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Implement the Knuth shuffle (aka the Fisher-Yates shuffle) for an integer array (or, if possible, an array of any type). The Knuth shuffle is used to create a random permutation of an array.

set array to {} repeat with i from 1 to n set end of array to i end repeat copy {array, array} to {unshuffled, shuffled} repeat with i from n to 1 by -1 set j to (((random number) * (i - 1)) as integer) + 1 set shuffled's item i to array's item j if j ≠ i's contents then set array's item j to array's item i end repeat

return {unshuffled, shuffled}</lang>Example:<lang AppleScript>{{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25}, {14, 25, 3, 1, 12, 18, 11, 20, 16, 15, 21, 5, 22, 19, 2, 24, 8, 10, 13, 6, 17, 23, 9, 7, 4}}</lang>

AutoHotkey

ahk forum: discussion <lang AutoHotkey>MsgBox % shuffle("1,2,3,4,5,6,7,8,9") MsgBox % shuffle("1,2,3,4,5,6,7,8,9")

shuffle(list) { ; shuffle comma separated list, converted to array

  StringSplit a, list, `,               ; make array (length = a0)
  Loop % a0-1 {
     Random i, A_Index, a0              ; swap item 1,2... with a random item to the right of it
     t := a%i%, a%i% := a%A_Index%, a%A_Index% := t
  }
  Loop % a0                             ; construct string from sorted array
     s .= "," . a%A_Index%
  Return SubStr(s,2)                    ; drop leading comma

}</lang>

BASIC

<lang qbasic>RANDOMIZE TIMER

DIM cards(51) AS INTEGER DIM L0 AS LONG, card AS LONG

PRINT "before:" FOR L0 = 0 TO 51

   cards(L0) = L0
   PRINT LTRIM$(STR$(cards(L0))); " ";

   card = INT(RND * (L0 + 1))
   IF card <> L0 THEN SWAP cards(card), cards(L0)

   PRINT LTRIM$(STR$(cards(L0))); " ";

NEXT PRINT</lang>

Sample output:

before:
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
after:
27 14 37 35 3 44 25 38 46 1 22 49 2 51 16 32 20 30 4 33 36 6 31 21 41 34 9 13 0
50 47 48 40 39 7 18 19 26 24 10 29 5 12 28 11 17 43 45 8 23 42 15

Brat

<lang brat>shuffle = { a |

 (a.length - 1).to 1 { i |
   random_index = random(0, i)
   temp = a[i]
   a[i] = a[random_index]
   a[random_index] = temp
 }

}

p shuffle [1 2 3 4 5 6 7]</lang>

C

This shuffles any "object"; it imitates qsort in the syntax.

<lang c>#include <stdlib.h>

include <string.h>

int rrand(int m) {

 return (int)((double)m * ( rand() / (RAND_MAX+1.0) ));

}

define BYTE(X) ((unsigned char *)(X))

void shuffle(void *obj, size_t nmemb, size_t size) {

 void *temp = malloc(size);
 size_t n = nmemb;
 while ( n > 1 ) {
   size_t k = rrand(n--);
   memcpy(temp, BYTE(obj) + n*size, size);
   memcpy(BYTE(obj) + n*size, BYTE(obj) + k*size, size);
   memcpy(BYTE(obj) + k*size, temp, size);
 }
 free(temp);

} </lang>

C++

Compiler: g++ (version 4.3.2 20081105 (Red Hat 4.3.2-7))

<lang cpp>#include <cstdlib>

include <algorithm>
include <iterator>

template<typename RandomAccessIterator> void knuthShuffle(RandomAccessIterator begin, RandomAccessIterator end) {

 for(unsigned int n = end - begin - 1; n >= 1; --n) {
   unsigned int k = rand() % (n + 1);
   if(k != n) {
     std::iter_swap(begin + k, begin + n);
   }
 }

}</lang>

The standard library provides this in the form of std::random_shuffle.

<lang cpp>#include <algorithm>

include <vector>

int main() {

   int array[] = { 1,2,3,4,5,6,7,8,9 }; // C-ctyle array of integers
   std::vector<int> vec(array, array + 9); // build STL container from int array

   std::random_shuffle(array, array + 9); // shuffle C-style array
   std::random_shuffle(vec.begin(), vec.end()); // shuffle STL container

}</lang>

C#

<lang csharp>public static void KnuthShuffle<T>(T[] array) {

   System.Random random = new System.Random();
   for (int i = 0; i < array.Length; i++)
   {
       int j = random.Next(array.Length);
       T temp = array[i]; array[i] = array[j]; array[j] = temp;
   }

}</lang>

Clojure

<lang lisp>(defn shuffle [vect]

 (reduce (fn [v i] (let [r (rand-int i)]
                     (assoc v i (v r) r (v i)))
         vect (range (dec (count vect)) 1 -1)))</lang>

This works by generating a sequence of end-indices from n-1 to 1, then reducing that sequence (starting with the original vector) through a function that, given a vector and end-index, performs a swap between the end-index and some random index less than the end-index.

Common Lisp

<lang lisp>(defun nshuffle (sequence)

 (loop for i from (length sequence) downto 2
       do (rotatef (elt sequence (random i))
                   (elt sequence (1- i))))
 sequence)</lang>

This operates on arbitrary sequences, but will be inefficient applied to a list as opposed to a vector. Dispatching on type, and using an intermediate vector to hold the contents of list can make both cases more efficient (since the array specific case can use aref rather than elt):

<lang lisp>(defun nshuffle (sequence)

 (etypecase sequence
   (list  (nshuffle-list sequence))
   (array (nshuffle-array sequence))))

(defun nshuffle-list (list)

 "Shuffle the list using an intermediate vector."
 (let ((array (nshuffle-array (coerce list 'vector))))
   (declare (dynamic-extent array))
   (map-into list 'identity array)))

(defun nshuffle-array (array)

 (loop for i from (length array) downto 2
       do (rotatef (aref array (random i))
                   (aref array (1- i)))
       finally (return array)))</lang>

D

This shuffles any collection that supports random access and defines length, the items must be copyable (such template constraints may be added to shuffle): <lang d>import std.stdio, std.algorithm, std.random;

void shuffle(Range)(Range r) {

   foreach_reverse (i; 1 .. r.length)
       swap(r[i], r[uniform(0, i + 1)]);

}

void main() {

   auto a = [1, 2, 3, 4, 5, 6, 7, 8, 9];
   shuffle(a);
   writeln(a);

} </lang> Knuth shuffle variant using the standard library: <lang d>import std.stdio, std.random;

void main() {

   auto a = [1, 2, 3, 4, 5, 6, 7, 8, 9];
   randomShuffle(a);
   writeln(a);

}</lang>

E

<lang e>def shuffle(array, random) {

   for bound in (2..(array.size())).descending() {
       def i := random.nextInt(bound)
       def swapTo := bound - 1
       def t := array[swapTo]
       array[swapTo] := array[i]
       array[i] := t
   }

}</lang>

<lang e>? def arr := [1,2,3,4,5,6,7,8,9,10].diverge()

value: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10].diverge()

? shuffle(arr, entropy) ? arr

value: [4, 5, 2, 9, 7, 8, 1, 3, 6, 10].diverge()</lang>

Factor

There is a randomize word already in the standard library. Implementation: <lang factor>: randomize ( seq -- seq )

   dup length [ dup 1 > ]
   [ [ iota random ] [ 1 - ] bi [ pick exchange ] keep ]
   while drop ;</lang>

Fantom

<lang fantom> class Main {

 static Void knuthShuffle (List array)
 {
   ((array.size-1)..1).each |Int i|
   {
     r := Int.random(0..i)
     array.swap (i, r)
   }
 }

 public static Void main ()
 {
   List a := [1,2,3,4,5]
   knuthShuffle (a)
   echo (a)

   List b := ["apples", "oranges", "pears", "bananas"]
   knuthShuffle (b)
   echo (b)
 }

} </lang>

Forth

<lang forth>include random.fs

shuffle ( deck size -- )

 2 swap do
   dup i random cells +
   over @ over @  swap
   rot  ! over !
   cell+
 -1 +loop drop ;

.array 0 do dup @ . cell+ loop drop ;

create deck 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 ,

deck 10 2dup shuffle .array</lang>

Fortran

Works with: Fortran version 90 and later

<lang fortran>program Knuth_Shuffle

 implicit none

 integer, parameter :: reps = 1000000
 integer :: i, n
 integer, dimension(10) :: a, bins = 0, initial = (/ (n, n=1,10) /)

 do i = 1, reps
   a = initial
	call Shuffle(a)
   where (a == initial) bins = bins + 1  ! skew tester
 end do
 write(*, "(10(i8))") bins

! prints 100382 100007 99783 100231 100507 99921 99941 100270 100290 100442

contains

subroutine Shuffle(a)

 integer, intent(inout) :: a(:)
 integer :: i, randpos, temp
 real :: r

 do i = size(a), 2, -1
   call random_number(r)
   randpos = int(r * i) + 1
   temp = a(randpos)
   a(randpos) = a(i)
   a(i) = temp
 end do

end subroutine Shuffle

end program Knuth_Shuffle</lang>

F#

Allows a shuffle of arrays of arbitrary items. Requires 2010 beta of F#. Lazily returns a sequence.

This is the original Fisher-Yates shuffle as described by the link: <lang fsharp>open System

let FisherYatesShuffle (initialList : array<'a>) = // '

   let availableFlags = Array.init initialList.Length (fun i -> (i, true))
                                                                   // Which items are available and their indices
   let rnd = new Random()  
   let nextItem nLeft =
       let nItem = rnd.Next(0, nLeft)                              // Index out of available items
       let index =                                                 // Index in original deck
           availableFlags                                          // Go through available array
           |> Seq.filter (fun (ndx,f) -> f)                        // and pick out only the available tuples
           |> Seq.nth nItem                                        // Get the one at our chosen index
           |> fst                                                  // and retrieve it's index into the original array
       availableFlags.[index] <- (index, false)                    // Mark that index as unavailable
       initialList.[index]                                         // and return the original item
   seq {(initialList.Length) .. -1 .. 1}                           // Going from the length of the list down to 1
   |> Seq.map (fun i -> nextItem i)                                // yield the next item

</lang> Here's the modified Knuth shuffle which shuffles the original array in place <lang fsharp>let KnuthShuffle (lst : array<'a>) = // '

   let Swap i j =                                                  // Standard swap
       let item = lst.[i]
       lst.[i] <- lst.[j]
       lst.[j] <- item
   let rnd = new Random()
   let ln = lst.Length
   [0..(ln - 2)]                                                   // For all indices except the last
   |> Seq.iter (fun i -> Swap i (rnd.Next(i, ln)))                 // swap th item at the index with a random one following it (or itself)
   lst                                                             // Return the list shuffled in place</lang>

Example: <lang fsharp>> KnuthShuffle [| "Darrell"; "Marvin"; "Doug"; "Greg"; "Sam"; "Ken" |];; val it : string array = [|"Marvin"; "Doug"; "Sam"; "Darrell"; "Ken"; "Greg"|] </lang>

GAP

<lang gap># Return the list L after applying Knuth shuffle. Shuffle := function(L)

 local i, j, n;
 n := Length(L);
 for i in [n, n-1 .. 1] do
   j := Random(1, i);
   x := L[i];
   L[i] := L[j];
   L[j] := x;
 od;
 return L;

end;

Return a Permutation object (a permutation of 1..n).
They are printed in gap, in cycle decomposition form.

PermShuffle := n -> PermListList([1 .. n], Shuffle([1 .. n]));

Shuffle([1..10]);

[ 4, 7, 1, 5, 8, 2, 6, 9, 10, 3 ]

PermShuffle(10);

(1,9)(2,3,6,4,5,10,8,7)

One may also call the built-in random generator on the symmetric group :

Random(SymmetricGroup(10)); (1,8,2,5,9,6)(3,4,10,7)</lang>

Go

<lang go>package main

import (

   "fmt"
   "rand"
   "time"

)

func main() {

   var a [20]int
   for i := range a {
       a[i] = i
   }
   fmt.Println(a)

   rand.Seed(time.Nanoseconds())
   for i := len(a) - 1; i >= 1; i-- {
       j := rand.Intn(i + 1)
       a[i], a[j] = a[j], a[i]
   }
   fmt.Println(a)

}</lang>

Haskell

<lang Haskell>import System.Random import Data.List import Control.Monad import Control.Arrow

mkRands = mapM (randomRIO.(,)0 ). enumFromTo 1. pred

replaceAt :: Int -> a -> [a] -> [a] replaceAt i c = let (a,b) = splitAt i l in a++x:(drop 1 b)

swapElems :: (Int, Int) -> [a] -> [a] swapElems (i,j) xs | i==j = xs

                  | otherwise = replaceAt j (xs!!i) $ replaceAt i (xs!!j) xs

knuthShuffle :: [a] -> IO [a] knuthShuffle xs =

 liftM (foldr swapElems xs. zip [1..]) (mkRands (length xs))</lang>

Examples of use:

*Main> knuthShuffle  ['a'..'k']
"bhjdgfciake"

*Main> knuthShuffle $ map(ap (,)(+10)) [0..9]
[(0,10),(8,18),(2,12),(3,13),(9,19),(4,14),(7,17),(1,11),(6,16),(5,15)]

Function for showing intermediate results: <lang Haskell>knuthShuffleProcess :: (Show a) => [a] -> IO () knuthShuffleProcess =

  (mapM_ print. reverse =<<). ap (fmap. (. zip [1..]). scanr swapElems) (mkRands. length)</lang>

Detailed output example:

*Main> knuthShuffleProcess  ['a'..'k']
"abcdefghijk"
"abckefghijd"
"jbckefghiad"
"jbckeighfad"
"jbckeihgfad"
"jbhkeicgfad"
"jbhiekcgfad"
"jbeihkcgfad"
"ibejhkcgfad"
"iebjhkcgfad"
"iebjhkcgfad"

An imperative implementation using arrays and the ST monad:

<lang haskell>import Data.Array.ST import Data.STRef import Control.Monad import Control.Monad.ST import Control.Arrow import System.Random

shuffle :: RandomGen g => [a] -> g -> ([a], g) shuffle list g = runST $ do

   r <- newSTRef g
   let rand range = liftM (randomR range) (readSTRef r) >>=
           runKleisli (second (Kleisli $ writeSTRef r) >>> arr fst)
   a <- newAry (1, len) list
   forM_ [len, len - 1 .. 2] $ \n -> do
       k <- rand (1, n)
       liftM2 (,) (readArray a k) (readArray a n) >>=
          runKleisli (Kleisli (writeArray a n) *** Kleisli (writeArray a k))
   liftM2 (,) (getElems a) (readSTRef r)
 where len = length list
       newAry :: (Int, Int) -> [a] -> ST s (STArray s Int a)
       newAry = newListArray</lang>

Icon and Unicon

The shuffle method used here can shuffle lists, record fields, and strings:

<lang icon>procedure main()

   show(shuffle([3,1,4,1,5,9,2,6,3]))
   show(shuffle("this is a string"))

end

procedure shuffle(A)

   every A[i := *A to 1 by -1] :=: A[?i]
   return A

end

procedure show(A)

   every writes(!A," ")
   write()

end</lang>

Output:

->ks
9 6 1 4 3 1 3 5 2 
i n   t i s   r t g   h s a i s 
->

Note that the gloriously succinct 'standard' Icon shuffle: <lang icon>procedure shuffle(A)

   every !A :=: ?A

end</lang> is subtly biased.

J

<lang j>KS=:{~ (2&{.@[ {`(|.@[)`]} ])/@(,~(,.?@>:))@i.@#</lang> The input array is transformed to a rectangular array of indexes. By doing this all kinds of arrays can serve as input (see examples below). The process is imitated by using using a fold, swapping elements in a restricted part of this index-array in each fold step. <lang j>proces J

fold swap transform array   <==>  f / g y</lang>

Example of a transformed input: <lang j>(,~(,.?@>:))@i.@# 1+i.6 0 0 0 0 0 0 1 1 0 0 0 0 2 0 0 0 0 0 3 2 0 0 0 0 4 3 0 0 0 0 5 0 0 0 0 0 0 1 2 3 4 5</lang> The last row is the index-array that has to be shuffled. The other rows have valid indexes in the first two columns. The second column has a randomized value <= value first column.

The index-swapping is done by the part: <lang j>2&{.@[ {`(|.@[)`]} ]</lang> Finally, the shuffled indexes select elements from the original array. <lang j>input { ~ shuffled indexes</lang> Alternatively, instead of creating a rectangular array, the swapping indices and the original data can be individually boxed.

In other words, (,~ (,. ?@>:))@i.@# can be replaced with |.@; ;&~./@(,. ?@>:)@i.@#, and the swapping can be achieved using (<@C. >)/ instead of (2&{.@[ {`(|.@[)`]} ])/.

With this approach, the data structure with the swapping indices and the original data could look like this:

<lang j> (|.@; ;&~./@(,. ?@>:)@i.@#)'abcde' +---+-+---+---+-+-----+ |4 2|3|2 1|1 0|0|abcde| +---+-+---+---+-+-----+</lang>

Note that we have the original data here, instead of indices to select all of its items. Note also that we have only a single value in a box where an item is being "swapped" with itself (this is required by J's cycle operation (C.)).

The resulting definition looks like this:

Note that here we did not wind up with a list of indices which we used to permute the original data set. That data set is permuted directly. However, it is in a box and we do have to remove it from that box.

Permuting the data directly, instead of permuting indices, has performance implications when the items being swapped are large, but see the note at the end of this entry for J for how you would do this operation in a "real" J program.

Examples:<lang j>]A=: 5+i.9 5 6 7 8 9 10 11 12 13</lang> Shuffle: <lang j>KS A 13 10 7 5 11 9 8 6 12</lang>Input <lang j>]M=: /:~(1 2 3,:2 3 4),(11 2 3,: 0 11 2),(1 1 1,:1 0),:1 1 1,:1 0 1

1  1 1
1  0 0

1  1 1
1  0 1

1  2 3
2  3 4

11 2 3

0 11 2</lang>Shuffle

<lang j>KS M 11 2 3

0 11 2

1  1 1
1  0 1

1  1 1
1  0 0

1  2 3
2  3 4</lang>Input

<lang j>]L=:'aA';'bbB';'cC%$';'dD@' +--+---+----+---+ |aA|bbB|cC%$|dD@| +--+---+----+---+</lang>Shuffle <lang j>KS L +--+----+---+---+ |aA|cC%$|dD@|bbB| +--+----+---+---+</lang> In J the shuffling of an arbitrary array can easily be implemented by the phrase ( ref http://www.jsoftware.com/jwiki/JPhrases/RandomNumbers ): <lang j>({~?~@#)</lang> Applied on the former examples: <lang j>({~?~@#) A 8 7 13 6 10 11 5 9 12

  ({~?~@#) M
1  1 1
1  0 1

1  2 3
2  3 4

11 2 3

0 11 2

1  1 1
1  0 0

  ({~?~@#) L

+----+---+--+---+ |cC%$|bbB|aA|dD@| +----+---+--+---+</lang>

Java

<lang java>import java.util.Random;

public static final Random gen = new Random();

// version for array of ints public static void shuffle (int[] array) {

   int n = array.length;
   while (n > 1) {
       int k = gen.nextInt(n--); //decrements after using the value
       int temp = array[n];
       array[n] = array[k];
       array[k] = temp;
   }

} // version for array of references public static void shuffle (Object[] array) {

   int n = array.length;
   while (n > 1) {
       int k = gen.nextInt(n--); //decrements after using the value
       Object temp = array[n];
       array[n] = array[k];
       array[k] = temp;
   }

}</lang>

JavaScript

Translation of: Java

<lang javascript>function knuth_shuffle(a) {

   var n = a.length,
       r,
       temp;
   while (n > 1) {
       r = Math.floor(n * Math.random());
       n -= 1;
       temp = a[n];
       a[n] = a[r];
       a[r] = temp;
   }
   return a;

}

var res, i, key;

res = {

   '1,2,3': 0, '1,3,2': 0,
   '2,1,3': 0, '2,3,1': 0,
   '3,1,2': 0, '3,2,1': 0

};

for (i = 0; i < 100000; i++) {

   res[knuth_shuffle([1,2,3]).join(',')] += 1;

} for (key in res) {

   print(key + "\t" + res[key]);

}</lang>

results in:

1,2,3   16619
1,3,2   16614
2,1,3   16752
2,3,1   16959
3,1,2   16460
3,2,1   16596

LabVIEW

Works with: LabVIEW version 8.0 Full Development System

Liberty BASIC

<lang lb>'Declared the UpperBound to prevent confusion with lots of 9's floating around.... UpperBound = 9 Dim array(UpperBound)

For i = 0 To UpperBound

   array(i) = Int(Rnd(1) * 10)
   Print array(i)

Next i

For i = 0 To UpperBound

   'set a random value because we will need to use the same value twice
   randval = Int(Rnd(1) * (UpperBound - i))
   temp1 = array(randval)
   temp2 = array((UpperBound - i))
   array(randval) = temp2
   array((UpperBound - i)) = temp1

Next i

Print For i = 0 To UpperBound

   Print array(i)

Next i</lang>

Logo

<lang logo>to swap :i :j :a

 localmake "t item :i :a
 setitem :i :a item :j :a
 setitem :j :a :t

end to shuffle :a

 for [i [count :a] 2] [swap 1 + random :i :i :a]

end

make "a {1 2 3 4 5 6 7 8 9 10} shuffle :a show :a</lang>

Lua

<lang lua>function table.shuffle(t)

 local n = #t
 while n > 1 do
   local k = math.random(n)
   t[n], t[k] = t[k], t[n]
   n = n - 1
 end

 return t

end math.randomseed( os.time() ) a = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} table.shuffle(a) for i,v in ipairs(a) do print(i,v) end</lang>

M4

<lang M4>divert(-1) define(`randSeed',141592653) define(`rand_t',`eval(randSeed^(randSeed>>13))') define(`random',

  `define(`randSeed',eval((rand_t^(rand_t<<18))&0x7fffffff))randSeed')

define(`for',

  `ifelse($#,0,``$0,
  `ifelse(eval($2<=$3),1,
  `pushdef(`$1',$2)$4`'popdef(`$1')$0(`$1',incr($2),$3,`$4')')')')

define(`set',`define(`$1[$2]',`$3')') define(`get',`defn($1[$2])') define(`new',`set($1,size,0)') define(`deck',

  `new($1)for(`x',1,$2,
        `set(`$1',x,x)')`'set(`$1',size,$2)')

define(`show',

  `for(`x',1,get($1,size),`get($1,x)`'ifelse(x,get($1,size),`',`, ')')')

define(`swap',`set($1,$2,get($1,$4))`'set($1,$4,$3)') define(`shuffle',

  `define(`s',get($1,size))`'for(`x',1,decr(s),
     `swap($1,x,get($1,x),eval(x+random%(s-x+1)))')')

divert

deck(`b',52) show(`b') shuffle(`b') show(`b')</lang>

Output:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23,
24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43,
44, 45, 46, 47, 48, 49, 50, 51, 52

6, 22, 33, 51, 35, 45, 16, 32, 7, 34, 10, 44, 5, 38, 43, 25, 29, 9, 37, 20, 21,
48, 24, 46, 8, 26, 41, 47, 49, 36, 14, 31, 15, 39, 12, 17, 13, 1, 3, 4, 27, 11,
28, 2, 19, 30, 42, 50, 18, 52, 40, 23

Mathematica

Usage of built-in function: <lang Mathematica>RandomSample[{1, 2, 3, 4, 5, 6}]</lang> Custom function: <lang Mathematica>Shuffle[input_List /; Length[input] >= 1] :=

Module[{indices = {}, allindices = Range[Length[input]]},
 Do[
  AppendTo[indices, 
    Complement[allindices, indices][[RandomInteger[{1, i}]]]];
  ,
  {i, Length[input], 1, -1}
  ];
 inputindices
 ]</lang>

Example: <lang Mathematica>Shuffle[{1, 2, 3, 4, 5, 6}]</lang>

MATLAB

Because this shuffle is done using rounds of operations on subsets of decreasing size, this is not an algorithm that can be vectorized using built-in MATLAB functions. So, we have to go old-school, no fancy MATLAB trickery.

<lang MATLAB>function list = knuthShuffle(list)

   for i = (numel(list):-1:2)  
       
       j = floor(i*rand(1) + 1); %Generate random int between 1 and i
       
       %Swap element i with element j.
       list([j i]) = list([i j]);    
   end

end</lang>

There is an alternate way to do this that is not a true Knuth Shuffle, but operates with the same spirit. This alternate version produces the same output, saves some space, and can be implemented in-line without the need to encapsulate it in a function call like the Knuth Shuffle. <lang MATLAB>function list = randSort(list)

   list = list( randperm(numel(list)) );

end</lang>

Modula-3

<lang modula3>MODULE Shuffle EXPORTS Main;

IMPORT IO, Fmt, Random;

VAR a := ARRAY [0..9] OF INTEGER {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};

PROCEDURE Shuffle(VAR a: ARRAY OF INTEGER) =

 VAR temp: INTEGER;
     n: INTEGER := NUMBER(a);

BEGIN

 WITH rand = NEW(Random.Default).init() DO
   WHILE n > 1 DO
     WITH k = rand.integer(0, n - 1) DO
       DEC(n);
       temp := a[n];
       a[n] := a[k];
       a[k] := temp;
     END;
   END;
 END;

END Shuffle;

BEGIN

 Shuffle(a);
 FOR i := FIRST(a) TO LAST(a) DO
   IO.Put(Fmt.Int(a[i]) & " ");
 END;
 IO.Put("\n");

END Shuffle.</lang> Output:

martin@thinkpad:~$ ./shuffle
9 2 7 3 6 8 4 5 1 10 
martin@thinkpad:~$ ./shuffle
1 7 8 10 5 4 6 3 9 2

MUMPS

<lang MUMPS>Shuffle(items,separator) New ii,item,list,n Set list="",n=0 Set ii="" For Set ii=$Order(items(ii)) Quit:ii="" Do . Set n=n+1,list(n)=items(ii),list=list_$Char(n) . Quit For Quit:list="" Do . Set n=$Random($Length(list))+1 . Set item=list($ASCII(list,n)) . Set $Extract(list,n)="" . Write item,separator . Quit Quit CardDeck New card,ii,suite Set ii=0 For suite="Spades","Hearts","Clubs","Diamonds" Do . For card=2:1:10,"Jack","Queen","King","Ace" Do . . Set ii=ii+1,items(ii)=card_" of "_suite . . Quit . Quit Quit

Kill items Set items(91)="Red" Set items(82)="White" Set items(73)="Blue" Set items(64)="Yellow" Set items(55)="Green" Do Shuffle(.items," ") ; Red Yellow White Green Blue Do Shuffle(.items," ") ; Red Blue Yellow White Green Do Shuffle(.items," ") ; Green Blue Yellow White Red

Kill items Do CardDeck,Shuffle(.items,$Char(13,10)) Queen of Hearts 9 of Diamonds 10 of Hearts King of Hearts 7 of Diamonds 9 of Clubs 6 of Diamonds 8 of Diamonds Jack of Spades Ace of Hearts Queen of Diamonds 9 of Hearts 2 of Hearts King of Clubs 10 of Spades 7 of Clubs 6 of Clubs 3 of Diamonds 3 of Spades Queen of Clubs Ace of Spades 4 of Hearts Ace of Diamonds 7 of Spades Ace of Clubs King of Spades 10 of Diamonds Jack of Diamonds 8 of Clubs 4 of Spades Jack of Hearts 10 of Clubs 4 of Diamonds 3 of Hearts 2 of Diamonds 5 of Hearts Jack of Clubs 2 of Clubs 5 of Diamonds 6 of Hearts 4 of Clubs 9 of Spades 3 of Clubs 5 of Spades 6 of Spades 7 of Hearts 8 of Spades 8 of Hearts 2 of Spades Queen of Spades King of Diamonds 5 of Clubs</lang>

OCaml

<lang ocaml>let shuffle arr =

 for n = Array.length arr - 1 downto 1 do
   let k = Random.int (n + 1) in
   let temp = arr.(n) in
   arr.(n) <- arr.(k);
   arr.(k) <- temp
 done</lang>

Oz

<lang oz>declare

 proc {Shuffle Arr}
    Low = {Array.low Arr}
    High = {Array.high Arr}
 in
    for I in High..Low;~1 do

J = Low + {OS.rand} mod (I - Low + 1)

       OldI = Arr.I
    in

Arr.I := Arr.J

       Arr.J := OldI
    end
 end

 X = {Tuple.toArray unit(0 1 2 3 4 5 6 7 8 9)}

in

 {Show {Array.toRecord unit X}}
 {Shuffle X}
 {Show {Array.toRecord unit X}}</lang>

PARI/GP

<lang>FY(v)={

 forstep(n=#v,2,-1,
   my(i=random(n)+1,t=v[i]);
   v[i]=v[n];
   v[n]=t
 );
 v

};

FY(vector(52,i,i))</lang>

Pascal

<lang Pascal>program Knuth;

const

 max = 10;

type

 list = array [1..max] of integer;

procedure shuffle(var a: list); var

 i,k,tmp: integer;

begin

 randomize;
 for i := max downto 2 do begin
    k := random(i) + 1;
    if (a[i] <> a[k]) then begin
      tmp := a[i]; a[i] := a[k]; a[k] := tmp
    end
 end

end;

{ Test and display } var

a: list;
i: integer;

begin

 for i := 1 to max do
   a[i] := i;
 shuffle(a);
 for i := 1 to max do
   write(a[i], ' ');
 writeln

end.</lang>

Sample output:

2 7 10 4 3 5 1 9 6 8

Perl

<lang perl>sub shuffle {

 my @a = @_;
 foreach my $n (1 .. $#a) {
   my $k = int rand $n + 1;
   $k == $n or @a[$k, $n] = @a[$n, $k];
 }
 return @a;

}</lang>

Perl 6

Works with: Rakudo version #21 "Seattle"

<lang perl6>sub shuffle (@a is copy) {

   for 1 ..^ @a -> $n {
       my $k = (0 .. $n).pick;
       $k == $n or @a[$k, $n] = @a[$n, $k];
   }
   return @a;

}</lang> The shuffle is also built into the pick method on lists when you pass it a "whatever" for the number to pick:

<lang perl6>my @deck = @cards.pick(*);</lang>

PHP

<lang php>//The Fisher-Yates original Method function yates_shuffle($arr){ $shuffled = Array(); while($arr){ $rnd = array_rand($arr); $shuffled[] = $arr[$rnd]; array_splice($arr, $rnd, 1); } return $shuffled; }

//The modern Durstenfeld-Knuth algorithm function knuth_shuffle(&$arr){ for($i=count($arr)-1;$i>0;$i--){ $rnd = mt_rand(0,$i); list($arr[$i], $arr[$rnd]) = array($arr[$rnd], $arr[$i]); } }</lang>

PicoLisp

<lang PicoLisp>(de shuffle (Lst)

  (make
     (for (N (length Lst) (gt0 N))
        (setq Lst
           (conc
              (cut (rand 0 (dec 'N)) 'Lst)
              (prog (link (car Lst)) (cdr Lst)) ) ) ) ) )</lang>

PL/I

<lang PL/I> declare T(0:10) fixed binary initial (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11); declare (i, j, temp) fixed binary; do i = lbound(T,1) to hbound(T,1);

  j = min(random() * 12, 11);
  temp = T(j);   T(j) = T(i);   T(i) = temp;

end; </lang>

PowerShell

Works with: PowerShell version 2

<lang powershell>function shuffle ($a) {

   $c = $a.Clone()  # make copy to avoid clobbering $a
   1..($c.Length - 1) | ForEach-Object {
       $i = Get-Random -Minimum $_ -Maximum $c.Length
       $c[$_-1],$c[$i] = $c[$i],$c[$_-1]
       $c[$_-1]  # return newly-shuffled value
   }
   $c[-1]  # last value

}</lang> This yields the values one by one instead of returning the array as a whole, so the rest of the pipeline can work on the values while shuffling is still in progress.

PureBasic

<lang PureBasic>Procedure KnuthShuffle (Array a(1))

 Protected i, size = ArraySize(a())
 For i = 0 To size             
   Swap a(i), a(Random(size)) 
 Next

EndProcedure

Procedure displayArray(Array a(1))

 Protected i, size = ArraySize(a())
 
 For i = 0 To size
   Print(Str(a(i)))
   If i = size
     Continue
   EndIf 
   Print(", ")
 Next
 PrintN("")

EndProcedure

NumElements = 20

Dim b(#NumElements - 1)

Define i For i = 0 To #NumElements - 1

 b(i) = i

 PrintN("Before shuffle:")
 displayArray(b())
 KnuthShuffle(b())
 PrintN("After shuffle:")
 displayArray(b())
 
 Print(#CRLF$ + #CRLF$ + "Press ENTER to exit")
 Input()
 CloseConsole()

EndIf

 </lang>

Sample output:

Before shuffle:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
After shuffle:
12, 2, 10, 4, 17, 7, 9, 14, 5, 1, 0, 16, 3, 11, 8, 18, 15, 13, 19, 6

Python

Python's standard library function random.shuffle uses this algorithm and so should normally be used. The function below is very similar: <lang python>from random import randrange

def knuth_shuffle(x):

   for i in range(len(x)-1, 0, -1):
       j = randrange(i + 1)
       x[i], x[j] = x[j], x[i]

x = list(range(10)) knuth_shuffle(x) print("shuffled:", x)</lang> Sample output

shuffled: [5, 1, 6, 0, 8, 4, 2, 3, 9, 7]

R

See also, the built-in function 'sample'.

Original Fisher-Yates version <lang r>fisheryatesshuffle <- function(n) {

 pool <- seq_len(n)
 a <- c()
 while(length(pool) > 0)
 {
    k <- sample.int(length(pool), 1)
    a <- c(a, pool[k])
    pool <- pool[-k]
 }
 a

}</lang> Knuth variation: <lang r>fisheryatesknuthshuffle <- function(n) {

  a <- seq_len(n)
  while(n >=2)
  {     
     k <- sample.int(n, 1)
     if(k != n)
     {
        temp <- a[k]
        a[k] <- a[n]
        a[n] <- temp
     }
     n <- n - 1
  }
  a

}

Example usage:

fisheryatesshuffle(6) # e.g. 1 3 6 2 4 5 x <- c("foo", "bar", "baz", "quux") x[fisheryatesknuthshuffle(4)] # e.g. "bar" "baz" "quux" "foo"</lang>

REBOL

REBOL [
    Title: "Fisher-Yates"
    Purpose: {Fisher-Yates shuffling algorithm}
]

fisher-yates: func [b [block!] /local n i j k] [
    n: length? b: copy b
    i: n
    while [i > 1] [
        if i <> j: random i [
            error? set/any 'k pick b j
            change/only at b j pick b i
            change/only at b i get/any 'k
        ]
        i: i - 1
    ]
    b
]

REXX

<lang rexx> /*REXX program shuffles a deck of playing cards using the Knuth shuffle.*/

rank='ace duece trey 4 5 6 7 8 9 10 jack queen king' suit='club spade diamond heart' deck.1=' color joker' /*good decks have a color joker,*/ deck.2=' b&w joker' /* and a black & white joker.*/ cards=2 say '------------------ getting a new deck out of the box...'

 do j  =1 for words(suit)
   do k=1 for words(rank)
   cards=cards+1
   deck.cards=right(word(suit,j),7) word(rank,k)
   end
 end

call showDeck 'ace' say '------------------ shuffling' cards "cards..."

 do j=cards by -1 to 1
 rand=random(1,j)
 if rand\==j then do                      /*swap two cards in the deck.*/
                  _=deck.rand
                  deck.rand=deck.j
                  deck.j=_
                  end
 end

call showDeck say '------------------ ready to play schafkopf (take out jokers first).' exit

/*----------------------------------SHOWDECK subroutine-----------------*/ showDeck: parse arg break; say

 do m=1 for cards
 if pos(break,deck.m)\==0 then say         /*easier to read the cards. */
 say 'card' right(m,2) deck.m
 end

say return </lang> Output:

------------------ getting a new deck out of the box...

card  1   color joker
card  2     b&w joker

card  3    club ace
card  4    club duece
card  5    club trey
card  6    club 4
card  7    club 5
card  8    club 6
card  9    club 7
card 10    club 8
card 11    club 9
card 12    club 10
card 13    club jack
card 14    club queen
card 15    club king

card 16   spade ace
card 17   spade duece
card 18   spade trey
card 19   spade 4
card 20   spade 5
card 21   spade 6
card 22   spade 7
card 23   spade 8
card 24   spade 9
card 25   spade 10
card 26   spade jack
card 27   spade queen
card 28   spade king

card 29 diamond ace
card 30 diamond duece
card 31 diamond trey
card 32 diamond 4
card 33 diamond 5
card 34 diamond 6
card 35 diamond 7
card 36 diamond 8
card 37 diamond 9
card 38 diamond 10
card 39 diamond jack
card 40 diamond queen
card 41 diamond king

card 42   heart ace
card 43   heart duece
card 44   heart trey
card 45   heart 4
card 46   heart 5
card 47   heart 6
card 48   heart 7
card 49   heart 8
card 50   heart 9
card 51   heart 10
card 52   heart jack
card 53   heart queen
card 54   heart king

------------------ shuffling 54 cards...

card  1   spade king
card  2   heart ace
card  3 diamond duece
card  4    club 6
card  5 diamond 5
card  6 diamond jack
card  7   spade ace
card  8   heart 4
card  9 diamond queen
card 10    club 5
card 11    club 10
card 12 diamond ace
card 13   heart queen
card 14   heart 9
card 15 diamond 7
card 16    club king
card 17   heart 7
card 18    club 4
card 19    club duece
card 20   spade queen
card 21     b&w joker
card 22 diamond trey
card 23 diamond 4
card 24 diamond 8
card 25    club jack
card 26    club ace
card 27   heart 6
card 28   heart 5
card 29   spade 10
card 30   heart 8
card 31   heart trey
card 32 diamond 6
card 33   spade 6
card 34    club 7
card 35   spade 4
card 36   spade jack
card 37    club trey
card 38    club 9
card 39    club 8
card 40   spade 7
card 41    club queen
card 42   heart king
card 43   spade 9
card 44   spade duece
card 45   heart duece
card 46 diamond 10
card 47 diamond king
card 48   heart 10
card 49 diamond 9
card 50   heart jack
card 51   spade trey
card 52   spade 5
card 53   spade 8
card 54   color joker

------------------ ready to play schafkopf (take out jokers first).

Ruby

Translation of: Tcl

<lang ruby>class Array

 def knuth_shuffle!
   j = length
   i = 0
   while j > 1
     r = i + rand(j)
     self[i], self[r] = self[r], self[i]
     i += 1
     j -= 1
   end
   self
 end

end

r = Hash.new(0) 100_000.times do |i|

 a = [1,2,3].knuth_shuffle!
 r[a] += 1

end

r.keys.sort.each {|a| puts "#{a.inspect} => #{r[a]}"}</lang> results in

[1, 2, 3] => 16572
[1, 3, 2] => 16610
[2, 1, 3] => 16633
[2, 3, 1] => 16714
[3, 1, 2] => 16838
[3, 2, 1] => 16633

More idomatic: <lang ruby>class Array

 def knuth_shuffle!
   (length - 1).downto(1) do |i|
     j = rand(i + 1)
     self[i], self[j] = self[j], self[i]
   end
   self
 end

end</lang>

Scala

<lang Scala>def shuffle[T](a: Array[T]) = {

 for (i <- 1 until a.size reverse) {
   val j = util.Random nextInt (i + 1)
   val t = a(i)
   a(i) = a(j)
   a(j) = t
 }
 a

}</lang>

Scheme

Works with: PLT Scheme

<lang scheme> (define (swap vec i j)

 (let ([tmp (vector-ref vec i)])
   (vector-set! vec i (vector-ref vec j))
   (vector-set! vec j tmp)))

(define (shuffle vec)

 (for ((i (in-range (- (vector-length vec) 1) 0 -1)))
   (let ((r (random i)))
     (swap vec i r)))
 vec)

</lang>

> (shuffle (list->vector (for/list ((i (in-range 0 12))) i)))
#(11 9 7 5 10 6 2 0 1 3 8 4)

Smalltalk

Works with: GNU Smalltalk

<lang smalltalk>"The selector swap:with: is documented, but it seems not

implemented (GNU Smalltalk version 3.0.4); so here it is an implementation"

SequenceableCollection extend [

 swap: i with: j [
   |t|
   t := self at: i.
   self at: i put: (self at: j).
   self at: j put: t.
 ]

].

Object subclass: Shuffler [

 Shuffler class >> Knuth: aSequenceableCollection [
   |n k|
   n := aSequenceableCollection size.
   [ n > 1 ] whileTrue: [
     k := Random between: 1 and: n.
     aSequenceableCollection swap: n with: k.
     n := n - 1
   ]      
 ]

].</lang>

Testing

<lang smalltalk>"Test" |c| c := OrderedCollection new. c addAll: #( 1 2 3 4 5 6 7 8 9 ). Shuffler Knuth: c. c display.</lang>

SNOBOL4

<lang SNOBOL4>* Library for random() -include 'Random.sno'

# String -> array

       define('s2a(str,n)i') :(s2a_end)

s2a s2a = array(n); str = str ' ' sa1 str break(' ') . s2a span(' ') = :s(sa1)f(return) s2a_end

# Array -> string
define('a2s(a)i') :(a2s_end)
a2s a2s = a2s a ' ' :s(a2s)f(return) a2s_end
# Knuth shuffle in-place
define('shuffle(a)alen,n,k,tmp') :(shuffle_end)
shuffle n = alen = prototype(a); sh1 k = convert(random() * alen,'integer') + 1
eq(a<n>,a<k>) :s(sh2) tmp = a<n>; a<n> = a<k>; a<k> = tmp
sh2 n = gt(n,1) n - 1 :s(sh1)
shuffle = a :(return)
shuffle_end
# Test and display
a = s2a('1 2 3 4 5 6 7 8 9 10',10) output = a2s(a) '->' shuffle(a) output = a2s(a)
end</lang>
Sample Output:
1 2 3 4 5 6 7 8 9 10 -> 2 10 4 9 1 5 6 8 7 3
Tcl
<lang tcl>proc knuth_shuffle lst {
set j [llength $lst] for {set i 0} {$j > 1} {incr i;incr j -1} { set r [expr {$i+int(rand()*$j)}] set t [lindex $lst $i] lset lst $i [lindex $lst $r] lset lst $r $t } return $lst
}
% knuth_shuffle {1 2 3 4 5} 2 1 3 5 4 % knuth_shuffle {1 2 3 4 5} 5 2 1 4 3 % knuth_shuffle {tom dick harry peter paul mary} tom paul mary harry peter dick</lang> As a test of skewing (an indicator of a poor implementation) this code was used: <lang tcl>% for {set i 0} {$i<100000} {incr i} {
foreach val [knuth_shuffle {1 2 3 4 5}] pos {pos0 pos1 pos2 pos3 pos4} { incr tots($pos) $val }
} % parray tots tots(pos0) = 300006 tots(pos1) = 300223 tots(pos2) = 299701 tots(pos3) = 299830 tots(pos4) = 300240</lang>
TI-83 BASIC
Input L₁, output L₂.
:"SHUFFLE" :L₁→L₂ :dim(L₂)→A :For(B,1,dim(L₂)-1) :randInt(1,A)→C :L₂(C)→D :L₂(A)→L₂(C) :D→L₂(A) :A-1→A :End :DelVar A :DelVar B :DelVar C :DelVar D :Return
Ursala
This function works on lists of any type and length, including character strings.
<lang Ursala>shuffle = @iNX ~&l->r ^jrX/~&l ~&lK8PrC</lang>
test program: <lang Ursala>#cast %s
example = shuffle 'abcdefghijkl'</lang> output:
'keacfjlbdigh'
VBScript
Implementation
<lang vb> function shuffle( a ) dim i dim r randomize timer for i = lbound( a ) to ubound( a ) r = int( rnd * ( ubound( a ) + 1 ) ) if r <> i then swap a(i), a(r) end if next shuffle = a end function
sub swap( byref a, byref b ) dim tmp tmp = a a = b b = tmp end sub </lang>
Invocation
<lang vb> dim a a = array( 1,2,3,4,5,6,7,8,9) wscript.echo "before: ", join( a, ", " ) shuffle a wscript.echo "after: ", join( a, ", " ) shuffle a wscript.echo "after: ", join( a, ", " ) wscript.echo "--" a = array( now(), "cow", 123, true, sin(1), 16.4 ) wscript.echo "before: ", join( a, ", " ) shuffle a wscript.echo "after: ", join( a, ", " ) shuffle a wscript.echo "after: ", join( a, ", " ) </lang>
Output
before: 1, 2, 3, 4, 5, 6, 7, 8, 9 after: 6, 4, 1, 2, 7, 3, 5, 8, 9 after: 8, 7, 3, 2, 6, 5, 9, 1, 4 -- before: 16/02/2010 5:46:58 PM, cow, 123, True, 0.841470984807897, 16.4 after: True, 16.4, 16/02/2010 5:46:58 PM, 123, cow, 0.841470984807897 after: 16.4, 16/02/2010 5:46:58 PM, 123, 0.841470984807897, True, cow
Vedit macro language
The shuffle routine in Playing Cards shuffles text lines in edit buffer. This example shuffles numeric registers #0 to #19.
The output will be inserted in current edit buffer.
<lang vedit>// Test main
90 = Time_Tick // seed for random number generator

99 = 20 // number of items in the array
IT("Before:") IN for (#100 = 0; #100 < #99; #100++) {
#@100 = #100 Num_Ins(#@100, LEFT+NOCR) IT(" ")
} IN
Call("SHUFFLE_NUMBERS")
IT("After:") IN for (#100 = 0; #100 < #99; #100++) {
Num_Ins(#@100, LEFT+NOCR) IT(" ")
} IN Return
//-------------------------------------------------------------- // Shuffle numeric registers #0 to #nn // #99 = number of registers to shuffle (nn-1) //
SHUFFLE_NUMBERS:
for (#91 = #99-1; #91 > 0; #91--) {
Call("RANDOM") #101 = Return_Value #102 = #@101; #@101 = #@91; #@91 = #102
} Return
//-------------------------------------------------------------- // Generate random numbers in range 0 <= Return_Value < #91 // #90 = Seed (0 to 0x7fffffff) // #91 = Scaling (0 to 0x10000) //
RANDOM:
92 = 0x7fffffff / 48271

93 = 0x7fffffff % 48271

90 = (48271 * (#90 % #92) - #93 * (#90 / #92)) & 0x7fffffff
Return ((#90 & 0xffff) * #91 / 0x10000)</lang>
Output:
Before: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 After: 9 13 8 18 10 1 17 15 0 16 14 19 3 2 7 11 6 4 5 12