

}

{{out}}

<pre>[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]</pre>

 

Copy the following as an HTML file and load in a browser.

<body><pre id="result"></pre>

<script type="text/javascript">

 

perm([1, 2, 'A', 4], []);

 

Alternatively: 'Genuine' js code, assuming no duplicate.

 

function perm(a) {

if (a.length < 2) return [a];

 

console.log(perm(['Aardvarks', 'eat', 'ants']).join("\n"));

 

{{Out}}

Aardvarks,ants,eat

eat,Aardvarks,ants

eat,ants,Aardvarks

ants,Aardvarks,eat

 

====Functional composition====

(Simple version – assuming a unique list of objects comparable by the JS === operator)

 

'use strict';

 

// TEST

return permutations(['Aardvarks', 'eat', 'ants']);

 

{{Out}}

["eat", "Aardvarks", "ants"], ["eat", "ants", "Aardvarks"],

 

===ES6===

Recursively, in terms of concatMap and delete:

'use strict';

 

permutations(['Aardvarks', 'eat', 'ants'])

);

{{Out}}

["eat", "Aardvarks", "ants"], ["eat", "ants", "Aardvarks"],

 

 

Or, without recursion, in terms of concatMap and reduce:

'use strict';

 

permutations([1, 2, 3])

);

{{Out}}

<pre>[[1,2,3],[2,1,3],[2,3,1],[1,3,2],[3,1,2],[3,2,1]]</pre>

=={{header|jq}}==

"permutations" generates a stream of the permutations of the input array.

if length == 0 then []

else

| [.[$i]] + (del(.[$i])|permutations)

end ;

'''Example 1''': list them

[range(0;3)] | permutations

=={{header|Julia}}==

 

julia> perms(l) = isempty(l) ? [l] : [[x; y] for x in l for y in perms(setdiff(l, x))]

 

{{out}}

julia> perms([1,2,3])

6-element Vector{Vector{Int64}}:

[3, 1, 2]

[3, 2, 1]

 

Further support for permutation creation and processing is available in the <tt>Combinatorics.jl</tt> package.

<tt>permutations(v)</tt> creates an iterator over all permutations of <tt>v</tt>. Julia 0.7 and 1.0+ require the line global i inside the for to update the i variable.

using Combinatorics

 

end

println()

 

{{out}}

</pre>

 

# Generate all permutations of size t from an array a with possibly duplicated elements.

collect(Combinatorics.multiset_permutations([1,1,0,0,0],3))

{{out}}

<pre>

=={{header|K}}==

{{trans|J}}

perm 2

(0 1

random text some

text some random

 

Alternative:

perm:{x@m@&n=(#?:)'m:!n#n:#x}

text some random

text random some

 

=={{header|Kotlin}}==

Translation of C# recursive 'insert' solution in Wikipedia article on Permutations:

 

fun <T> permute(input: List<T>): List<List<T>> {

println("There are ${perms.size} permutations of $input, namely:\n")

for (perm in perms) println(perm)

 

{{out}}

[d, c, a, b]

[d, c, b, a]

</pre>

 

=={{header|Lambdatalk}}==

 

{def inject

{lambda {:x :a}

->

[[1,2,3,4],[2,1,3,4],[2,3,1,4],[2,3,4,1],[1,3,2,4],[3,1,2,4],[3,2,1,4],[3,2,4,1],[1,3,4,2],[3,1,4,2],[3,4,1,2],[3,4,2,1],[1,2,4,3],[2,1,4,3],[2,4,1,3],[2,4,3,1],[1,4,2,3],[4,1,2,3],[4,2,1,3],[4,2,3,1],[1,4,3,2],[4,1,3,2],[4,3,1,2],[4,3,2,1]]

 

And this is an illustration of the way lambdatalk builds an interface for javascript functions (the first one is given in this page):

 

1) permutations on sentences

 

321

 

 

=={{header|langur}}==

This follows the Go language non-recursive example, but is not limited to integers, or even to numbers.

 

 

 

val .limit = 10

 

var .ordinals = pseries len .elements

 

var .i, .j

 

.i = .n - 1

.j = .n

for .e in .permute([1, 3.14, 7]) {

writeln .e

 

{{out}}

=={{header|LFE}}==

 

(defun permute

(('())

(<- y (permute (-- l `(,x)))))

(cons x y))))

REPL usage:

> (permute '(1 2 3))

((1 2 3) (1 3 2) (2 1 3) (2 3 1) (3 1 2) (3 2 1))

 

=={{header|Lobster}}==

// Lobster implementation of the (very fast) Go example

// http://rosettacode.org/wiki/Permutations#Go

 

permi(se): print(_)

{{out}}

<pre>

 

=={{header|Logtalk}}==

 

:- public(permutation/2).

select(Head, Tail, Tail2).

 

{{out|Usage example}}

 

[1,2,3]

[3,1,2]

[3,2,1]

 

=={{header|Lua}}==

 

local function permutation(a, n, cb)

if n == 0 then

end

permutation({1,2,3}, 3, callback)

{{out}}

<pre>

</pre>

 

 

-- Iterative version

 

ipermutations(3, 3)

 

<pre>

 

=== fast, iterative with coroutine to use as a generator ===

#!/usr/bin/env luajit

-- Iterative version

print(table.concat(p, " "))

end

 

{{out}}

=={{header|M2000 Interpreter}}==

===All permutations in one module===

Module Checkit {

Global a$

}

Checkit

===Step by step Generator===

Module StepByStep {

Function PermutationStep (a) {

StepByStep

 

{{out}}

<pre style="height:30ex;overflow:scroll">

A peculiarity of this implementation is my use of arithmetic rather than branching to compute Sedgewick’s ‘k’. (I use arithmetic similarly in my Ratfor 77 implementation.)

 

 

# 1-based indexing of a string's characters.

divert`'dnl

permutations(`123')

 

{{out}}

 

=={{header|Maple}}==

[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]

 

combinat:-permute([a,b,c]);

 

An implementation based on Mathematica solution:

 

insert:=(v,a,n)->`if`(n>nops(v),[op(v),a],subsop(n=(a,v[n]),v)):

perm:=s->fold((a,b)->map(u->seq(insert(u,b,k+1),k=0..nops(u)),a),[[]],s):

perm([$1..3]);

 

=={{header|Mathematica}}/{{header|Wolfram Language}}==

===Version from scratch===

 

(***Standard list functions:*)

fold[f_, x_, {}] := x

Table[insert[L, #2, k + 1], {k, 0, Length[L]}]] /@ #1) &, {{}},

S]

 

{{out}}

 

===Built-in version===

{{out}}

<pre>{{1, 2, 3, 4}, {1, 2, 4, 3}, {1, 3, 2, 4}, {1, 3, 4, 2}, {1, 4, 2, 3}, {1, 4, 3, 2}, {2, 1, 3, 4}, {2, 1, 4, 3}, {2, 3, 1, 4}, {2, 3,

 

=={{header|MATLAB}} / {{header|Octave}}==

{{out}}

<pre>4321

 

=={{header|Maxima}}==

n: length(v), i: 0,

for k: n - 1 thru 1 step -1 do (if v[k] < v[k + 1] then (i: k, return())),

[2, 3, 1]

[3, 1, 2]

 

===Builtin version===

(%i1) permutations([1, 2, 3]);

(%o1) {[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]}

 

=={{header|Mercury}}==

:- module permutations2.

:- interface.

nl(!IO),

print(all_permutations2([1,2,3,4]),!IO).

 

{{out}}

sol([[1, 2, 3, 4], [1, 2, 4, 3], [1, 3, 2, 4], [1, 3, 4, 2], [1, 4, 2, 3], [1, 4, 3, 2], [2, 1, 3, 4], [2, 1, 4, 3], [2, 3, 1, 4], [2, 3, 4, 1], [2, 4, 1, 3], [2, 4, 3, 1], [3, 1, 2, 4], [3, 1, 4, 2], [3, 2, 1, 4], [3, 2, 4, 1], [3, 4, 1, 2], [3, 4, 2, 1], [4, 1, 2, 3], [4, 1, 3, 2], [4, 2, 1, 3], [4, 2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]])

sol([[1, 2, 3, 4], [1, 2, 4, 3], [1, 3, 2, 4], [1, 3, 4, 2], [1, 4, 2, 3], [1, 4, 3, 2], [2, 1, 3, 4], [2, 1, 4, 3], [2, 3, 1, 4], [2, 3, 4, 1], [2, 4, 1, 3], [2, 4, 3, 1], [3, 1, 2, 4], [3, 1, 4, 2], [3, 2, 1, 4], [3, 2, 4, 1], [3, 4, 1, 2], [3, 4, 2, 1], [4, 1, 2, 3], [4, 1, 3, 2], [4, 2, 1, 3], [4, 2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]]) 

</pre>

 

=={{header|Modula-2}}==

{{works with|ADW Modula-2 (1.6.291)}}

 

FROM Terminal

IF n > 0 THEN permute(n) END;

(*Wait*)

 

=={{header|Modula-3}}==

This implementation merely prints out the orbit of the list (1, 2, ..., n) under the action of <i>S_n</i>. It shows off Modula-3's built-in <code>Set</code> type and uses the standard <code>IntSeq</code> library module.

 

 

IMPORT IO, IntSeq;

GeneratePermutations(chosen, values);

 

 

{{out}}

Suppose that <code>D</code> is the domain of elements to be permuted. This module requires a <code>DomainSeq</code> (<code>Sequence</code> of <code>D</code>), a <code>DomainSet</code> (<code>Set</code> of <code>D</code>), and a <code>DomainSeqSeq</code> (<code>Sequence</code> of <code>Sequence</code>s of <code>Domain</code>).

 

 

(*

*)

 

 

;implementation

In addition to the interface's specifications, this requires a generic <code>Domain</code>. Some implementations of a set are not safe to iterate over while modifying (e.g., a tree), so this copies the values and iterates over them.

 

 

(*

 

BEGIN

 

;Sample Usage

Here the domain is <code>Integer</code>, but the interface doesn't require that, so we "merely" need <code>IntSeq</code> (a <code>Sequence</code> of <code>Integer</code>), <code>IntSetTree</code> (a set type I use, but you could use <code>SetDef</code> or <code>SetList</code> if you prefer; I've tested it and it works), <code>IntSeqSeq</code> (a <code>Sequence</code> of <code>Sequence</code>s of <code>Integer</code>), and <code>IntPermutations</code>, which is <code>GenericPermutations</code> instantiated for <code>Integer</code>.

 

 

IMPORT IO, IntSeq, IntSetTree, IntSeqSeq, IntPermutations;

END;

 

 

{{out}} (somewhat edited!)

 

=={{header|NetRexx}}==

options replace format comments java crossref symbols nobinary

 

end thing

return

{{out}}

<pre style="height:55ex;overflow:scroll">

 

===Using the standard library===

var v = [1, 2, 3] # List has to start sorted

echo v

while v.nextPermutation():

 

{{out}}

 

===Single yield iterator===

iterator inplacePermutations[T](xs: var seq[T]): var seq[T] =

assert xs.len <= 24, "permutation of array longer than 24 is not supported"

c[i] = int8(t)

i = t

verification

import intsets

from math import fac

# check exactly l! unique number of permutations

assert len(s) == fac(l)

 

===Translation of C===

{{trans|C}}

iterator permutations[T](ys: openarray[T]): seq[T] =

var

 

for i in permutations(x):

Output:

<pre>@[1, 2, 3]

===Translation of Go===

{{trans|Go}}

# http://rosettacode.org/wiki/Permutations#Go

# implementing a recursive https://en.wikipedia.org/wiki/Steinhaus–Johnson–Trotter_algorithm

var se = @[0, 1, 2, 3] #, 4, 5, 6, 7, 8, 9, 10]

 

 

=={{header|OCaml}}==

Translation of Ada version. *)

let next_perm p =

2 3 1

3 1 2

Permutations can also be defined on lists recursively:

let n = List.length l in

if n = 1 then [l] else

let print l = List.iter (Printf.printf " %d") l; print_newline() in

or permutations indexed independently:

let a, b = let c = k/n in c, k-(n*c) in

let e = List.nth l b in

done

 

 

=={{header|ooRexx}}==

Essentially derived fom the program shown under rexx.

This program works also with Regina (and other REXX implementations?)

/* REXX Compute bunch permutations of things elements */

Parse Arg bunch things

Say 'rexx perm 2 4 -> Permutations of 1 2 3 4 in 2 positions'

Say 'rexx perm 2 a b c d -> Permutations of a b c d in 2 positions'

{{out}}

<pre>H:\>rexx perm 2 U V W X

 

=={{header|OpenEdge/Progress}}==

DEFINE VARIABLE charArray AS CHARACTER EXTENT 3 INITIAL ["A","B","C"].

DEFINE VARIABLE sizeofArray AS INTEGER.

charArray[a] = charArray[b].

charArray[b] = temp.

{{out}}

<pre>ABC

 

=={{header|PARI/GP}}==

 

=={{header|Pascal}}==

 

var

next;

until is_last;

===alternative===

a little bit more speed.I take n = 12.

But you have to use the integers [1..n] directly or as Index to your data.

1 to n are in lexicographic order.

{$MODE DELPHI}

{$ELSE}

writeln(permcnt);

writeln(FormatDateTime('HH:NN:SS.zzz',T1-T0));

{{Out}}

{fpc 2.64/3.0 32Bit or 3.1 64 Bit i4330 3.5 Ghz same timings.

===Permutations from integers===

A console application in Free Pascal, created with the Lazarus IDE.

program Permutations;

(*

end;

end.

{{out}}

<pre>

=={{header|Perl}}==

A simple recursive implementation.

my ($perm,@set) = @_;

print "$perm\n" || return unless (@set);

}

my @input = (qw/a b c d/);

{{out}}

<pre>abcd

For better performance, use a module like <code>ntheory</code> or <code>Algorithm::Permute</code>.

{{libheader|ntheory}}

my @tasks = (qw/party sleep study/);

forperm {

print "@tasks[@_]\n";

{{out}}

<pre>

 

=={{header|Phix}}==

<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>

<span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.0.2"</span><span style="color: #0000FF;">)</span>

<span style="color: #0000FF;">?</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">permutes</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"abcd"</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"elements"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)</span>

{{out}}

<pre>

 

=={{header|Phixmonti}}==

 

def save

( ) >ps

( ) ( 1 2 3 4 ) permute

 

=={{header|Picat}}==

===Recursion===

Use <code>findall/2</code> to find all permutations. See example below.

permutation_rec1(Y,W),

select(X,Z,W).

append(L1, L2, H1),

append(L1, [T], X1),

 

===Constraint modelling===

 

<code>permutation_cp_list(L)</code> permutes a list via <code>permutation_cp2/1</code>.

 

% Returns all permutations

% Use the cp approach on a list L.

permutation_cp_list(L) = Perms =>

 

===Tests===

Here is a test of the different approaches, including the two built-ins.

main =>

N = 3,

println(permutation_cp1=permutation_cp1(N)),

println(permutation_cp2=findall(P,permutation_cp2(N,P))),

 

{{out}}

 

=={{header|PicoLisp}}==

 

{{out}}

<pre>-> ((1 2 3) (1 3 2) (2 1 3) (2 3 1) (3 1 2) (3 2 1))</pre>

 

=={{header|PowerShell}}==

function permutation ($array) {

function generate($n, $array, $A) {

}

permutation @('A','B','C')

<b>Output:</b>

<pre>

=={{header|Prolog}}==

Works with SWI-Prolog and library clpfd,

 

permut_clpfd(L, N) :-

L ins 1..N,

all_different(L),

{{out}}

[1,2,3]

[1,3,2]

[3,2,1]

false.

A declarative way of fetching permutations:

% P is a permutation of L

 

permut_Prolog([H | T], NL) :-

select(H, NL, NL1),

{{out}}

[ab,cd,ef]

[ab,ef,cd]

[ef,ab,cd]

[ef,cd,ab]

{{Trans|Curry}}

insert(X, L, [X|L]).

insert(X, [Y|Ys], [Y|L2]) :- insert(X, Ys, L2).

permutation([], []).

permutation([X|Xs], P) :- permutation(Xs, L), insert(X, L, P).

{{Out}}

<pre>

false.

</pre>

 

=={{header|Python}}==

===Standard library function===

{{works with|Python|2.6+}}

for values in itertools.permutations([1,2,3]):

{{out}}

<pre>

The follwing functions start from a list [0 ... n-1] and exchange elements to always have a valid permutation. This is done recursively: first exchange a[0] with all the other elements, then a[1] with a[2] ... a[n-1], etc. thus yielding all permutations.

 

a = list(range(n))

def sub(i):

a[k - 1] = a[k]

a[n - 1] = x

 

These two solutions make use of a generator, and "yield from" introduced in [https://www.python.org/dev/peps/pep-0380/ PEP-380]. They are slightly different: the latter produces permutations in lexicographic order, because the "remaining" part of a (that is, a[i+1:]) is always sorted, whereas the former always reverses the exchange just after the recursive call.

On three elements, the difference can be seen on the last two permutations:

 

(0, 1, 2)

(0, 2, 1)

(1, 2, 0)

(2, 0, 1)

 

=== Iterative implementation ===

Given a permutation, one can easily compute the ''next'' permutation in some order, for example lexicographic order, here. Then to get all permutations, it's enough to start from [0, 1, ... n-1], and store the next permutation until [n-1, n-2, ... 0], which is the last in lexicographic order.

 

n = len(a)

i = n - 1

(1, 2, 0)

(2, 0, 1)

 

=== Implementation using destructive list updates ===

def permutations(xs):

ac = [[]]

 

print(permutations([1,2,3,4]))

 

===Functional :: type-preserving===

 

{{Works with|Python|3.7}}

 

from functools import (reduce)

# MAIN ---

if __name__ == '__main__':

{{Out}}

<pre>[1, 2, 3] -> [[1,2,3],[2,3,1],[3,1,2],[2,1,3],[1,3,2],[3,2,1]]

'abc' -> ['abc','bca','cab','bac','acb','cba']

(1, 2, 3) -> [(1, 2, 3),(2, 3, 1),(3, 1, 2),(2, 1, 3),(1, 3, 2),(3, 2, 1)]</pre>

 

=={{header|Qi}}==

{{trans|Erlang}}

(define insert

L 0 E -> [E|L]

(insert P N H))

(seq 0 (length P))))

 

 

The word ''perms'' solves a more general task; generate permutations of between ''a'' and ''b'' items (inclusive) from the specified nest.

 

 

[ stack ] is perms.max ( --> [ )

' [ 1 2 3 ] permutations echo cr

$ "quack" permutations 60 wrap$

 

'''Output:'''

by stuffing the 0 into each of the 4 possible positions that it could go.

 

 

'''Some aids to reading the code.'''

<code>nested join</code> adds a nest to the end of a nest as its last item.

 

[ [] i rot witheach

[ dup size 1+ times

unrot ] drop ] drop ] ] is perms ( n --> [ )

 

 

{{out}}

=={{header|R}}==

===Iterative version===

n <- length(a)

i <- n

}

unname(e)

 

'''Example'''

 

[,1] [,2] [,3] [,4] [,5] [,6]

[1,] 1 1 2 2 3 3

[2,] 2 3 1 3 1 2

 

===Recursive version===

linsert <- function(x,s) lapply(0:length(s), function(k) append(s,x,k))

 

# permutations of a vector s

permutation <- function(s) lapply(perm(length(s)), function(i) s[i])

 

Output:

[[1]]

[1] "c" "b" "a"

 

[[6]]

 

=={{header|Racket}}==

#lang racket

 

(next-perm (permuter))))))

;; -> (A B C)(A C B)(B A C)(B C A)(C A B)(C B A)

 

=={{header|Raku}}==

{{works with|rakudo|2018.10}}

First, you can just use the built-in method on any list type.

{{out}}

<pre>a b c

 

Here is some generic code that works with any ordered type. To force lexicographic ordering, change <tt>after</tt> to <tt>gt</tt>. To force numeric order, replace it with <tt>&gt;</tt>.

my $j = @a.end - 1;

return Nil if --$j < 0 while @a[$j] after @a[$j+1];

}

 

{{out}}

<pre>a b c

</pre>

Here is another non-recursive implementation, which returns a lazy list. It also works with any type.

my @seq := 1..+@items;

gather for (^[*] @seq) -> $n is copy {

}

}

{{out}}

<pre>(a b c)

(c b a)</pre>

Finally, if you just want zero-based numbers, you can call the built-in function:

{{out}}

<pre>0 1 2

For translation to FORTRAN 77 with the public domain ratfor77 preprocessor.

 

# Robert Sedgewick, 1977. Permutation generation methods. ACM

# Comput. Surv. 9, 2 (June 1977), 137-164.

}

 

 

Here is what the generated FORTRAN 77 code looks like:

implicit none

integer a(1: 3)

endif

23005 continue

 

{{out}}

This program could be simplified quite a bit if the "things" were just restricted to numbers (numerals),

<br>but that would make it specific to numbers and not "things" or objects.

parse arg things bunch inbetweenChars names /*obtain optional arguments from the CL*/

if things=='' | things=="," then things= 3 /*Not specified? Then use the default.*/

@.?= $.q; call .permSet ?+1

end /*q*/

{{out|output|text=&nbsp; when the following was used for input: &nbsp; &nbsp; <tt> 3 &nbsp; 3 </tt>}}

<pre>

 

=={{header|Ring}}==

load "stdlib.ring"

 

last -= 1

end

Output:

<pre>

 

=={{header|Ring}}==

 

Another Solution

 

 

Output:

<pre>

 

=={{header|Ruby}}==

{{out}}

<pre>

[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]

</pre>

 

=={{header|Rust}}==

===Iterative===

Uses Heap's algorithm. An in-place version is possible but is incompatible with <code>Iterator</code>.

Permutations { idxs: (0..size).collect(), swaps: vec![0; size], i: 0 }

}

vec![2, 1, 0],

]);

 

===Recursive===

 

fn permute<T, F: Fn(&[T])>(used: &mut Vec<T>, unused: &mut VecDeque<T>, action: &F) {

let mut queue = (1..4).collect::<VecDeque<_>>();

permute(&mut Vec::new(), &mut queue, &|perm| println!("{:?}", perm));

 

=={{header|SAS}}==

<!-- oh god this code -->

data perm;

n=6;

return;

keep p1-p6;

 

=={{header|Scala}}==

There is a built-in function in the Scala collections library, that is part of the language's standard library. The permutation function is available on any sequential collection. It could be used as follows given a list of numbers:

 

 

{{out}}

The following function returns all the permutations of a list:

 

case Nil => List(Nil)

case xs => {

}

}

 

If you need the unique permutations, use <code>distinct</code> or <code>toSet</code> on either the result or on the input.

=={{header|Scheme}}==

{{trans|Erlang}}

(if (= 0 n)

(cons e l)

(insert p n (car l)))

(seq 0 (length p))))

{{trans|OCaml}}

(define (vector-swap! v i j)

(let ((tmp (vector-ref v i)))

; 1 2 0

; 2 0 1

Completely recursive on lists:

(cond ((null? s) '())

((null? (cdr s)) (list s))

(splice (cons m l) (car r) (cdr r))))))))

 

 

=={{header|Seed7}}==

 

const type: permutations is array array integer;

writeln;

end for;

{{out}}

<pre>

 

=={{header|Shen}}==

(define permute

[] -> []

 

(permute [a b c d])

{{out}}

<pre>

</pre>

For lexical order, make a small change:

(define permute-helper

_ [] -> []

Done [X|Rest] -> (append (prepend-all X (permute (append Done Rest))) (permute-helper (append Done [X]) Rest))

)

 

=={{header|Sidef}}==

===Built-in===

 

===Iterative===

var idx = @^n

 

loop {

 

var p = n-1

}

 

 

===Recursive===

for i in ^set {

__FUNC__(callback, [

], [perm..., set[i]])

}

}

 

{{out}}

<pre>

{{works with|Squeak}}

{{works with|Pharo}}

{{works with|GNU Smalltalk}}

ArrayedCollection extend [

 

[:g |

c map permuteAndDo: [g yield: (c copyFrom: 1 to: c size)]]]

 

Use example:

st> 'Abc' permutations contents

('bcA' 'cbA' 'cAb' 'Acb' 'bAc' 'Abc' )

 

=={{header|Stata}}==

For instance:

 

 

'''Program'''

 

local n=`1'

local r=1

} while (i > 1)

}

 

=={{header|Swift}}==

return heaps(&ar, ar.count)

}

}

 

 

=={{header|Tailspin}}==

This solution seems to be the same as the Kotlin solution. Permutations flow independently without being collected until the end.

templates permutations

when <=1> do [1] !

def alpha: ['ABCD'...];

[ $alpha::length -> permutations -> '$alpha($)...;' ] -> !OUT::write

{{out}}

<pre>

 

If we collect all the permutations of the next size down, we can output permutations in lexical order

templates lexicalPermutations

when <=1> do [1] !

def alpha: ['ABCD'...];

[ $alpha::length -> lexicalPermutations -> '$alpha($)...;' ] -> !OUT::write

{{out}}

<pre>

 

That algorithm can also be written from the bottom up to produce an infinite stream of sets of larger and larger permutations, until we stop

templates lexicalPermutations2

def N: $;

end lexicalPermutations2

 

[ $alpha::length -> lexicalPermutations2 -> '$alpha($)...;' ] -> !OUT::write

{{out}}

<pre>

 

The solutions above create a lot of new arrays at various stages. We can also use mutable state and just emit a copy for each generated solution.

templates perms

templates findPerms

def alpha: ['ABCD'...];

[4 -> perms -> '$alpha($)...;' ] -> !OUT::write

{{out}}

<pre>

=={{header|Tcl}}==

{{tcllib|struct::list}}

 

# Make the sequence of digits to be permuted

struct::list foreachperm p $sequence {

puts $p

Testing with <code>tclsh listPerms.tcl 3</code> produces this output:

<pre>

</pre>

 

 

 

 

 

=={{header|Ursala}}==

In practice there's no need to write this because it's in the standard library.

 

permutations =

~&a, # insert the head at the first position

~&ar&& ~&arh2falrtPXPRD), # if the rest is non-empty, recursively insert at all subsequent positions

test program:

 

{{out}}

<pre><

=={{header|VBA}}==

{{trans|Pascal}}

'Generate, count and print (if printem is not false) all permutations of first n integers

Debug.Print "Number of permutations: "; count

{{out|Sample dialogue}}

<pre>

=={{header|VBScript}}==

A recursive implementation. Arrays can contain anything, I stayed with with simple variables. (Elements could be arrays but then the printing routine should be recursive...)

'permutation ,recursive

a=array("Hello",1,True,3.141592)

next

end sub

Output

<pre>

===Recursive===

{{trans|Kotlin}}

permute = Fn.new { |input|

if (input.count == 1) return [input]

var perms = permute.call(input)

System.print("There are %(perms.count) permutations of %(input), namely:\n")

 

{{out}}

{{libheader|Wren-math}}

Output modified to follow the pattern of the recursive version.

 

var input = [1, 2, 3]

}

System.print("There are %(perms.count) permutations of %(input), namely:\n")

 

{{out}}

===Library based===

{{libheader|Wren-perm}}

 

var a = [1, 2, 3]

System.print(Perm.list(a)) // not lexicographic

System.print()

 

{{out}}

 

=={{header|XPL0}}==

def N=4; \number of objects (letters)

char S0, S1(N);

[S0:= "rose "; \N different objects (letters)

Permute(0); \(space char avoids MSb termination)

 

Output:

=={{header|zkl}}==

Using the solution from task [[Permutations by swapping#zkl]]:

L("rose","roes","reos","eros","erso","reso","rseo","rsoe","sroe","sreo",...)

 

 

zkl: Utils.Helpers.permute(T(1,2,3,4))