Knuth shuffle

The Knuth shuffle (a.k.a. the Fisher-Yates shuffle) is an algorithm for randomly shuffling the elements of an array.

Task

Implement the Knuth shuffle for an integer array (or, if possible, an array of any type).

Specification

Given an array items with indices ranging from 0 to last, the algorithm can be defined as follows (pseudo-code):

       for i from last downto 1 do:
           let j = random integer in range 0  $\leq$  j  $\leq$  i
           swap items[i] with items[j]

Notes

It modifies the input array in-place.
If that is unreasonable in your programming language, you may amend the algorithm to return the shuffled items as a new array instead.
The algorithm can also be amended to iterate from left to right, if that is more convenient.

Test cases

Input array	Possible output arrays
`[]`	`[]`
`[10]`	`[10]`
`[10, 20]`	`[10, 20]` `[20, 10]`
`[10, 20, 30]`	`[10, 20, 30]` `[10, 30, 20]` `[20, 10, 30]` `[20, 30, 10]` `[30, 10, 20]` `[30, 20, 10]`

(These are listed here just for your convenience; no need to demonstrate them on the page.)

Related task

Sattolo cycle

Other tasks related to string operations:

Metrics

Counting

Remove/replace

Anagrams/Derangements/shuffling

Find/Search/Determine

Formatting

Song lyrics/poems/Mad Libs/phrases

Tokenize

Sequences

11l

Translation of: Python

F knuth_shuffle(&x)
   L(i) (x.len - 1 .< 0).step(-1)
      V j = random:(0..i)
      swap(&x[i], &x[j])

V x = Array(0..9)
knuth_shuffle(&x)
print(‘shuffled: ’x)

Output:

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

360 Assembly

Translation of: BBC BASIC

*        Knuth shuffle             02/11/2015
KNUTHSH  CSECT
         USING  KNUTHSH,R15
         LA     R6,1               i=1
LOOPI1   C      R6,=A(CARDS)       do i=1 to cards
         BH     ELOOPI1
         STC    R6,PACK(R6)        pack(i)=i
         LA     R6,1(R6)           i=i+1
         B      LOOPI1
ELOOPI1  LA     R7,CARDS           n=cards
LOOPN    C      R7,=F'2'           do n=cards to 2 by -1
         BL     ELOOPN
         L      R5,RANDSEED        r5=seed
         M      R4,=F'397204094'   r4r5=seed*const
         D      R4,=X'7FFFFFFF'    r5=r5 div (2^31-1)
         ST     R4,RANDSEED        r4=r5 mod (2^31-1); seed=r4
         LR     R5,R4              r5=seed
         LA     R4,0               r4=0
         DR     R4,R7              r5=seed div n; r4=seed mod n
         LA     R9,1(R4)           r2=randint(n)+1 [1:n]
         LA     R4,PACK(R7)        @pack(n)
         LA     R5,PACK(R9)        @pack(nw)
         MVC    TMP,0(R4)          tmp=pack(n)
         MVC    0(1,R4),0(R5)      pack(n)=pack(nw)
         MVC    0(1,R5),TMP        pack(nw)=tmp
         BCTR   R7,0               n=n-1
         B      LOOPN
ELOOPN   LA     R6,1               i=1
         LA     R8,PG              pgi=@pg
LOOPI2   C      R6,=A(CARDS)       do i=1 to cards
         BH     ELOOPI2
         XR     R2,R2              r2=0
         IC     R2,PACK(R6)        pack(i)
         XDECO  R2,XD              edit pack(i)
         MVC    0(3,R8),XD+9       output pack(i)
         LA     R8,3(R8)           pgi=pgi+3
         LA     R6,1(R6)           i=i+1
         B      LOOPI2
ELOOPI2  XPRNT  PG,80              print buffer
         XR     R15,R15            set return code
         BR     R14                return to caller
CARDS    EQU    20                 number of cards
PACK     DS     (CARDS+1)C         pack of cards
TMP      DS     C                  temp for swap
PG       DC     CL80' '            buffer
XD       DS     CL12               to decimal
RANDSEED DC     F'16807'           running seed
         YREGS  
         END    KNUTHSH

Output:

 13 16 10 18 19 14  6 17  2  5  1 15  7 11 12  9  8 20  4  3

Runs on easy6502, which has a random number generated memory-mapped at zero page address $FE that updates after every instruction. Works on any array size up to and including 256 bytes. (The code I wrote here prior to this edit was much faster but only worked on arrays of exactly 256 bytes in size). The reason for this was that constraining a random number generator that can produce any 8-bit value to a subset is tricky, since just "rolling again" if out of range will eventually cause the program to lock up if it can't produce a value in range purely by chance. This method uses a bit mask that shifts right as the loop counter decreases to zero, which means that even when only a few bytes still need to be shuffled, the routine is just as quick as it was at the beginning.

define sysRandom $fe
define tempMask $ff
define range $00
define tempX $01
define tempY $02
define tempRandIndex $03
define temp $04
CreateIdentityTable:
    txa
    sta $0200,x
    sta $1000,x
    inx
    bne CreateIdentityTable
;creates a sorted array from 0-255 starting at addr $1000
;also creates another one at $0200 for our test input

lda #1
sta range

ConstrainRNG:
ldx #255
;max range of RNG
lda range
bne outerloop
jmp end

outerloop:
cpx range
bcc continue	;if X >= range, we need to lower X
pha
  txa
  sta tempX

  lsr
  cmp range
  bcc continue2

  tax
pla
jmp outerloop

continue2:
pla
ldx tempX

continue:
ldy range

KnuthShuffle:
lda sysRandom
and $1000,x	;and with range constrictor
tay

lda $0200,y
sty tempRandIndex
sta temp
ldy range
lda $0200,y
pha
    lda temp
    sta $0200,y
pla
ldy tempRandIndex
sta $0200,y
dec range
jmp ConstrainRNG

end:
brk

AArch64 Assembly

Works with: as version Raspberry Pi 3B version Buster 64 bits

/* ARM assembly AARCH64 Raspberry PI 3B */
/*  program knuthshuffle64.s   */

/*******************************************/
/* Constantes file                         */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly*/
.include "../includeConstantesARM64.inc"
/*********************************/
/* Initialized data              */
/*********************************/
.data
sMessResult:      .asciz "Value  : @ \n"
szCarriageReturn: .asciz "\n"

.align 4
TableNumber:         .quad   1,2,3,4,5,6,7,8,9,10
                     .equ NBELEMENTS, (. - TableNumber) / 8
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConversion:         .skip 30
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main 
main:                                        // entry of program 
    ldr x0,qAdrTableNumber                   // address number table
    mov x1,NBELEMENTS                       // number of élements 
    bl knuthShuffle
    ldr x2,qAdrTableNumber
    mov x3,0
1:                                           // loop display table
    ldr x0,[x2,x3,lsl 3]
    ldr x1,qAdrsZoneConversion               // display value
    bl conversion10S                          // call function
    ldr x0,qAdrsMessResult
    ldr x1,qAdrsZoneConversion 
    bl strInsertAtCharInc
    bl affichageMess                         // display message
    add x3,x3,1
    cmp x3,NBELEMENTS - 1
    ble 1b

    ldr x0,qAdrszCarriageReturn
    bl affichageMess   
    /*    2e shuffle             */
    ldr x0,qAdrTableNumber                   // address number table
    mov x1,NBELEMENTS                        // number of élements 
    bl knuthShuffle
    ldr x2,qAdrTableNumber
    mov x3,0
2:                                           // loop display table
    ldr x0,[x2,x3,lsl 3]
    ldr x1,qAdrsZoneConversion               // display value
    bl conversion10S                         // call function
    ldr x0,qAdrsMessResult
    ldr x1,qAdrsZoneConversion 
    bl strInsertAtCharInc
    bl affichageMess                         // display message
    add x3,x3,1
    cmp x3,NBELEMENTS - 1
    ble 2b

100:                                         // standard end of the program 
    mov x0,0                                 // return code
    mov x8,EXIT                              // request to exit program
    svc 0                                    // perform the system call

qAdrszCarriageReturn:     .quad szCarriageReturn
qAdrsMessResult:          .quad sMessResult
qAdrTableNumber:          .quad TableNumber
qAdrsZoneConversion:      .quad sZoneConversion
/******************************************************************/
/*     Knuth Shuffle                                  */ 
/******************************************************************/
/* x0 contains the address of table */
/* x1 contains the number of elements */
knuthShuffle:
    stp x1,lr,[sp,-16]!         // save  registers
    stp x2,x3,[sp,-16]!         // save  registers
    stp x4,x5,[sp,-16]!         // save  registers
    stp x6,x7,[sp,-16]!         // save  registers
    mov x5,x0                   // save table address
    mov x6,x1                   // save number of elements
    mov x2,0                    // start index
1:
    mov x0,0
    mov x1,x2                   // generate aleas
    bl extRandom
    ldr x3,[x5,x2,lsl 3]        // swap number on the table
    ldr x4,[x5,x0,lsl 3]
    str x4,[x5,x2,lsl 3]
    str x3,[x5,x0,lsl 3]
    add x2,x2,1                 // next number
    cmp x2,x6                   // end ?
    blt 1b                      // no -> loop

100:
    ldp x6,x7,[sp],16           // restaur  2 registers
    ldp x4,x5,[sp],16           // restaur  2 registers
    ldp x2,x3,[sp],16           // restaur  2 registers
    ldp x1,lr,[sp],16           // restaur  2 registers
    ret
/******************************************************************/
/*     random number                                          */ 
/******************************************************************/
/*  x0 contains inferior value */
/*  x1 contains maxi value */
/*  x0 return random number */
extRandom:
    stp x1,lr,[sp,-16]!        // save  registers
    stp x2,x8,[sp,-16]!        // save  registers
    stp x19,x20,[sp,-16]!      // save  registers
    sub sp,sp,16               // reserve 16 octets on stack
    mov x19,x0
    add x20,x1,1
    mov x0,sp                  // store result on stack
    mov x1,8                   // length 8 bytes
    mov x2,0
    mov x8,278                 //  call system Linux 64 bits Urandom
    svc 0
    mov x0,sp                  // load résult on stack
    ldr x0,[x0]
    sub x2,x20,x19             // calculation of the range of values 
    udiv x1,x0,x2              // calculation range modulo
    msub x0,x1,x2,x0
    add  x0,x0,x19             // and add inferior value
100:
    add sp,sp,16               // alignement stack 
    ldp x19,x20,[sp],16        // restaur  2 registers
    ldp x2,x8,[sp],16          // restaur  2 registers
    ldp x1,lr,[sp],16          // restaur  2 registers
    ret                        // return to address lr x30
/********************************************************/
/*        File Include fonctions                        */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"

ACL2

:set-state-ok t

(defun array-swap (name array i j)
   (let ((ai (aref1 name array i))
         (aj (aref1 name array j)))
      (aset1 name
             (aset1 name array j ai)
             i aj)))

(defun shuffle-r (name array m state)
   (if (zp m)
       (mv array state)
       (mv-let (i state)
               (random$ m state)
          (shuffle-r name
                     (array-swap name array i m)
                     (1- m)
                     state))))

(defun shuffle (name array state)
   (shuffle-r name
              array
              (1- (first (dimensions name array)))
              state))

Action!

PROC PrintTable(INT ARRAY tab BYTE size)
  BYTE i

  FOR i=0 TO size-1
  DO
    PrintF("%I ",tab(i))
  OD
  PutE()
RETURN

PROC KnuthShuffle(INT ARRAY tab BYTE size)
  BYTE i,j
  INT tmp

  i=size-1
  WHILE i>0
  DO
    j=Rand(i+1)
    tmp=tab(i)
    tab(i)=tab(j)
    tab(j)=tmp
    i==-1
  OD
RETURN

PROC Main()
  BYTE i,size=[20]
  INT ARRAY tab(size)

  FOR i=0 TO size-1
  DO
    tab(i)=-50+10*i
  OD

  PrintE("Original data:")
  PrintTable(tab,size)
  PutE()

  KnuthShuffle(tab,size)

  PrintE("Shuffled data:")
  PrintTable(tab,size)
RETURN

Output:

Screenshot from Atari 8-bit computer

Original data:
-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

Shuffled data:
0 60 70 90 80 120 10 50 30 -30 -20 110 -50 140 100 -10 -40 40 20 130

Ada

This implementation is a generic shuffle routine, able to shuffle an array of any type.

generic
   type Element_Type is private;
   type Array_Type is array (Positive range <>) of Element_Type;
   
procedure Generic_Shuffle (List : in out Array_Type);

with Ada.Numerics.Discrete_Random;

procedure Generic_Shuffle (List : in out Array_Type) is
   package Discrete_Random is new Ada.Numerics.Discrete_Random(Result_Subtype => Integer);
   use Discrete_Random;
   K : Integer;
   G : Generator;
   T : Element_Type;
begin
   Reset (G);
   for I in reverse List'Range loop
      K := (Random(G) mod I) + 1;
      T := List(I);
      List(I) := List(K);
      List(K) := T;
   end loop;
end Generic_Shuffle;

An example using Generic_Shuffle.

with Ada.Text_IO;
with Generic_Shuffle;

procedure Test_Shuffle is
   
   type Integer_Array is array (Positive range <>) of Integer;

   Integer_List : Integer_Array
     := (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18);
   procedure Integer_Shuffle is new Generic_Shuffle(Element_Type => Integer,
                                                    Array_Type => Integer_Array);
begin

   for I in Integer_List'Range loop
      Ada.Text_IO.Put(Integer'Image(Integer_List(I)));
   end loop;
   Integer_Shuffle(List => Integer_List);
   Ada.Text_IO.New_Line;
   for I in Integer_List'Range loop
      Ada.Text_IO.Put(Integer'Image(Integer_List(I)));
   end loop;
end Test_Shuffle;

Aime

The shuffle function works on any type (the lists are heterogenous).

void
shuffle(list l)
{
    integer i;

    i = ~l;
    if (i) {
        i -= 1;
        while (i) {
            l.spin(i, drand(i));
            i -= 1;
        }
    }
}

ALGOL 68

Works with: ALGOL 68G

PROC between = (INT a, b)INT :
(
  ENTIER (random * ABS (b-a+1) + (a<b|a|b))
);

PROC knuth shuffle = (REF[]INT a)VOID:
(
  FOR i FROM LWB a TO UPB a DO
    INT j = between(LWB a, UPB a);
    INT t = a[i];
    a[i] := a[j];
    a[j] := t
  OD
);

main:(
  [20]INT a;
  FOR i FROM 1 TO 20 DO a[i] := i OD;
  knuth shuffle(a);
  print(a)
)

Amazing Hopper

#include <basico.h>

algoritmo
     
     v={},n=19
     '0,1,2,3,4,5,6,7,8,9,"\t","\v","\v","A","B","C","D","E","F"' enlistar en 'v'
     
     imprimir ("Original:\n[",v,"]\n\n")
     imprimir (rareti( n, #(ceil(rand(n))), n, intercambiar en (v)),\
               "Processed:\n[", v,"]\n" )
terminar

Output:

Original:
[0,1,2,3,4,5,6,7,8,9,	,
                         ,
                          ,A,B,C,D,E,F]

Processed:
[F,B,	,1,9,
             ,2,D,5,6,4,8,C,7,A,
                                ,3,0,E]

AppleScript

Iteration

set n to 25

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}

Example:

{{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}}

Better:

-- Fisher-Yates (aka Durstenfeld, aka Knuth) shuffle.
on shuffle(theList, l, r)
    set listLength to (count theList)
    if (listLength < 2) then return array
    if (l < 0) then set l to listLength + l + 1
    if (r < 0) then set r to listLength + r + 1
    if (l > r) then set {l, r} to {r, l}
    script o
        property lst : theList
    end script
    
    repeat with i from l to (r - 1)
        set j to (random number from i to r)
        set v to o's lst's item i
        set o's lst's item i to o's lst's item j
        set o's lst's item j to v
    end repeat
    
    return theList
end shuffle

local array
set array to {"Alpha", "Bravo", "Charlie", "Delta", "Echo", "Foxtrot", "Golf", "Hotel", "India", "Juliett", "Kilo", "Lima", "Mike"}
-- Shuffle all items (1 thru -1).
shuffle(array, 1, -1)

Output:

eg.

{"Golf", "Foxtrot", "Echo", "Delta", "Kilo", "Charlie", "Mike", "Alpha", "Lima", "Juliett", "India", "Bravo", "Hotel"}

When a large number of random indices is required, it can actually be faster to create a list of integers and select from these using AppleScript's 'some' specifier than to call the StandardAdditions' 'random number' function repeatedly. But a better solution since Mac OS X 10.11 is to use the system's GameplayKit framework:

use AppleScript version "2.5" -- OS X 10.11 (El Capitan) or later
use framework "Foundation"
use framework "GameplayKit"

on shuffle(theList, l, r)
    set listLength to (count theList)
    if (listLength < 2) then return theList
    if (l < 0) then set l to listLength + l + 1
    if (r < 0) then set r to listLength + r + 1
    if (l > r) then set {l, r} to {r, l}
    script o
        property lst : theList
    end script
    
    set rndGenerator to current application's class "GKRandomDistribution"'s distributionWithLowestValue:(l) highestValue:(r)
    repeat with i from r to (l + 1) by -1
        set j to (rndGenerator's nextIntWithUpperBound:(i))
        set v to o's lst's item i
        set o's lst's item i to o's lst's item j
        set o's lst's item j to v
    end repeat
    
    return theList
end shuffle

Functional composition

-- KNUTH SHUFFLE -------------------------------------------------------------

-- knuthShuffle :: [a] -> [a]
on knuthShuffle(xs)
    
    -- randomSwap :: [Int] -> Int -> [Int]
    script randomSwap
        on |λ|(a, i)
            if i > 1 then
                set iRand to random number from 1 to i
                tell a
                    set tmp to item iRand
                    set item iRand to item i
                    set item i to tmp
                    it
                end tell
            else
                a
            end if
        end |λ|
    end script
    
    foldr(randomSwap, xs, enumFromTo(1, length of xs))
end knuthShuffle


-- TEST ----------------------------------------------------------------------
on run
    knuthShuffle(["alpha", "beta", "gamma", "delta", "epsilon", ¬
        "zeta", "eta", "theta", "iota", "kappa", "lambda", "mu"])
end run


-- GENERIC FUNCTIONS ---------------------------------------------------------

-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
    if m > n then
        set d to -1
    else
        set d to 1
    end if
    set lst to {}
    repeat with i from m to n by d
        set end of lst to i
    end repeat
    return lst
end enumFromTo

-- foldr :: (a -> b -> a) -> a -> [b] -> a
on foldr(f, startValue, xs)
    tell mReturn(f)
        set v to startValue
        set lng to length of xs
        repeat with i from lng to 1 by -1
            set v to |λ|(v, item i of xs, i, xs)
        end repeat
        return v
    end tell
end foldr

-- Lift 2nd class handler function into 1st class script wrapper 
-- mReturn :: Handler -> Script
on mReturn(f)
    if class of f is script then
        f
    else
        script
            property |λ| : f
        end script
    end if
end mReturn

Output:

e.g.

{"mu", "theta", "alpha", "delta", "zeta", "gamma", 
"iota", "kappa", "lambda", "epsilon", "beta", "eta"}

ARM Assembly

Works with: as version Raspberry Pi

/* ARM assembly Raspberry PI  */
/*  program knuthShuffle.s   */

/************************************/
/* Constantes                       */
/************************************/
.equ STDOUT, 1     @ Linux output console
.equ EXIT,   1     @ Linux syscall
.equ WRITE,  4     @ Linux syscall
/*********************************/
/* Initialized data              */
/*********************************/
.data
sMessResult:      .ascii "Value  : "
sMessValeur:       .fill 11, 1, ' '            @ size => 11
szCarriageReturn: .asciz "\n"

.align 4
iGraine:  .int 123456
.equ NBELEMENTS,      10
TableNumber:	     .int   1,2,3,4,5,6,7,8,9,10

/*********************************/
/* UnInitialized data            */
/*********************************/
.bss  
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main 
main:                                           @ entry of program 
    ldr r0,iAdrTableNumber                      @ address number table
    mov r1,#NBELEMENTS                          @ number of élements 
    bl knuthShuffle
    ldr r2,iAdrTableNumber
    mov r3,#0
1:                                              @ loop display table
    ldr r0,[r2,r3,lsl #2]
    ldr r1,iAdrsMessValeur                      @ display value
    bl conversion10                             @ call function
    ldr r0,iAdrsMessResult
    bl affichageMess                            @ display message
    add r3,#1
    cmp r3,#NBELEMENTS - 1
    ble 1b

    ldr r0,iAdrszCarriageReturn
    bl affichageMess   
    /*    2e shuffle             */
    ldr r0,iAdrTableNumber                     @ address number table
    mov r1,#NBELEMENTS                         @ number of élements 
    bl knuthShuffle
    ldr r2,iAdrTableNumber
    mov r3,#0
2:                                             @ loop display table
    ldr r0,[r2,r3,lsl #2]
    ldr r1,iAdrsMessValeur                     @ display value
    bl conversion10                            @ call function
    ldr r0,iAdrsMessResult
    bl affichageMess                           @ display message
    add r3,#1
    cmp r3,#NBELEMENTS - 1
    ble 2b

100:                                            @ standard end of the program 
    mov r0, #0                                  @ return code
    mov r7, #EXIT                               @ request to exit program
    svc #0                                      @ perform the system call

iAdrsMessValeur:          .int sMessValeur
iAdrszCarriageReturn:     .int szCarriageReturn
iAdrsMessResult:          .int sMessResult
iAdrTableNumber:          .int TableNumber

/******************************************************************/
/*     Knuth Shuffle                                             */ 
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the number of elements */
knuthShuffle:
    push {r2-r5,lr}                                    @ save registers
    mov r5,r0                                          @ save table address
    mov r2,#0                                          @ start index
1:
    mov r0,r2                                          @ generate aleas
    bl genereraleas
    ldr r3,[r5,r2,lsl #2]                              @ swap number on the table
    ldr r4,[r5,r0,lsl #2]
    str r4,[r5,r2,lsl #2]
    str r3,[r5,r0,lsl #2]
    add r2,#1                                           @ next number
    cmp r2,r1                                           @ end ?
    blt 1b                                              @ no -> loop

100:
    pop {r2-r5,lr}
    bx lr                                               @ return 

/******************************************************************/
/*     display text with size calculation                         */ 
/******************************************************************/
/* r0 contains the address of the message */
affichageMess:
    push {r0,r1,r2,r7,lr}                          @ save  registres
    mov r2,#0                                      @ counter length 
1:                                                 @ loop length calculation 
    ldrb r1,[r0,r2]                                @ read octet start position + index 
    cmp r1,#0                                      @ if 0 its over 
    addne r2,r2,#1                                 @ else add 1 in the length 
    bne 1b                                         @ and loop 
                                                   @ so here r2 contains the length of the message 
    mov r1,r0                                      @ address message in r1 
    mov r0,#STDOUT                                 @ code to write to the standard output Linux 
    mov r7, #WRITE                                 @ code call system "write" 
    svc #0                                         @ call systeme 
    pop {r0,r1,r2,r7,lr}                           @ restaur des  2 registres */ 
    bx lr                                          @ return  
/******************************************************************/
/*     Converting a register to a decimal unsigned                */ 
/******************************************************************/
/* r0 contains value and r1 address area   */
/* r0 return size of result (no zero final in area) */
/* area size => 11 bytes          */
.equ LGZONECAL,   10
conversion10:
    push {r1-r4,lr}                                @ save registers 
    mov r3,r1
    mov r2,#LGZONECAL

1:	                                           @ start loop
    bl divisionpar10U                              @unsigned  r0 <- dividende. quotient ->r0 reste -> r1
    add r1,#48                                     @ digit
    strb r1,[r3,r2]                                @ store digit on area
    cmp r0,#0                                      @ stop if quotient = 0 
    subne r2,#1                                    @ else previous position
    bne 1b	                                   @ and loop
                                                   @ and move digit from left of area
    mov r4,#0
2:
    ldrb r1,[r3,r2]
    strb r1,[r3,r4]
    add r2,#1
    add r4,#1
    cmp r2,#LGZONECAL
    ble 2b
                                                      @ and move spaces in end on area
    mov r0,r4                                         @ result length 
    mov r1,#' '                                       @ space
3:
    strb r1,[r3,r4]                                   @ store space in area
    add r4,#1                                         @ next position
    cmp r4,#LGZONECAL
    ble 3b                                            @ loop if r4 <= area size

100:
    pop {r1-r4,lr}                                    @ restaur registres 
    bx lr                                             @return

/***************************************************/
/*   division par 10   unsigned                    */
/***************************************************/
/* r0 dividende   */
/* r0 quotient */	
/* r1 remainder  */
divisionpar10U:
    push {r2,r3,r4, lr}
    mov r4,r0                                          @ save value
    //mov r3,#0xCCCD                                   @ r3 <- magic_number lower  raspberry 3
    //movt r3,#0xCCCC                                  @ r3 <- magic_number higter raspberry 3
    ldr r3,iMagicNumber                                @ r3 <- magic_number    raspberry 1 2
    umull r1, r2, r3, r0                               @ r1<- Lower32Bits(r1*r0) r2<- Upper32Bits(r1*r0) 
    mov r0, r2, LSR #3                                 @ r2 <- r2 >> shift 3
    add r2,r0,r0, lsl #2                               @ r2 <- r0 * 5 
    sub r1,r4,r2, lsl #1                               @ r1 <- r4 - (r2 * 2)  = r4 - (r0 * 10)
    pop {r2,r3,r4,lr}
    bx lr                                              @ leave function 
iMagicNumber:  	.int 0xCCCCCCCD
/***************************************************/
/*   Generation random number                  */
/***************************************************/
/* r0 contains limit  */
genereraleas:
    push {r1-r4,lr}                                    @ save registers 
    ldr r4,iAdriGraine
    ldr r2,[r4]
    ldr r3,iNbDep1
    mul r2,r3,r2
    ldr r3,iNbDep1
    add r2,r2,r3
    str r2,[r4]                                        @ maj de la graine pour l appel suivant 
    cmp r0,#0
    beq 100f
    mov r1,r0                                          @ divisor
    mov r0,r2                                          @ dividende
    bl division
    mov r0,r3                                          @ résult = remainder
  
100:                                                   @ end function
    pop {r1-r4,lr}                                     @ restaur registers
    bx lr                                              @ return
/*****************************************************/
iAdriGraine: .int iGraine	
iNbDep1: .int 0x343FD
iNbDep2: .int 0x269EC3 
/***************************************************/
/* integer division unsigned                       */
/***************************************************/
division:
    /* r0 contains dividend */
    /* r1 contains divisor */
    /* r2 returns quotient */
    /* r3 returns remainder */
    push {r4, lr}
    mov r2, #0                                         @ init quotient
    mov r3, #0                                         @ init remainder
    mov r4, #32                                        @ init counter bits
    b 2f
1:                                                     @ loop 
    movs r0, r0, LSL #1                                @ r0 <- r0 << 1 updating cpsr (sets C if 31st bit of r0 was 1)
    adc r3, r3, r3                                     @ r3 <- r3 + r3 + C. This is equivalent to r3 ? (r3 << 1) + C 
    cmp r3, r1                                         @ compute r3 - r1 and update cpsr 
    subhs r3, r3, r1                                   @ if r3 >= r1 (C=1) then r3 <- r3 - r1 
    adc r2, r2, r2                                     @ r2 <- r2 + r2 + C. This is equivalent to r2 <- (r2 << 1) + C 
2:
    subs r4, r4, #1                                    @ r4 <- r4 - 1 
    bpl 1b                                             @ if r4 >= 0 (N=0) then loop
    pop {r4, lr}
    bx lr

Arturo

knuth: function [arr][
	if 0=size arr -> return []
 
 	loop ((size arr)-1)..0 'i [
 		j: random 0 i

 		tmp: arr\[i]
 		set arr i arr\[j]
 		set arr j tmp
 	]

 	return arr
]
 
print knuth []
print knuth [10]
print knuth [10 20]
print knuth [10 20 30]

AutoHotkey

ahk forum: discussion

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
}

For Arrays:

to MsgBox it, you can use p()

(translated from)

toShuffle:=[1,2,3,4,5,6]
shuffled:=shuffle(toShuffle)
;p(toShuffle) ;because it modifies the original array
;or
;p(shuffled)
shuffle(a) 
{
    i := a.Length()
    loop % i-1 {
        Random, j,1,% i
        x := a[i]
        a[i] := a[j]
        a[j] := x
        i--
    }
    return a
}

AutoIt

Dim $a[10]
ConsoleWrite('array before permutation:' & @CRLF)
For $i = 0 To 9
	$a[$i] = Random(20,100,1)
	ConsoleWrite($a[$i] & ' ')
Next
ConsoleWrite(@CRLF)

_Permute($a)
ConsoleWrite('array after permutation:' & @CRLF)
For $i = 0 To UBound($a) -1
	ConsoleWrite($a[$i] & ' ')
Next
ConsoleWrite(@CRLF)


Func _Permute(ByRef $array)
	Local $random, $tmp
	For $i = UBound($array) -1 To 0 Step -1
		$random = Random(0,$i,1)
		$tmp = $array[$random]
		$array[$random] = $array[$i]
		$array[$i] = $tmp
	Next
EndFunc

Output:

 array before permutation:
 43 57 37 20 97 98 69 76 97 70 
 array after permutation:
 57 69 97 70 37 97 20 76 43 98

AWK

Many arrays in AWK have the first index at 1. This example shows how to shuffle such arrays. The elements can be integers, floating-point numbers, or strings.

# Shuffle an _array_ with indexes from 1 to _len_.
function shuffle(array, len,    i, j, t) {
	for (i = len; i > 1; i--) {
		# j = random integer from 1 to i
		j = int(i * rand()) + 1

		# swap array[i], array[j]
		t = array[i]
		array[i] = array[j]
		array[j] = t
	}
}

# Test program.
BEGIN {
	len = split("11 22 33 44 55 66 77 88 99 110", array)
	shuffle(array, len)

	for (i = 1; i < len; i++) printf "%s ", array[i]
	printf "%s\n", array[len]
}

BASIC

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))); " ";
NEXT

FOR L0 = 51 TO 0 STEP -1
    card = INT(RND * (L0 + 1))
    IF card <> L0 THEN SWAP cards(card), cards(L0)
NEXT

PRINT : PRINT "after:"
FOR L0 = 0 TO 51
    PRINT LTRIM$(STR$(cards(L0))); " ";
NEXT
PRINT

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

Applesoft BASIC

As mentioned in the Sinclair ZX81 BASIC solution, for very small positive integer values, a string is a much more memory-efficient array, but here is an example of an array with numbers. Line 150 initializes and prints each element in the array. Line 190 performs the swap of the elements.

 100 :
 110  REM  KNUTH SHUFFLE
 120 :
 130  DIM A(25)
 140  FOR I = 1 TO 25
 150 A(I) = I: PRINT A(I);" ";: NEXT I
 160  PRINT : PRINT
 170  FOR I = 25 TO 2 STEP  - 1
 180 J =  INT ( RND (1) * I + 1)        
 190 T = A(I):A(I) = A(J):A(J) = T: NEXT I
 200  FOR I = 1 TO 25
 210  PRINT A(I);" ";: NEXT I
 220  END

Output:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1
7 18 19 20 21 22 23 24 25

When it has finished, the screen will show (for example):

20 5 6 9 15 23 22 8 4 24 7 11 16 21 2 17
 14 10 19 13 12 18 1 3 25

BBC BASIC

      cards% = 52
      DIM pack%(cards%)
      FOR I% = 1 TO cards%
        pack%(I%) = I%
      NEXT I%
      FOR N% = cards% TO 2 STEP -1
        SWAP pack%(N%),pack%(RND(N%))
      NEXT N%
      FOR I% = 1 TO cards%
        PRINT pack%(I%);
      NEXT I%
      PRINT

Chipmunk Basic

Works with: Chipmunk Basic version 3.6.4

The GW-BASIC solution works without any changes.

GW-BASIC

Works with: PC-BASIC version any

Works with: BASICA

Works with: Chipmunk Basic

100 CLS
110 RANDOMIZE TIMER
120 DIM CARDS(51)
130 PRINT "before:"
140 FOR L0 = 0 TO 51
150   CARDS(L0) = L0
160   PRINT STR$(CARDS(L0));" ";
170 NEXT L0
180 FOR L0 = 51 TO 0 STEP -1
190   CARD = INT(RND(1)*(L0+1))
200   IF CARD <> L0 THEN T = CARDS(CARD) : CARDS(CARD) = CARDS(L0) : CARDS(L0) = T
210 NEXT L0
220 PRINT : PRINT
230 PRINT "after:"
240 FOR L0 = 0 TO 51
250   PRINT STR$(CARDS(L0));" ";
260 NEXT L0
270 PRINT
280 END

IS-BASIC

100 PROGRAM "Shuffle.bas"
110 RANDOMIZE
120 NUMERIC ARRAY(1 TO 20)
130 CALL INIT(ARRAY)
140 CALL WRITE(ARRAY)
150 CALL SHUFFLE(ARRAY)
160 CALL WRITE(ARRAY)
170 DEF INIT(REF A)
180   FOR I=LBOUND(A) TO UBOUND(A)
190     LET A(I)=I
200   NEXT
210 END DEF
220 DEF WRITE(REF A)
230   FOR I=LBOUND(A) TO UBOUND(A)
240     PRINT A(I);
250   NEXT
260   PRINT
270 END DEF
280 DEF SHUFFLE(REF A)
290   FOR I=UBOUND(A) TO LBOUND(A) STEP-1
300     LET CARD=RND(UBOUND(A)-LBOUND(A))+LBOUND(A)+1
310     IF CARD<>I THEN LET T=A(CARD):LET A(CARD)=A(I):LET A(I)=T
320   NEXT
330 END DEF

Minimal BASIC

100 REM Knuth shuffle
110 RANDOMIZE
120 DIM B(51)
130 PRINT "BEFORE:"
140 FOR L0 = 0 TO 51
150   LET B(L0) = L0
160   PRINT B(L0);" ";
170 NEXT L0
180 FOR L0 = 51 TO 0 STEP -1
190   LET C = INT(RND*(L0+1))
200   IF C <> L0 THEN 220
210   GOTO 250
220   LET T = B(C)
230   LET B(C) = B(L0)
240   LET B(L0) = T
250 NEXT L0
260 PRINT
270 PRINT
280 PRINT "AFTER:"
290 FOR L0 = 0 TO 51
300   PRINT B(L0);" ";
310 NEXT L0
320 PRINT
330 END

OxygenBasic

uses chaos
uses timeutil
seed=GetTickCount
int i,j
int d[100] 'int array or any other type
...
for i=100 to 1 step -1
  j=irnd(1,100)
  swap d[i],d[j]
next

QB64

Shuffle and make sure that number does not take its place
and between cells at least 10% ... Shuffle from Russia

a = 100: DIM d(a): x=0: k=0: t$=CHR$(9): RANDOMIZE TIMER 'Shuffle_RUS.bas
PRINT ,: FOR i = 1 TO a: d(i)=i: NEXT
FOR i = 1 TO 5: PRINT d(i);: NEXT: PRINT ,
FOR i = a-3 TO a: PRINT d(i);: NEXT: z = TIMER
OPEN "b:/control.txt" FOR OUTPUT AS #1 ' ram disk
WHILE x < 1
    v = 0: FOR i = 1 TO a
       1 m = INT(RND*a)+1: IF ABS(d(i)-d(m)) < .1*a THEN v = v+1: GOTO 1
        PRINT #1, ABS(d(i)-d(m)); t$; d(i); t$; d(m); t$; i; t$; m; t$; d(i)/d(m); t$; d(m)/d(i) ' ram disk
        t = d(i): d(i) = d(m): d(m) = t
    NEXT
 
    s = 0: FOR i = 1 TO a
        IF d(i) = i THEN s = s+1 ' : goto 5
    NEXT
    5 k = k+1: PRINT: PRINT s; v,: IF s=0 THEN x = x+1

    FOR i = 1 TO 5
        IF d(i) = i THEN PRINT -d(i); ELSE PRINT d(i);
    NEXT: PRINT ,
    FOR i = a-3 TO a
        IF d(i) = i THEN PRINT -d(i); ELSE PRINT d(i);
    NEXT
WEND: PRINT: PRINT "    = "; k, TIMER-z: END

Sinclair ZX81 BASIC

For very small positive integer values, a string (which can be treated as an array of bytes) is much more memory-efficient than an array of numbers. In this program we shuffle a string consisting of the letters 'A' to 'Z'. The ZX81 is slow enough that we can watch the shuffle happening in real time, with items switching to inverse video display as they are shuffled. (This can be done, in the ZX81 character set, by setting the high bit in the character code.) Line 10 seeds the pseudo-random number generator. Note that strings (and arrays) are indexed from 1.

The program works with the unexpanded (1k RAM) ZX81.

 10 RAND
 20 LET A$=""
 30 FOR I=1 TO 26
 40 LET A$=A$+CHR$ (37+I)
 50 NEXT I
 60 PRINT A$
 70 FOR I=26 TO 2 STEP -1
 80 LET J=1+INT (RND*I)
 90 LET T$=A$(I)
100 LET A$(I)=A$(J)
110 LET A$(J)=T$
120 PRINT AT 0,I-1;CHR$ (CODE A$(I)+128)
130 PRINT AT 0,J-1;CHR$ (CODE A$(J)+128)
140 NEXT I

Output:

While the program is running, we will see something like this (using lower case as a stand-in for inverse video):

ABCuEFGzwJKLMNOPxySvdtiqrh

When it has finished, the screen will show (for example):

lcjbpxekzsaygumwnovfdtiqrh

True BASIC

Translation of: BASIC

OPTION BASE 0
RANDOMIZE

DIM cards(51)

PRINT "before:"
FOR L0 = 0 TO 51
    LET cards(L0) = L0
    PRINT LTRIM$(STR$(cards(L0))); " ";
NEXT L0

FOR L0 = 51 TO 0 STEP -1
    LET card = INT(RND * (L0 + 1))
    IF card <> L0 THEN
       LET t = cards(lb + L0)
       LET cards(lb + L0) = cards(lb + card)
       LET cards(lb + card) = t
    END IF
NEXT L0

PRINT
PRINT "after:"
FOR L0 = 0 TO 51
    PRINT LTRIM$(STR$(cards(L0))); " ";
NEXT L0
END

Output:

Same as BASIC entry.

bc

I provide a shuffle() function. It can only shuffle an array of numbers. It fails if the array has more than 32768 elements. It always shuffles the array named shuffle[]; the array is not a function parameter because bc passes arrays by copying.

This code requires a bc with long names; the test program also requires a bc with the print statement.

Works with: OpenBSD bc

seed = 1   /* seed of the random number generator */
scale = 0

/* Random number from 0 to 32767. */
define rand() {
	/* Formula (from POSIX) for random numbers of low quality. */
	seed = (seed * 1103515245 + 12345) % 4294967296
	return ((seed / 65536) % 32768)
}

/* Shuffle the first _count_ elements of shuffle[]. */
define shuffle(count) {
	auto b, i, j, t

	i = count
	while (i > 0) {
		/* j = random number in [0, i) */
		b = 32768 % i  /* want rand() >= b */
		while (1) {
			j = rand()
			if (j >= b) break
		}
		j = j % i

		/* decrement i, swap shuffle[i] and shuffle[j] */
		t = shuffle[--i]
		shuffle[i] = shuffle[j]
		shuffle[j] = t
	}
}

/* Test program. */
define print_array(count) {
	auto i
	for (i = 0; i < count - 1; i++) print shuffle[i], ", "
	print shuffle[i], "\n"
}

for (i = 0; i < 10; i++) shuffle[i] = 11 * (i + 1)
"Original array: "; trash = print_array(10)

trash = shuffle(10)
"Shuffled array: "; trash = print_array(10)
quit

Output:

Original array: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110
Shuffled array: 66, 44, 11, 55, 33, 77, 110, 22, 88, 99

BQN

BQN's arrays are immutable, but variable values can be changed using the `↩` symbol. This program repeatedly changes the array's value using under.

Knuth ← {
  𝕊 arr:
  l ← ≠arr
  {
    arr ↩ ⌽⌾(⟨•rand.Range l, 𝕩⟩⊸⊏)arr
  }¨↕l
  arr
}
P ← •Show Knuth

P ⟨⟩
P ⟨10⟩
P ⟨10, 20⟩
P ⟨10, 20, 30⟩

Try It!

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
  }

  a
}

p shuffle [1 2 3 4 5 6 7]

C

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

#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);
}

Alternatively, using Durstenfeld's method (swapping selected item and last item in each iteration instead of literally shifting everything), and macro'd function declaration/definition:

#include <stdio.h>
#include <stdlib.h>

/* define a shuffle function. e.g. decl_shuffle(double).
 * advantage: compiler is free to optimize the swap operation without
 *            indirection with pointers, which could be much faster.
 * disadvantage: each datatype needs a separate instance of the function.
 *            for a small funciton like this, it's not very big a deal.
 */
#define decl_shuffle(type)				\
void shuffle_##type(type *list, size_t len) {		\
	int j;						\
	type tmp;					\
	while(len) {					\
		j = irand(len);				\
		if (j != len - 1) {			\
			tmp = list[j];			\
			list[j] = list[len - 1];	\
			list[len - 1] = tmp;		\
		}					\
		len--;					\
	}						\
}							\

/* random integer from 0 to n-1 */
int irand(int n)
{
	int r, rand_max = RAND_MAX - (RAND_MAX % n);
	/* reroll until r falls in a range that can be evenly
	 * distributed in n bins.  Unless n is comparable to
	 * to RAND_MAX, it's not *that* important really. */
	while ((r = rand()) >= rand_max);
	return r / (rand_max / n);
}

/* declare and define int type shuffle function from macro */
decl_shuffle(int);

int main()
{
	int i, x[20];

	for (i = 0; i < 20; i++) x[i] = i;
	for (printf("before:"), i = 0; i < 20 || !printf("\n"); i++)
		printf(" %d", x[i]);

	shuffle_int(x, 20);

	for (printf("after: "), i = 0; i < 20 || !printf("\n"); i++)
		printf(" %d", x[i]);
	return 0;
}

C#

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(i, array.Length); // Don't select from the entire array on subsequent loops
        T temp = array[i]; array[i] = array[j]; array[j] = temp;
    }
}

C++

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

#include <cstdlib>
#include <algorithm>
#include <iterator>

template<typename RandomAccessIterator>
void knuthShuffle(RandomAccessIterator begin, RandomAccessIterator end) {
  if(begin == end) {
      return;
  }
  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);
    }
  }
}

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

#include <algorithm>
#include <vector>

int main()
{
    int array[] = { 1,2,3,4,5,6,7,8,9 }; // C-style 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
}

Clojure

(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)))

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.

CLU

knuth_shuffle = proc [T: type] (a: array[T])
    lo: int := array[T]$low(a)
    hi: int := array[T]$high(a)
    for i: int in int$from_to_by(hi, lo+1, -1) do
        j: int := lo + random$next(i-lo+1)
        temp: T := a[i]
        a[i] := a[j]
        a[j] := temp
    end
end knuth_shuffle

start_up = proc ()
    po: stream := stream$primary_output()
    d: date := now()
    random$seed(d.second + 60*(d.minute + 60*d.hour))
    arr: array[int] := array[int]$[1,2,3,4,5,6,7,8,9]
    knuth_shuffle[int](arr)
    for i: int in array[int]$elements(arr) do
        stream$puts(po, int$unparse(i) || " ")
    end
end start_up

Output:

7 9 2 3 4 8 1 6 5

(Or any other order.)

CMake

# shuffle(<output variable> [<value>...]) shuffles the values, and
# stores the result in a list.
function(shuffle var)
  set(forever 1)

  # Receive ARGV1, ARGV2, ..., ARGV${last} as an array of values.
  math(EXPR last "${ARGC} - 1")

  # Shuffle the array with Knuth shuffle (Fisher-Yates shuffle).
  foreach(i RANGE ${last} 1)
    # Roll j = a random number from 1 to i.
    math(EXPR min "100000000 % ${i}")
    while(forever)
      string(RANDOM LENGTH 8 ALPHABET 0123456789 j)
      if(NOT j LESS min)        # Prevent modulo bias when j < min.
        break()                 # Break loop when j >= min.
      endif()
    endwhile()
    math(EXPR j "${j} % ${i} + 1")

    # Swap ARGV${i} with ARGV${j}.
    set(t ${ARGV${i}})
    set(ARGV${i} ${ARGV${j}})
    set(ARGV${j} ${t})
  endforeach(i)

  # Convert array to list.
  set(answer)
  foreach(i RANGE 1 ${last})
    list(APPEND answer ${ARGV${i}})
  endforeach(i)
  set("${var}" ${answer} PARENT_SCOPE)
endfunction(shuffle)

shuffle(result 11 22 33 44 55 66)
message(STATUS "${result}")
# One possible output:
# -- 66;33;22;55;44;11

COBOL

       IDENTIFICATION DIVISION.
       PROGRAM-ID. knuth-shuffle.

       DATA DIVISION.
       LOCAL-STORAGE SECTION.
       01  i                       PIC 9(8).
       01  j                       PIC 9(8).

       01  temp                    PIC 9(8).

       LINKAGE SECTION.
       78  Table-Len               VALUE 10.
       01  ttable-area.
           03  ttable              PIC 9(8) OCCURS Table-Len TIMES.

       PROCEDURE DIVISION USING ttable-area.
           MOVE FUNCTION RANDOM(FUNCTION CURRENT-DATE (11:6)) TO i

           PERFORM VARYING i FROM Table-Len BY -1 UNTIL i = 0
               COMPUTE j =
                   FUNCTION MOD(FUNCTION RANDOM * 10000, Table-Len) + 1

               MOVE ttable (i) TO temp
               MOVE ttable (j) TO ttable (i)
               MOVE temp TO ttable (j)
           END-PERFORM

           GOBACK
           .

CoffeeScript

Translation of: JavaScript

knuth_shuffle = (a) ->
  n = a.length
  while n > 1
    r = Math.floor(n * Math.random())
    n -= 1
    [a[n], a[r]] = [a[r], a[n]]
  a

counts =
  "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 in [1..100000]
  counts[knuth_shuffle([ 1, 2, 3 ]).join(",")] += 1

for key, val of counts
  console.log "#{key}: #{val}"

Output:

> coffee knuth_shuffle.coffee 
1,2,3: 16714
1,3,2: 16566
2,1,3: 16460
2,3,1: 16715
3,1,2: 16750
3,2,1: 16795

Common Lisp

(defun nshuffle (sequence)
  (loop for i from (length sequence) downto 2
        do (rotatef (elt sequence (random i))
                    (elt sequence (1- i))))
  sequence)

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):

(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)))

Crystal

def knuthShuffle(items : Array)
    i = items.size-1
    while i > 1
        j = Random.rand(0..i)
        items.swap(i, j)

        i -= 1
    end
end

D

Standard Version

A variant of the Knuth shuffle is in the D standard library Phobos:

void main() {
    import std.stdio, std.random;

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

Output:

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

One Implementation

This shuffles any collection that supports random access, length and swapping of items:

import std.stdio, std.algorithm, std.random, std.range;

void knuthShuffle(Range)(Range r)
if (isRandomAccessRange!Range && hasLength!Range &&
    hasSwappableElements!Range) {
    foreach_reverse (immutable i, ref ri; r[1 .. $ - 1])
        ri.swap(r[uniform(0, i + 1)]);
}

void main() {
    auto a = [1, 2, 3, 4, 5, 6, 7, 8, 9];
    a.knuthShuffle;
    a.writeln;
}

Delphi

See Pascal or DWScript

DWScript

procedure KnuthShuffle(a : array of Integer);
var
   i, j, tmp : Integer;
begin
   for i:=a.High downto 1 do begin
      j:=RandomInt(a.Length);
      tmp:=a[i]; a[i]:=a[j]; a[j]:=tmp;
   end;
end;

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
    }
}

? 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()

EasyLang

proc shuffle . a[] .
   for i = len a[] downto 2
      r = random i
      swap a[r] a[i]
   .
.
arr[] = [ 1 2 3 ]
shuffle arr[]
print arr[]

EchoLisp

Remark- The native '''shuffle''' function implementation  in EchoLisp has been replaced by this one.
 Thx Rosetta Code.
(lib 'list) ;; for list-permute

;; use "inside-out" algorithm, no swapping needed.
;; returns a random permutation vector of [0 .. n-1]
(define (rpv n (j))
(define v (make-vector n))
	(for [(i n)]
		(set! j (random (1+ i)))
		(when (!= i j) (vector-set! v i [v j]))
		(vector-set! v j i))
	v)
	
;; apply to any kind of list
(define (k-shuffle list)
	(list-permute list (vector->list (rpv (length list)))))
	
;; out 
(k-shuffle (iota 17))
    → (16 7 11 10 0 9 15 12 13 8 4 2 14 3 6 5 1)
	
(k-shuffle 
'(adrien 🎸 alexandre 🚂  antoine  🍼 ben 📚   georges 📷   julie 🎥 marine 🐼 nathalie 🍕 ))
    → (marine alexandre 🎥 julie 🎸 ben 🍼 nathalie 📚 georges 🚂 antoine adrien 🐼 📷 🍕)
    
(shuffle ;; native
'(adrien 🎸 alexandre 🚂 antoine 🍼 ben 📚 georges 📷 julie 🎥 marine 🐼 nathalie 🍕 ))
    → (antoine 🎥 🚂 marine adrien nathalie 🍼 🍕 ben 🐼 julie 📷 📚 🎸 alexandre georges)

Egel

import "prelude.eg"
import "random.ego"

using System
using List
using Math

def swap =
    [ I J XX -> insert I (nth J XX) (insert J (nth I XX) XX) ]

def shuffle =
    [ XX ->
        let INDICES = reverse (fromto 0 ((length XX) - 1)) in
        let SWAPS = map [ I -> I (between 0 I) ] INDICES in
            foldr [I J -> swap I J] XX SWAPS ]

def main = shuffle (fromto 1 9)

Eiffel

class
	APPLICATION

create
	make

feature {NONE} -- Initialization

	make
		do
			test := <<1, 2>>
			io.put_string ("Initial: ")
			across
				test as t
			loop
				io.put_string (t.item.out + " ")
			end
			test := shuffle (test)
			io.new_line
			io.put_string ("Shuffled: ")
			across
				test as t
			loop
				io.put_string (t.item.out + " ")
			end
		end

	test: ARRAY [INTEGER]

	shuffle (ar: ARRAY [INTEGER]): ARRAY [INTEGER]
			-- Array containing the same elements as 'ar' in a shuffled order.
		require
			more_than_one_element: ar.count > 1
		local
			count, j, ith: INTEGER
			random: V_RANDOM
		do
			create random
			create Result.make_empty
			Result.deep_copy (ar)
			count := ar.count
			across
				1 |..| count as c
			loop
				j := random.bounded_item (c.item, count)
				ith := Result [c.item]
				Result [c.item] := Result [j]
				Result [j] := ith
				random.forth
			end
		ensure
			same_elements: across ar as a all Result.has (a.item) end
		end

end

Output:

Initial: 1 2 3 4 5 6 7
Shuffeld: 1 5 3 4 7 6 2

Elena

ELENA 6.x:

import system'routines;
import extensions;
 
const int MAX = 10;
 
extension randomOp
{
    randomize()
    {
        var max := self.Length;
 
        for(int i := 0; i < max; i += 1)
        {
            var j := randomGenerator.nextInt(i,max);
 
            self.exchange(i,j)
        };
 
        ^ self
    }
}
 
public program()
{
    var a := Array.allocate(MAX).populate::(i => i );
 
    console.printLine(a.randomize())
}

Output:

3,8,4,5,1,2,6,0,7,9

Elixir

Translation of: Erlang

defmodule Knuth do
  def shuffle( inputs ) do
    n = length( inputs )
    {[], acc} = Enum.reduce( n..1, {inputs, []}, &random_move/2 )
    acc
  end
  
  defp random_move( n, {inputs, acc} ) do
    item = Enum.at( inputs, :rand.uniform(n)-1 )
    {List.delete( inputs, item ), [item | acc]}
  end
end

seq = Enum.to_list( 0..19 )
IO.inspect Knuth.shuffle( seq )

seq = [1,2,3]
Enum.reduce(1..100000, Map.new, fn _,acc ->
  k = Knuth.shuffle(seq)
  Map.update(acc, k, 1, &(&1+1))
end)
|> Enum.each(fn {k,v} -> IO.inspect {k,v} end)

Output:

[17, 13, 4, 2, 16, 1, 8, 19, 9, 12, 14, 5, 0, 11, 6, 10, 18, 3, 15, 7]
{[1, 2, 3], 16702}
{[1, 3, 2], 16635}
{[2, 1, 3], 16518}
{[2, 3, 1], 16935}
{[3, 1, 2], 16500}
{[3, 2, 1], 16710}

Erlang

-module( knuth_shuffle ).

-export( [list/1] ).

list( Inputs ) ->
	N = erlang:length( Inputs ),
	{[], Acc} = lists:foldl( fun random_move/2, {Inputs, []}, lists:reverse(lists:seq(1, N)) ),
	Acc.



random_move( N, {Inputs, Acc} ) ->
	Item = lists:nth( random:uniform(N), Inputs ),
	{lists:delete(Item, Inputs), [Item | Acc]}.

Output:

21> knuth_shuffle:list(lists:seq(1,9)).
[5,7,8,1,4,2,3,9,6]

ERRE

PROGRAM KNUTH_SHUFFLE

CONST CARDS%=52

DIM PACK%[CARDS%]

BEGIN
   RANDOMIZE(TIMER)
   FOR I%=1 TO CARDS% DO
      PACK%[I%]=I%
   END FOR
   FOR N%=CARDS% TO 2 STEP -1 DO
      SWAP(PACK%[N%],PACK%[1+INT(N%*RND(1))])
   END FOR
   FOR I%=1 TO CARDS% DO
      PRINT(PACK%[I%];)
   END FOR
   PRINT
END PROGRAM

Euphoria

Translation of: BASIC

sequence cards
cards = repeat(0,52)
integer card,temp

puts(1,"Before:\n")
for i = 1 to 52 do
    cards[i] = i
    printf(1,"%d ",cards[i])
end for

for i = 52 to 1 by -1 do
    card = rand(i)
    if card != i then
        temp = cards[card]
        cards[card] = cards[i]
        cards[i] = temp
    end if
end for

puts(1,"\nAfter:\n")
for i = 1 to 52 do
    printf(1,"%d ",cards[i])
end for

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:

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

Here's the modified Knuth shuffle which shuffles the original array in place

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

Example:

> KnuthShuffle [| "Darrell"; "Marvin"; "Doug"; "Greg"; "Sam"; "Ken" |];;
val it : string array = [|"Marvin"; "Doug"; "Sam"; "Darrell"; "Ken"; "Greg"|]

Factor

There is a randomize word already in the standard library. Implementation:

: randomize ( seq -- seq )
    dup length [ dup 1 > ]
    [ [ iota random ] [ 1 - ] bi [ pick exchange ] keep ]
    while drop ;

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)
  }
}

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

Fortran

Works with: Fortran version 90 and later

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

FreeBASIC

' version 22-10-2016
' compile with: fbc -s console
' for boundry checks on array's compile with: fbc -s console -exx

' sort from lower bound to the highter bound
' array's can have subscript range from -2147483648 to +2147483647

Sub knuth_down(a() As Long)

    Dim As Long lb = LBound(a)
    Dim As ULong n = UBound(a) - lb +1
    Dim As ULong i, j

    Randomize Timer

    For i = n -1 To 1 Step -1
        j =Fix(Rnd * (i +1))       ' 0 <= j <= i
        Swap a(lb + i), a(lb + j)
    Next

End Sub

Sub knuth_up(a() As Long)

    Dim As Long lb = LBound(a)
    Dim As ULong n = UBound(a) - lb +1
    Dim As ULong i, j

    Randomize Timer

    For i = 0 To n -2
        j = Fix(Rnd * (n - i) + i)   '  0 <= j < n-i, + i ==> i <= j < n
        Swap a(lb + i), a(lb + j)
    Next

End Sub

' ------=< MAIN >=------

Dim As Long i
Dim As Long array(1 To 52), array2(-7 To 7)

For i = 1 To 52 : array(i) = i : Next

Print "Starting array"
For i = 1 To 52
    Print Using " ###";array(i);
Next : Print : Print

knuth_down(array())

Print "After Knuth shuffle downwards"
For i = 1 To 52
    Print Using " ###";array(i);
Next : Print : Print

For i = LBound(array2) To UBound(array2)
    array2(i) = i - LBound(array2) + 1
Next

Print "Starting array, first index <> 0 "
For i = LBound(array2) To UBound(array2)
    Print Using " ##";array2(i);
Next : Print : Print

knuth_up(array2())
Print "After Knuth shuffle upwards"
For i = LBound(array2) To UBound(array2)
    Print Using " ##";array2(i);
Next : Print : Print


' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End

Output:

Starting array
   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

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

Starting array, first index <> 0 
  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15

After Knuth shuffle upwards
  4  1  9 10 15 11 12  7  3  5  8 13  6 14  2

Frink

The built-in method array.shuffle[] implements the Fisher-Yates-Knuth shuffle algorithm:

a = [1,2,3]
a.shuffle[]

FunL

def shuffle( a ) =
  res = array( a )
  n = a.length()
  
  for i <- 0:n
    r = rnd( i:n )
    res(i), res(r) = res(r), res(i)
    
  res.toList()

FutureBasic

include "NSLog.incl"

void local fn KnuthShuffle( mutArr as CFMutableArrayRef )
  NSUInteger i, j, count
  
  count = len(mutArr)
  for i = count-1 to 1 step -1    
    j = rnd(i+1)-1    
    MutableArrayExchangeObjects( mutArr, i, j )
  next
end fn

randomize

CFMutableArrayRef mutArr
NSUInteger        i
mutArr = fn MutableArrayWithObjects( @0, @1, @2, @3, @4, @5, @6, @7, @8, @9, NULL )
NSLog( @"Before shuffle: %@", fn ArrayComponentsJoinedByString( mutArr, @"" ) )

for i = 1 to 100
  fn KnuthShuffle( mutArr )
  NSLog( @"%@", fn ArrayComponentsJoinedByString( mutArr, @"" ) )
next

HandleEvents

Output:

Before shuffle: 0123456789
1274860395
2715638904
7182035964
1297658403
2916574083
9162507843
1875962034
8721965034
7968402351
9347510862

Gambas

Click this link to run this code

Public Sub Main()
Dim iTotal As Integer = 40
Dim iCount, iRand1, iRand2 As Integer
Dim iArray As New Integer[]

For iCount = 0 To iTotal
  iArray.add(iCount)
Next

Print "Original = ";
For iCount = 0 To iArray.Max
  If iCount = iArray.max Then Print iArray[iCount]; Else Print iArray[iCount] & ",";
Next

For iCount = iTotal DownTo 0
  iRand1 = Rand(iTotal)
  iRand2 = Rand(iTotal)
  Swap iArray[iRand1], iArray[iRand2]
Next

Print gb.NewLine & "Shuffled = ";
For iCount = 0 To iArray.Max
  If iCount = iArray.max Then Print iArray[iCount]; Else Print iArray[iCount] & ",";
Next

End

Output:

Original = 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
Shuffled = 8,23,12,31,4,38,39,40,37,34,14,0,21,22,3,10,27,26,17,15,6,7,19,2,24,35,25,16,18,36,1,13,32,33,20,5,9,11,29,28,30

GAP

# Return the list L after applying Knuth shuffle. GAP also has the function Shuffle, which does the same.
ShuffleAlt := function(a)
    local i, j, n, t;
    n := Length(a);
    for i in [n, n - 1 .. 2] do
        j := Random(1, i);
        t := a[i];
        a[i] := a[j];
        a[j] := t;
    od;
    return a;
end;

# Return a "Permutation" object (a permutation of 1 .. n).
# They are printed in GAP, in cycle decomposition form.
PermShuffle := n -> PermList(ShuffleAlt([1 .. n]));

ShuffleAlt([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)

Go

(Note, in addition to these examples, rand.Shuffle was added in Go1.10 implementing a Fisher–Yates shuffle.)

package main

import (
    "fmt"
    "math/rand"
    "time"
)

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

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

To shuffle any type:

package main

import (
    "fmt"
    "math/rand"
    "time"
)

// Generic Knuth Shuffle algorithm.  In Go, this is done with interface
// types.  The parameter s of function shuffle is an interface type.
// Any type satisfying the interface "shuffler" can be shuffled with
// this function.  Since the shuffle function uses the random number
// generator, it's nice to seed the generator at program load time.
func init() {
    rand.Seed(time.Now().UnixNano())
}
func shuffle(s shuffler) {
    for i := s.Len() - 1; i >= 1; i-- {
        j := rand.Intn(i + 1)
        s.Swap(i, j)
    }
}

// Conceptually, a shuffler is an indexed collection of things.
// It requires just two simple methods.
type shuffler interface {
    Len() int      // number of things in the collection
    Swap(i, j int) // swap the two things indexed by i and j
}

// ints is an example of a concrete type implementing the shuffler
// interface.
type ints []int

func (s ints) Len() int      { return len(s) }
func (s ints) Swap(i, j int) { s[i], s[j] = s[j], s[i] }

// Example program.  Make an ints collection, fill with sequential numbers,
// print, shuffle, print.
func main() {
    a := make(ints, 20)
    for i := range a {
        a[i] = i
    }
    fmt.Println(a)
    shuffle(a)
    fmt.Println(a)
}

Example output:

(of either program)

[0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19]
[11 10 12 19 4 13 15 17 14 2 5 18 8 0 6 9 7 3 1 16]

Groovy

Solution:

def shuffle = { list ->
    if (list == null || list.empty) return list
    def r = new Random()
    def n = list.size()
    (n..1).each { i ->
        def j = r.nextInt(i)
        list[[i-1, j]] = list[[j, i-1]]
    }
    list
}

Test:

def list = [] + (0..20)
println list
println shuffle(list)
println shuffle(list)
println shuffle(list)

Output:

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]
[12, 16, 7, 13, 1, 9, 17, 20, 15, 3, 5, 6, 8, 0, 18, 10, 14, 4, 2, 11, 19]
[17, 6, 10, 1, 18, 5, 7, 13, 2, 11, 16, 3, 14, 0, 4, 20, 19, 12, 8, 9, 15]
[6, 20, 11, 4, 7, 12, 5, 14, 19, 18, 13, 15, 1, 2, 8, 16, 17, 10, 0, 9, 3]

Haskell

import System.Random (randomRIO)

mkRands :: Int -> IO [Int]
mkRands = mapM (randomRIO . (,) 0) . enumFromTo 1 . pred

replaceAt :: Int -> a -> [a] -> [a]
replaceAt i c l =
  let (a, b) = splitAt i l
  in a ++ c : 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 = (foldr swapElems xs . zip [1 ..]) <$> mkRands (length xs)

or, as an alternative to making two indexed references into the list with (!!):

import System.Random (randomRIO)
import Data.Bool (bool)

knuthShuffle :: [a] -> IO [a]
knuthShuffle xs = (foldr swapped xs . zip [1 ..]) <$> randoms (length xs)

swapped :: (Int, Int) -> [a] -> [a]
swapped (i, j) xs =
  let go (a, b)
        | a == b = xs
        | otherwise =
          let (m, n) = bool (b, a) (a, b) (b > a)
              (l, hi:t) = splitAt m xs
              (ys, lo:zs) = splitAt (pred (n - m)) t
          in concat [l, lo : ys, hi : zs]
  in bool xs (go (i, j)) $ ((&&) . (i <) <*> (j <)) $ length xs

randoms :: Int -> IO [Int]
randoms x = mapM (randomRIO . (,) 0) [1 .. pred x]

main :: IO ()
main = knuthShuffle ['a' .. 'k'] >>= print

Examples of use of either of the two versions above:

*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:

knuthShuffleProcess :: (Show a) => [a] -> IO ()
knuthShuffleProcess = 
   (mapM_ print. reverse =<<). ap (fmap. (. zip [1..]). scanr swapElems) (mkRands. length)

Output:

Detailed 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:

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

Icon and Unicon

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

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

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:

procedure shuffle(A)
    every !A :=: ?A
end

is subtly biased.

Inform 6

[ shuffle a n i j tmp;
    for (i = n - 1: i > 0: i--) {
        j = random(i + 1) - 1;

        tmp = a->j;
        a->j = a->i;
        a->i = tmp;
    }
];

J

KS=:{~ (2&{.@[ {`(|.@[)`]} ])/@(,~(,.?@>:))@i.@#

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.

process                         J

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

Example of a transformed input:

(,~(,.?@>:))@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

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:

2&{.@[ {`(|.@[)`]} ]

Finally, the shuffled indexes select elements from the original array.

input { ~ shuffled indexes

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:

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

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:

KS=: [: > (<@C. >)/@(|.@; ;&~./@(,. ?@>:)@i.@#)

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:

]A=: 5+i.9
5 6 7 8 9 10 11 12 13

Shuffle:

KS A
13 10 7 5 11 9 8 6 12

Input

]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

Shuffle

Input

]L=:'aA';'bbB';'cC%$';'dD@'
+--+---+----+---+
|aA|bbB|cC%$|dD@|
+--+---+----+---+

Shuffle

KS L
+--+----+---+---+
|aA|cC%$|dD@|bbB|
+--+----+---+---+

In J the shuffling of an arbitrary array can easily be implemented by the phrase ( ref http://www.jsoftware.com/jwiki/JPhrases/RandomNumbers ):

({~?~@#)

Applied on the former examples:

({~?~@#) 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@|
+----+---+--+---+

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;
    }
}

JavaScript

ES5

function knuthShuffle(arr) {
    var rand, temp, i;

    for (i = arr.length - 1; i > 0; i -= 1) {
        rand = Math.floor((i + 1) * Math.random());//get random between zero and i (inclusive)
        temp = arr[rand];
        arr[rand] = arr[i]; //swap i (last element) with random element.
        arr[i] = temp;
    }
    return arr;
}

var 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 (var i = 0; i < 100000; i++) {
    res[knuthShuffle([1,2,3]).join(',')] += 1;
}

for (var key in res) {
    print(key + "\t" + res[key]);
}

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

ES6

Mutating in-place swap

(() => {

    // knuthShuffle :: [a] -> [a]
    const knuthShuffle = xs =>
        enumFromTo(0, xs.length - 1)
        .reduceRight((a, i) => {
            const
                iRand =  randomRInt(0, i),
                tmp = a[iRand];
            return iRand !== i ? (
                a[iRand] = a[i],
                a[i] = tmp,
                a
            ) : a;
        }, xs);

    const test = () => knuthShuffle(
        (`alpha beta gamma delta epsilon zeta
              eta theta iota kappa lambda mu`)
        .split(/\s+/)
    );

    // GENERIC FUNCTIONS ----------------------------------

    // enumFromTo :: Int -> Int -> [Int]
    const enumFromTo = (m, n) =>
        n >= m ? (
            iterateUntil(x => x >= n, x => 1 + x, m)
        ) : [];

    // iterateUntil :: (a -> Bool) -> (a -> a) -> a -> [a]
    const iterateUntil = (p, f, x) => {
        let vs = [x],
            h = x;
        while (!p(h))(h = f(h), vs.push(h));
        return vs;
    };

    // randomRInt :: Int -> Int -> Int
    const randomRInt = (low, high) =>
        low + Math.floor(
            (Math.random() * ((high - low) + 1))
        );

    return test();
})();

Output:

e.g.

["iota", "epsilon", "kappa", "theta", "gamma", "delta", 
"lambda", "eta", "zeta", "beta", "mu", "alpha"]

Non-mutating swap

(() => {

    // knuthShuffle :: [a] -> [a]
    const knuthShuffle = xs =>
        enumFromTo(0, xs.length - 1)
        .reduceRight((a, i) => {
            const iRand = randomRInt(0, i);
            return i !== iRand ? (
                swapped(i, iRand, a)
            ) : a;
        }, xs);

    const test = () => knuthShuffle(
        (`alpha beta gamma delta epsilon zeta
          eta theta iota kappa lambda mu`)
        .split(/\s+/)
    );

    // Non mutating version of swapped

    // swapped :: Int -> Int -> [a] -> [a]
    const swapped = (iFrom, iTo, xs) =>
        xs.map(
            (x, i) => iFrom !== i ? (
                iTo !== i ? (
                    x
                ) : xs[iFrom]
            ) : xs[iTo]
        );

    // GENERIC FUNCTIONS ----------------------------------

    // enumFromTo :: Int -> Int -> [Int]
    const enumFromTo = (m, n) =>
        n >= m ? (
            iterateUntil(x => x >= n, x => 1 + x, m)
        ) : [];

    // iterateUntil :: (a -> Bool) -> (a -> a) -> a -> [a]
    const iterateUntil = (p, f, x) => {
        let vs = [x],
            h = x;
        while (!p(h))(h = f(h), vs.push(h));
        return vs;
    };

    // randomRInt :: Int -> Int -> Int
    const randomRInt = (low, high) =>
        low + Math.floor(
            (Math.random() * ((high - low) + 1))
        );

    // zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
    const zipWith = (f, xs, ys) =>
        Array.from({
            length: Math.min(xs.length, ys.length)
        }, (_, i) => f(xs[i], ys[i], i));

    // MAIN ---
    return test();
})();

Output:

e.g.

["mu", "theta", "beta", "eta", "delta", "epsilon", 
"kappa", "alpha", "gamma", "lambda", "zeta", "iota"]

Joy

DEFINE knuth-shuffle ==
(* Take the size of the array (without destroying it) *)
dup dup size
(* Generate a list of as many random numbers *)
[rand] [rem] enconcat map
(* Zip the two lists *)
swap zip
(* Sort according to the new index number *)
[small] [] [uncons unswonsd [first >] split [swons] dip2]
[enconcat] binrec
(* Delete the new index number *)
[second] map.

Using knuth-shuffle (file shuffle.joy):

(* Sorted array of 21 integers *)
[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20]
knuth-shuffle.

Command line:

joy shuffle.joy

Output:

usrlib  is loaded
inilib  is loaded
agglib  is loaded
[12 6 8 4 14 18 7 15 1 0 11 13 5 10 16 2 19 17 9 20 3]

jq

Works with: jq

Works with gojq, the Go implementation of jq

Neither the C nor the Go implementations of jq has a built-in PRNG, but both are designed with the Unix toolset philosophy in mind, so in this entry we will use an external source of randomness rather than one of the PRNGs defined in jq as at RC.

Specifically, we will use /dev/urandom like so:

< /dev/urandom tr -cd '0-9' | fold -w 1 | jq -RMnrc -f program.jq

where program.jq is the following program:

# 52-card deck:
def deck:
  [range(127137; 127148), range(127149; 127151),  # Spades
   range(127153; 127164), range(127165; 127167),  # Hearts
   range(127169; 127180), range(127181; 127183),  # Diamonds
   range(127185; 127196), range(127197; 127199)]  # Clubs
  ;

# For splitting a deck into hands :-)
def nwise($n):
  def n: if length <= $n then . else .[0:$n] , (.[$n:] | n) end;
  n;

# Output: a prn in range(0;$n) where $n is ., and $n > 0
def prn:
  if . == 1 then 0
  else . as $n
  | (($n-1)|tostring|length) as $w
  | [limit($w; inputs)] | join("") | tonumber
  | if . < $n then . else ($n | prn) end
  end;

def knuthShuffle:
  length as $n
  | if $n <= 1 then .
    else {i: $n, a: .}
    | until(.i ==  0;
        .i += -1
        | (.i + 1 | prn) as $j
        | .a[.i] as $t
        | .a[.i] = .a[$j]
        | .a[$j] = $t)
    | .a 
    end;

def task:
  [],
  [10,20],
  [10,20,30]
  | knuthShuffle;

task,
 (deck|knuthShuffle | nwise(13) | implode)

Output:

[]
[10,20]
[20,30,10]

🂶🃚🃈🃘🃊🂥🃉🂽🂣🂸🃂🂺🃗
🂵🃁🃇🂮🂹🃝🃆🂱🂻🂩🃋🂭🃖
🂢🃛🃕🃃🂾🃙🃞🂨🂪🂲🂷🃍🂫
🂦🃒🃔🂳🂡🃓🃄🂴🃅🃎🃑🂤🂧

Julia

Works with: Julia version 0.6

function knuthshuffle!(r::AbstractRNG, v::AbstractVector)
    for i in length(v):-1:2
        j = rand(r, 1:i)
        v[i], v[j] = v[j], v[i]
    end
    return v
end
knuthshuffle!(v::AbstractVector) = knuthshuffle!(Base.Random.GLOBAL_RNG, v)

v = collect(1:20)
println("# v = $v\n   -> ", knuthshuffle!(v))

Output:

# v = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]
   -> [16, 5, 17, 10, 2, 7, 20, 14, 4, 8, 19, 15, 18, 12, 11, 1, 9, 13, 3, 6]

Kotlin

object Knuth {
    internal val gen = java.util.Random()
}

fun <T> Array<T>.shuffle(): Array<T> {
    val a = clone()
    var n = a.size
    while (n > 1) {
        val k = Knuth.gen.nextInt(n--)
        val t = a[n]
        a[n] = a[k]
        a[k] = t
    }
    return a
}

fun main(args: Array<String>) {
    val str = "abcdefghijklmnopqrstuvwxyz".toCharArray()
    (1..10).forEach {
        val s = str.toTypedArray().shuffle().toCharArray()
        println(s)
        require(s.toSortedSet() == str.toSortedSet())
    }

    val ia = arrayOf(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
    (1..10).forEach {
        val s = ia.shuffle()
        println(s.distinct())
        require(s.toSortedSet() == ia.toSet())
    }
}

Output:

xdhsvtnumjgbywiqoapcelkrfz
pjnegbiyzuhsrclodftwkmaqvx
bkmqwhzregifyanvsltxjupodc
ewhxrlybnjqpvdsozaimkucgft
pdqgoaymbzefnjrwuvilsckxht
kcpagyuehjswdtvnzfrlbxqomi
iztsmaygkblephcjfnwvxurdoq
pltdyjwivsehckzfaxruqogmbn
nytfbpmjicgkaueoxwrhlsqvdz
epucijbvrhwyzdlsqftagxmkon
[7, 4, 5, 9, 2, 1, 3, 8, 10, 6]
[8, 10, 5, 4, 3, 6, 1, 2, 7, 9]
[7, 9, 2, 1, 10, 4, 6, 5, 8, 3]
[9, 6, 1, 8, 2, 5, 10, 3, 4, 7]
[7, 3, 6, 9, 10, 2, 5, 4, 1, 8]
[2, 9, 1, 7, 5, 10, 8, 4, 6, 3]
[4, 2, 7, 3, 8, 5, 6, 10, 1, 9]
[4, 8, 7, 6, 10, 5, 2, 1, 3, 9]
[6, 3, 9, 4, 5, 2, 10, 8, 1, 7]
[3, 6, 9, 2, 10, 8, 7, 5, 1, 4]

LabVIEW

Works with: LabVIEW version 8.0 Full Development System

Lambdatalk

{def shuffle

 {def shuffle.in
  {lambda {:a}
   {S.map {{lambda {:a :i}
                   {A.swap :i
                           {floor {* {random} {+ :i 1}}}  // j = random integer from 0 to i+1
                           :a}} :a}
          {S.serie {- {A.length :a} 1} 0 -1}}}}           // from length-1 to 0

 {lambda {:a}
  {let { {:b {A.duplicate :a}} }        // optionnaly prevents modifying the original array
   {S.replace \s by in {shuffle.in :b}  // trim extra spaces
    :b}}}}                              // return the new array
-> shuffle  

{def A.swap                                    // should probably be promoted as a primitive
 {lambda {:i :j :a}
  {let { {:i :i} 
         {:gja {A.get :j :a}} 
         {:b {A.set! :j {A.get :i :a} :a}}          
       } {let { {_ {A.set! :i :gja :b} }}}}}}  // side effect without any return value
-> A.swap

{def B {A.new a b c d e f g h i j k l m n o p q r s t u v w x y z}} 
-> B

{shuffle {B}}
-> [z,t,q,w,c,n,a,u,r,y,i,s,f,d,g,m,h,x,b,e,k,p,l,o,j,v]

Lasso

define staticarray->swap(p1::integer,p2::integer) => {
    fail_if(
        #p1 < 1 or #p2 < 1 or
        #p1 > .size or #p2 > .size,
        'invalid parameters'
    )
    #p1 == #p2
        ? return

    local(tmp) = .get(#p2)
    .get(#p2)  = .get(#p1)
    .get(#p1)  = #tmp
}
define staticarray->knuthShuffle => {
    loop(-from=.size, -to=2, -by=-1) => {
        .swap(math_random(1, loop_count), loop_count)
    }
}

(1 to 10)->asStaticArray->knuthShuffle&asString

Output:

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

Liberty BASIC

'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

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

Lhogho does not have a setitem, and also does things more 'function'ally.

to slice :lst :start :finish
	local "res
	make "res []
	for "i [:start :finish 1] [
		make "j item :i :lst
		make "res se :res :j
	]
	op :res
end

to setitem :n :lst :val
	local "lhs
	local "rhs
	make "lhs slice :lst 1 :n-1
	make "rhs slice :lst :n+1 count :lst
	op (se :lhs :val :rhs)
end

to swap :i :j :a
	local "t
	make "t item :i :a
	make "a setitem :i :a item :j :a
	make "a setitem :j :a :t
	op :a
end

to shuffle :a
	for "i [count :a 2] 
	[
		make "a swap 1 + random :i :i :a
	]
	op :a
end
 
make "a ( list 1 2 3 4 5 6 7 8 9 10 )
make "a shuffle :a
show :a

Lua

function table.shuffle(t)
  for n = #t, 1, -1 do
    local k = math.random(n)
    t[n], t[k] = t[k], t[n]
  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

M2000 Interpreter

Dim Base 0, A(3)
For k=1 to 6 {
      A(0):=10,20, 30
      For i=len(A())-1 to 0 {
            let j=random(0,i)
            Swap a(i), a(j)
      }
 Print A()           
}

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')

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 /Wolfram Language

Usage of built-in function:

RandomSample[{1, 2, 3, 4, 5, 6}]

Custom function:

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}
   ];
  input[[indices]]
  ]

Example:

Shuffle[{1, 2, 3, 4, 5, 6}]

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.

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

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.

function list = randSort(list)
    
    list = list( randperm(numel(list)) );
    
end

Maxima

/* Maxima has an implementation of Knuth shuffle */
random_permutation([a, b, c]);

Modula-3

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.

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

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

Nemerle

Shuffle[T] (arr : array[T]) : array[T]
{
    def rnd = Random();
    
    foreach (i in [0 .. (arr.Length - 2)])
        arr[i] <-> arr[(rnd.Next(i, arr.Length))];
    arr
}

NetRexx

version 1

/* NetRexx */
options replace format comments java crossref savelog symbols nobinary

import java.util.List

cards = [String -
    'hA', 'h2', 'h3', 'h4', 'h5', 'h6', 'h7', 'h8', 'h9', 'h10', 'hJ', 'hQ', 'hK' -
  , 'cA', 'c2', 'c3', 'c4', 'c5', 'c6', 'c7', 'c8', 'c9', 'c10', 'cJ', 'cQ', 'cK' -
  , 'dA', 'd2', 'd3', 'd4', 'd5', 'd6', 'd7', 'd8', 'd9', 'd10', 'dJ', 'dQ', 'dK' -
  , 'sA', 's2', 's3', 's4', 's5', 's6', 's7', 's8', 's9', 's10', 'sJ', 'sQ', 'sK' -
]
cardsLen = cards.length
deck = ArrayList(cardsLen)
loop c_ = 0 to cardsLen - 1
  deck.add(String(cards[c_]))
  end c_

showHand(deck)
deck = ArrayList shuffle(deck)
showHand(deck)

return

method shuffle(deck = List) public static binary returns List

  rn = Random()
  dl = deck.size

  loop i_ = dl - 1 to 1 by -1
    j_ = rn.nextInt(i_)
    __ = deck.get(i_)
    deck.set(i_, deck.get(j_))
    deck.set(j_, __)
    end i_

  return deck

method showHand(deck = ArrayList) public static binary

  dl = deck.size
  hl = dl % 4
  loop c_ = 0 to dl - 1 by hl
    d_ = c_ + hl
    if d_ >= dl then d_ = dl
    say ArrayList(deck.subList(c_, d_)).toString
    end c_
    say

  return

Output:

[hA, h2, h3, h4, h5, h6, h7, h8, h9, h10, hJ, hQ, hK]
[cA, c2, c3, c4, c5, c6, c7, c8, c9, c10, cJ, cQ, cK]
[dA, d2, d3, d4, d5, d6, d7, d8, d9, d10, dJ, dQ, dK]
[sA, s2, s3, s4, s5, s6, s7, s8, s9, s10, sJ, sQ, sK]

[s8, c10, sJ, c8, h10, h3, s3, d6, hJ, d3, c7, h5, s5]
[h8, d10, cK, s6, dQ, d9, d4, c4, c6, h6, cA, sA, dK]
[dJ, dA, d7, c2, d2, s10, sK, h2, c5, s7, cJ, d5, h9]
[c9, d8, c3, s9, cQ, sQ, h4, s4, hQ, h7, hK, hA, s2]

version 2

/* NetRexx ------------------------------------------------------------
* 08.01.2014 Walter Pachl modified to show state development a la Rexx
*--------------------------------------------------------------------*/
options replace format comments java crossref savelog symbols nobinary

import java.util.List

cards = [String '1','2','3','4','5','6','7','8','9','10']
cardsLen = cards.length
deck = ArrayList(cardsLen)
loop c_ = 0 to cardsLen - 1
  deck.add(String(cards[c_]))
  end c_

showHand(deck,'In ')
deck = ArrayList shuffle(deck)
showHand(deck,'Out')
return

method shuffle(deck = List) public static binary returns List
  rn = Random()
  dl = deck.size
  loop i_ = dl - 1 to 1 by -1
    j_ = rn.nextInt(i_)
    __ = deck.get(i_)
    deck.set(i_, deck.get(j_))
    deck.set(j_, __)
    say i_ j_ ArrayList(deck.subList(0,i_+1)).toString
    end i_
  return deck

method showHand(deck = ArrayList,tag=REXX) public static binary
  say tag ArrayList(deck.subList(0,deck.size)).toString
  return

Output:

In  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
9 5 [1, 2, 3, 4, 5, 10, 7, 8, 9, 6]
8 4 [1, 2, 3, 4, 9, 10, 7, 8, 5]
7 2 [1, 2, 8, 4, 9, 10, 7, 3]
6 0 [7, 2, 8, 4, 9, 10, 1]
5 4 [7, 2, 8, 4, 10, 9]
4 1 [7, 10, 8, 4, 2]
3 2 [7, 10, 4, 8]
2 0 [4, 10, 7]
1 0 [10, 4]
Out [10, 4, 7, 8, 2, 9, 1, 3, 5, 6]

Nim

Note that the function "shuffle" exists in the standard module "random" and that it uses the Knuth shuffle.

import random
randomize()

proc shuffle[T](x: var openArray[T]) =
  for i in countdown(x.high, 1):
    let j = rand(i)
    swap(x[i], x[j])

var x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
shuffle(x)
echo x

Objective-C

#import <Foundation/Foundation.h>

@interface NSMutableArray (KnuthShuffle)
- (void)knuthShuffle;
@end
@implementation NSMutableArray (KnuthShuffle)
- (void)knuthShuffle {
  for (NSUInteger i = self.count-1; i > 0; i--) {
    NSUInteger j = arc4random_uniform(i+1);
    [self exchangeObjectAtIndex:i withObjectAtIndex:j];
  }
}
@end

int main() {
  @autoreleasepool {
    NSMutableArray *x = [NSMutableArray arrayWithObjects:@0, @1, @2, @3, @4, @5, @6, @7, @8, @9, nil];
    [x knuthShuffle];
    NSLog(@"%@", x);
  }
  return 0;
}

Output:

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

Oforth

Works with any object that has the property to be Indexable (Lists, Intervals, ...) Returns a new list

Indexable method: shuffle
| s i l |
   self asListBuffer ->l
   self size dup ->s 1- loop: i [ s i - rand i +  i  l swapValues ]
   l dup freeze ;

Ol

There are two functions - one for tuples (that speedy) and second for lists (that uses previous one).

Ol is functional language, so we should make a copy of shuffling tuple and return this shuffled copy.

(define (shuffle tp)
   (let ((items (vm:cast tp (type tp)))) ; make a copy
      (for-each (lambda (i)
            (let ((a (ref items i))
                  (j (+ 1 (rand! i))))
               (set-ref! items i (ref items j))
               (set-ref! items j a)))
         (reverse (iota (size items) 1)))
      items))

(define (list-shuffle tp)
   (map (lambda (i)
         (list-ref tp i))
      (tuple->list
         (shuffle (list->tuple (iota (length tp)))))))

Testing:

(define items (tuple 1 2 3 4 5 6 7 8 9))
(print "tuple before: " items)
(print "tuple after: " (shuffle items))

(define items (list 1 2 3 4 5 6 7 8 9))
(print "list before: " items)
(print "list after: " (list-shuffle items))

Output:

tuple before: #[1 2 3 4 5 6 7 8 9]
tuple after: #[9 4 1 3 7 2 5 6 8]
list before: (1 2 3 4 5 6 7 8 9)
list after: (8 2 4 9 5 3 6 1 7)

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}}

PARI/GP

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))

Pascal

program Knuth;

const
  startIdx = -5;
  max = 11;
type
  tmyData = string[9];
  tmylist = array [startIdx..startIdx+max-1] of tmyData;

procedure InitList(var a: tmylist);
var
  i: integer;
Begin
  for i := Low(a) to High(a) do
    str(i:3,a[i])
end;

procedure shuffleList(var a: tmylist);
var
  i,k : integer;
  tmp: tmyData;
begin
  for i := High(a)-low(a) downto 1 do begin
    k := random(i+1) + low(a);
    tmp := a[i+low(a)]; a[i+low(a)] := a[k]; a[k] := tmp
  end
end;

procedure DisplayList(const a: tmylist);
var
  i : integer;
Begin
  for i := Low(a) to High(a) do
    write(a[i]);
  writeln
end;

{ Test and display }
var
 a: tmylist;
 i: integer;
begin
  randomize;
  InitList(a);
  DisplayList(a);
  writeln;
  For i := 0 to 4 do
  Begin
    shuffleList(a);
    DisplayList(a);
  end;
end.

Output:

 -5 -4 -3 -2 -1  0  1  2  3  4  5

 -5  4  0 -4  3 -1 -3  1 -2  5  2
  2  0  1 -5 -1  5 -3  4 -2  3 -4
  3 -1 -2  5 -4  1  2 -5 -3  4  0
 -4  1 -1 -5  5  2  0  3 -2 -3  4
 -3 -5  4  2 -4  0  5  3  1 -1 -2

PascalABC.NET

procedure Shuffle<T>(a: array of T);
begin
  for var i := a.Length - 1 downto 1 do
    Swap(a[i], a[Random(i + 1)]);
end;

begin
  var a := Arr(1..9);
  Shuffle(a);
  a.Print;
end.

Output:

5 8 6 1 3 4 2 9 7

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;
}

Phix

sequence cards = tagset(52)
puts(1,"Before: ")      ?cards
for i=52 to 1 by -1 do
    integer r = rand(i)
    {cards[r],cards[i]} = {cards[i],cards[r]}
end for
puts(1,"After:  ")      ?cards
puts(1,"Sorted: ")      ?sort(cards)

Output:

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

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]);
	}
}

Picat

go =>
  _ = random2(),
  L = 1..10,
  println(l_before=L),
  knuth_shuffle(L),
  println('l_after '=L),
  nl.

knuth_shuffle(L) => 
  foreach(I in L.len..-1..1)
    J = random(1,I),
    Tmp = L[I],
    L[I] := L[J],
    L[J] := Tmp
  end.

Output:

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

PicoLisp

(seed (in "/dev/urandom" (rd 8)))

(de knuth (Lst)
   (for (N (length Lst) (>= N 2) (dec N))
      (let I (rand 1 N)
         (xchg (nth Lst N) (nth Lst I)) ) ) )

(let L (range 1 15)
   (println 'before L)
   (knuth L)
   (println 'after L) )

Output:

before (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15)
after (12 15 4 13 11 9 7 1 2 14 5 6 8 3 10)

PL/I

version 1

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;

version 2

 kn: Proc Options(main);
 /*--------------------------------------------------------------------
 * 07.01.2014 Walter Pachl  translated from REXX version 2
 * Iteration i: only the first i elements are candidates for swapping
 *-------------------------------------------------------------------*/
 Dcl T(10) Bin Fixed(15) Init(1,2,3,4,5,6,7,8,9,10);
 Dcl (i,j,temp) Bin Fixed(15) init(0);
 Dcl h Char(6);
 Call show('In',10);                   /* show start                 */
 do i = 10 To 2 By -1;                 /* shuffle                    */
   j=random()*i+1;
   Put string(h)Edit(i,j)(f(2),f(3));
   temp=t(i); t(i)=t(j); t(j)=temp;    /* t(i) <-> t(j)              */
   Call show(h,i);                     /* show intermediate states   */
   end;
 Call show('Out',10);                  /* show final state           */

 show: Proc(txt,n);
 Dcl txt Char(*);
 Dcl n   Bin Fixed(15);
 Put Edit(txt,(t(k) do k=1 To n))(Skip,a(7),10(f(3)));
 End;
 end;

Output:

In       1  2  3  4  5  6  7  8  9 10
10  5    1  2  3  4 10  6  7  8  9  5
 9  1    9  2  3  4 10  6  7  8  1
 8  7    9  2  3  4 10  6  8  7
 7  2    9  8  3  4 10  6  2
 6  6    9  8  3  4 10  6
 5  3    9  8 10  4  3
 4  2    9  4 10  8
 3  3    9  4 10
 2  1    4  9
Out      4  9 10  8  3  6  2  7  1  5

PowerShell

Works with: PowerShell version 3

$A = 1, 2, 3, 4, 5
Get-Random $A -Count $A.Count

Works with: PowerShell version 2

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
}

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

EnableExplicit

Procedure KnuthShuffle(Array a(1))
   Protected i, last = ArraySize(a())
   
   For i = last To 1 Step -1
      Swap a(i), a(Random(i)) 
   Next 
EndProcedure

Procedure.s ArrayToString(Array a(1))
   Protected ret$, i, last = ArraySize(a())
   
   ret$ = Str(a(0))
   For i = 1 To last
      ret$ + "," + Str(a(i))
   Next
   ProcedureReturn ret$
EndProcedure


#NumElements = 10

Dim a(#NumElements-1)
Define i

For i = 0 To #NumElements-1
   a(i) = i
Next

KnuthShuffle(a())
Debug "shuffled: " + ArrayToString(a())

Output:

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

Python

Python's standard library function random.shuffle uses this algorithm and so should normally be used. The function below is very similar:

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)

Output:

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

We could also write our own Knuth shuffle function as a fold, with a non-mutating swap function:

Works with: Python version 3.7

'''Knuth shuffle as a fold'''

from functools import reduce
from random import randint


# knuthShuffle :: [a] -> IO [a]
def knuthShuffle(xs):
    '''A pseudo-random shuffle of the elements in xs.'''
    return reduce(
        swapped,
        enumerate(randoms(len(xs))), xs
    )


# swapped :: (Int, Int) -> [a] -> [a]
def swapped(xs, ij):
    '''New list in which the elements at indices
       i and j of xs are swapped.
    '''
    def go(a, b):
        if a != b:
            m, n = (a, b) if b > a else (b, a)
            l, ht = splitAt(m)(xs)
            ys, zs = splitAt((n - m) - 1)(ht[1:])
            return l + [zs[0]] + ys + [ht[0]] + zs[1:]
        else:
            return xs
    i, j = ij
    z = len(xs) - 1
    return xs if i > z or j > z else go(i, j)


# randoms :: Int -> IO [Int]
def randoms(n):
    '''Pseudo-random list of n - 1 indices.
    '''
    return list(map(randomRInt(0)(n - 1), range(1, n)))


# TEST ----------------------------------------------------
# main :: IO ()
def main():
    '''Repeated Knuth shuffles of ['a' .. 'k']'''

    print(
        fTable(main.__doc__ + ':\n')(str)(lambda x: ''.join(x))(
            lambda _: knuthShuffle(list('abcdefghijk'))
        )(range(1, 11))
    )


# GENERIC -------------------------------------------------

# randomRInt :: Int -> Int -> IO () -> Int
def randomRInt(m):
    '''The return value of randomRInt is itself
       a function. The returned function, whenever
       called, yields a a new pseudo-random integer
       in the range [m..n].
    '''
    return lambda n: lambda _: randint(m, n)


# splitAt :: Int -> [a] -> ([a], [a])
def splitAt(n):
    '''A tuple pairing the prefix of length n
       with the rest of xs.
    '''
    return lambda xs: (xs[0:n], xs[n:])


# FORMATTING -----------------------------------------------------------

# fTable :: String -> (a -> String) ->
#                     (b -> String) -> (a -> b) -> [a] -> String
def fTable(s):
    '''Heading -> x display function -> fx display function ->
                     f -> xs -> tabular string.
    '''
    def go(xShow, fxShow, f, xs):
        ys = [xShow(x) for x in xs]
        w = max(map(len, ys))
        return s + '\n' + '\n'.join(map(
            lambda x, y: y.rjust(w, ' ') + ' -> ' + fxShow(f(x)),
            xs, ys
        ))
    return lambda xShow: lambda fxShow: lambda f: lambda xs: go(
        xShow, fxShow, f, xs
    )


# MAIN ---
if __name__ == '__main__':
    main()

Output:

Repeated Knuth shuffles of ['a' .. 'k']:

 1 -> kdafbhigejc
 2 -> jhdkgeicabf
 3 -> aciebghdfkj
 4 -> fjahegibckd
 5 -> cabejfidkgh
 6 -> gbecahfkijd
 7 -> jegchkdifba
 8 -> fcjkghiadeb
 9 -> ihfebdajgkc
10 -> hjkigbadcfe

Quackery

The word shuffle is predefined in Quackery (and shown below) - it shuffles a nest (an immutable dynamic array) by removing random items from the nest (i.e. creating a new array with that item removed) and appending them to an (initially empty) nest (i.e. creating a new array with that item appended). It fits the criteria for this task with the relaxations noted at the end of the task description.

The word knuffle is probably an entirely in-place shuffle, if the dynamic memory allocation routines for a particular implementation of Quackery allow in-place modification of a dynamic array when there is only a single pointer to the array. (After the first invocation of poke inside [exch] there will definitely only be a single pointer to the array.)

  [ [] swap dup size times
      [ dup size random pluck
        nested rot join swap ]
    drop ]                      is shuffle (     [ --> [ )

  [ temp put
    2dup swap
    temp share swap peek
    temp share rot peek
    dip 
      [ swap
        temp take 
        swap poke 
        temp put ]  
    swap 
    temp take 
    swap poke ]                 is [exch]  ( n n [ --> [ )

  [ dup size 1 - times
      [ i 1+ dup 1+ random
        rot [exch] ] ]         is knuffle (     [ --> [ )

Output:

Testing in the Quackery shell (REPL).

/O> ' [ 10 11 12 13 14 15 16 17 18 19 ] 
... 10 times [ knuffle dup echo cr ]
... 
[ 14 19 11 13 18 17 10 16 12 15 ]
[ 10 15 18 17 13 14 12 16 11 19 ]
[ 19 11 10 14 15 16 12 18 17 13 ]
[ 14 13 19 15 10 16 11 17 18 12 ]
[ 18 13 11 15 17 16 12 10 14 19 ]
[ 18 17 10 13 12 19 15 16 14 11 ]
[ 10 19 17 12 13 14 15 16 18 11 ]
[ 10 16 17 18 13 11 15 19 12 14 ]
[ 18 19 17 11 10 14 16 12 13 15 ]
[ 19 11 10 14 16 12 17 18 15 13 ]

Stack: [ 10 15 13 14 12 19 16 11 17 18 ] 

/O> 10 times [ shuffle dup echo cr ]
... 
[ 10 13 11 14 18 15 12 17 16 19 ]
[ 12 19 16 17 10 13 14 11 18 15 ]
[ 11 14 12 17 15 19 13 16 18 10 ]
[ 17 15 14 18 16 19 11 10 13 12 ]
[ 14 15 18 13 10 16 17 12 19 11 ]
[ 12 14 11 16 15 10 19 18 17 13 ]
[ 14 12 15 18 16 19 11 10 13 17 ]
[ 18 19 15 16 14 12 13 11 17 10 ]
[ 14 18 19 11 16 12 13 15 17 10 ]
[ 17 19 11 18 14 10 12 13 16 15 ]

Stack: [ 17 19 11 18 14 10 12 13 16 15 ]

R

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

Original Fisher-Yates version

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
}

Knuth variation

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"

Short version

After accounting for R being 1-indexed rather than 0-indexed, it's not hard to implement the pseudo-code given in the task almost exactly:

knuth <- function(vec)
{
  last <- length(vec)
  if(last >= 2)
  {
    for(i in last:2)
    {
      j <- sample(seq_len(i), size = 1)
      vec[c(i, j)] <- vec[c(j, i)]
    }
  }
  vec
}
#Demonstration:
knuth(integer(0))
knuth(c(10))
replicate(10, knuth(c(10, 20)))
replicate(10, knuth(c(10, 20, 30)))
knuth(c("Also", "works", "for", "strings"))

Output:

> knuth(integer(0))
integer(0)
> knuth(c(10))
[1] 10
> replicate(10, knuth(c(10, 20)))
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,]   20   20   10   10   20   10   20   10   20    10
[2,]   10   10   20   20   10   20   10   20   10    20
> replicate(10, knuth(c(10, 20, 30)))
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,]   30   10   20   20   30   30   10   30   10    10
[2,]   10   20   30   10   10   10   20   20   20    20
[3,]   20   30   10   30   20   20   30   10   30    30
> knuth(c("Also", "works", "for", "strings"))
[1] "strings" "Also"    "for"     "works"

Racket

#lang racket

(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 (knuth-shuffle x)
  (if (list? x)
    (vector->list (knuth-shuffle (list->vector x)))
    (begin (for ([i (in-range (sub1 (vector-length x)) 0 -1)])
             (define r (random (+ i 1)))
             (swap! x i r))
           x)))

(knuth-shuffle '(1 2 3 4))

Raku

(formerly Perl 6)

Works with: Rakudo version #21 "Seattle"

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;
}

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

my @deck = @cards.pick(*);

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

version 0, card pips

/*REXX program shuffles a deck of playing cards (with jokers)  using the  Knuth shuffle.*/
rank= 'A 2 3 4 5 6 7 8 9 10 J Q K'               /*pips  of the various playing cards.  */
suit= '♣♠♦♥'                                     /*suit   "  "     "       "      "     */
parse arg seed .                                 /*obtain optional argument from the CL.*/
if datatype(seed,'W')  then call random ,,seed   /*maybe use for  RANDOM  repeatability.*/
say '══════════════════ getting a new deck out of the box ···'
@.1= 'highJoker'                                 /*good decks have a color joker, and a */
@.2= 'lowJoker'                                  /*            ··· black & white joker. */
cards=2                                          /*now, there're 2 cards are in the deck*/
               do j     =1  for length(suit)
                    do k=1  for  words(rank);      cards=cards + 1
                    @.cards=substr(suit, j, 1)word(rank, k)
                    end  /*k*/
               end       /*j*/
call show
say;      say '══════════════════ shuffling' cards "cards ···"
     do s=cards  by -1  to 2;  ?=random(1,s);  parse value  @.?  @.s   with   @.s  @.?
                                                 /*  [↑]  swap two cards in the deck.   */
     end   /*s*/
call show
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
show: _=;      do m=1  for cards;   _=_ @.m;   end  /*m*/;         say _;           return

output

══════════════════ getting a new deck out of the box ···
 highJoker lowJoker ♣A ♣2 ♣3 ♣4 ♣5 ♣6 ♣7 ♣8 ♣9 ♣10 ♣J ♣Q ♣K ♠A ♠2 ♠3 ♠4 ♠5 ♠6 ♠7 ♠8 ♠9 ♠10 ♠J ♠Q ♠K ♦A ♦2 ♦3 ♦4 ♦5 ♦6 ♦7 ♦8 ♦9 ♦10 ♦J ♦Q ♦K ♥A ♥2 ♥3 ♥4 ♥5 ♥6 ♥7 ♥8 ♥9 ♥10 ♥J ♥Q ♥K

══════════════════ shuffling 54 cards ···
 ♣J ♦3 ♥5 ♣10 ♥2 ♥J ♣6 ♦4 ♠2 ♥8 ♥A ♠A ♣9 ♣5 ♠7 ♦6 ♥6 ♠10 ♥9 ♦2 lowJoker ♥3 ♠5 ♠K ♣K ♣8 ♣Q ♠Q ♣2 ♦8 ♠4 ♣7 ♦5 ♥K ♣A ♠6 ♠J ♦Q ♦7 ♠9 ♦10 ♦K ♣4 ♥7 ♣3 ♠3 highJoker ♦A ♥4 ♦J ♠8 ♦9 ♥Q ♥10

version 1, card names

This version handles items with (leading/trailing/embedded) blanks in them, so parse isn't an option for shuffling.

/*REXX program shuffles a deck of playing cards (with jokers)  using the  Knuth shuffle.*/
rank = 'ace deuce trey 4 5 6 7 8 9 10 jack queen king'         /*use pip names for cards*/
suit = 'club spade diamond heart'                              /* "  suit  "    "    "  */
say '══════════════════ getting a new deck out of the box ···'
@.1= '  color joker'                             /*good decks have a color joker, and a */
@.2= '    b&w joker'                             /*            ··· black & white joker. */
cards=2                                          /*now, there're 2 cards are in the deck*/
          do j     =1  for words(suit)
               do k=1  for words(rank);       cards=cards+1    /*bump the card counter. */
               @.cards=right(word(suit,j),7)  word(rank,k)     /*assign a card name.    */
               end  /*k*/
          end       /*j*/

call show 'ace'                                  /*inserts blank when an  ACE  is found.*/
say;  say '══════════════════ shuffling' cards "cards ···"

          do s=cards  by -1  to 2;   ?=random(1,s);   _=@.?;   @.?=@.s;    @.s=_
          end   /*s*/                            /* [↑]  swap two cards in the deck.    */
call show
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
show: parse arg break;    say                    /*get separator card, show blank line. */
        do m=1  for cards                        /* [↓]  traipse through the card deck. */
        if pos(break,@.m)\==0  then say          /*show a blank to read cards easier.   */
        say 'card'  right(m, 2)    '───►'   @.m  /*display a particular card from deck. */
        end   /*m*/
return

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

version 2

/* REXX ---------------------------------------------------------------
* 05.01.2014 Walter Pachl
*            borrow one improvement from version 1
* 06.01.2014 removed    -"-  (many tests cost more than few "swaps")
*--------------------------------------------------------------------*/
Call random ,,123456                   /* seed for random            */
Do i=1 To 10; a.i=i; End;              /* fill array                 */
Call show 'In',10                      /* show start                 */
do i = 10 To 2 By -1                   /* shuffle                    */
  j=random(i-1)+1;
  h=right(i,2) right(j,2)
  Parse Value a.i a.j With a.j a.i     /* a.i <-> a.j                */
  Call show h,i                        /* show intermediate states   */
  end;
Call show 'Out',10                     /* show fomaö state           */
Exit

show: Procedure Expose a.
Parse Arg txt,n
ol=left(txt,6);
Do k=1 To n; ol=ol right(a.k,2); End
Say ol
Return

Output:

In      1  2  3  4  5  6  7  8  9 10
10  2   1 10  3  4  5  6  7  8  9  2
 9  6   1 10  3  4  5  9  7  8  6
 8  6   1 10  3  4  5  8  7  9
 7  3   1 10  7  4  5  8  3
 6  5   1 10  7  4  8  5
 5  1   8 10  7  4  1
 4  1   4 10  7  8
 3  1   7 10  4
 2  1  10  7
Out    10  7  4  8  1  5  3  9  6  2

Ring

# Project : Knuth shuffle

items = list(52)
for n = 1 to len(items) 
      items[n] = n
next
knuth(items)
showarray(items)

func knuth(items)
       for i = len(items) to 1 step -1
            j = random(i-1) + 1 
            if i != j
               temp = items[i]
               items[i] = items[j]
               items[j] = temp
            ok
       next

func showarray(vect)
       see "["
       svect = ""
       for n = 1 to len(vect)
           svect = svect + vect[n] + " "
       next
       svect = left(svect, len(svect) - 1)
       see svect
       see "]" + nl

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

RPL

Indexes of RPL lists and arrays start at 1.

Works with: Halcyon Calc version 4.2.7

RPL code

Comment

≪ 
   DUP SIZE 2 FOR j
      j RAND * CEIL
      GET LAST OVER j GET PUT j ROT PUT
   -1 STEP
≫ 'KNUTH' STO

KNUTH ( {items} ➝ {items} ) // works also with [items]
for j from last downto 2 do:
   let k = random integer in range 1 ≤ k ≤ j
   swap items[j] with items[k]

Ruby

Translation of: Tcl

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]}"}

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 idiomatic:

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

Run BASIC

dim cards(52) 
for i = 1 to 52                ' make deck
  cards(i) = i
next
 
for i = 52 to 1 step -1        ' shuffle deck
   r = int((rnd(1)*i) + 1)
   if r <> i then 
     hold     = cards(r)
     cards(r) = cards(i)
     cards(i) = hold
   end if
next
 
print "== Shuffled Cards =="  ' print shuffled cards
for i = 1 to 52
    print cards(i);" ";
    if i mod 18 = 0 then print
next
print

Rust

Library: rand

use rand::Rng;

extern crate rand;

fn knuth_shuffle<T>(v: &mut [T]) {
    let mut rng = rand::thread_rng();
    let l = v.len();

    for n in 0..l {
        let i = rng.gen_range(0, l - n);
        v.swap(i, l - n - 1);
    }
}

fn main() {
    let mut v: Vec<_> = (0..10).collect();

    println!("before: {:?}", v);
    knuth_shuffle(&mut v);
    println!("after:  {:?}", v);
}

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
}

Scheme

A functional version, using lists (inefficient), somewhat unusual in reversing the entire initial sublist on each pass instead of just swapping:

#!r6rs
(import (rnrs base (6))
        (srfi :27 random-bits))

(define (semireverse li n)
  (define (continue front back n)
    (cond
      ((null? back) front)
      ((zero? n) (cons (car back) (append front (cdr back))))
      (else (continue (cons (car back) front) (cdr back) (- n 1)))))
  (continue '() li n))

(define (shuffle li)
  (if (null? li)
      ()
      (let
          ((li-prime (semireverse li (random-integer (length li)))))
        (cons (car li-prime) (shuffle (cdr li-prime))))))

A mutable version, using vectors (efficient):

#!r6rs
(import (rnrs base (6))
        (srfi :27 random-bits))

(define (vector-swap! vec i j)
  (let
      ((temp (vector-ref vec i)))
    (vector-set! vec i (vector-ref vec j))
    (vector-set! vec j temp)))

(define (countdown n)
  (if (zero? n)
      ()
      (cons n (countdown (- n 1)))))

(define (vector-shuffle! vec)
  (for-each
   (lambda (i)
     (let
         ((j (random-integer i)))
       (vector-swap! vec (- i 1) j)))
   (countdown (vector-length vec))))

Scratch

See Knuth's shuffle in action. Visit this Scratch implementation to see a demo and inspect its source.

Seed7

$ include "seed7_05.s7i";

const type: intArray is array integer;

const proc: shuffle (inout intArray: a) is func
  local
    var integer: i is 0;
    var integer: k is 0;
    var integer: tmp is 0;
  begin
    for i range maxIdx(a) downto 2 do
      k := rand(1, i);
      tmp := a[i];
      a[i] := a[k];
      a[k] := tmp;
    end for;
  end func;

const proc: main is func
  local
    var intArray: a is 10 times 0;
    var integer: i is 0;
  begin
    for key i range a do
      a[i] := i;
    end for;
    shuffle(a);
    for i range a do
      write(i <& " ");
    end for;
    writeln;
  end func;

Output:

7 5 6 8 3 10 9 4 2 1

SenseTalk

set list to 1..9 -- a range, will become a list as needed
set last to the number of items in list

repeat with i = last down to 2 -- in SenseTalk, the first index in a list is 1
	set j = random (1,i-1)
	set [item i of list, item j of list] to [item j of list, item i of list] -- swap items
end repeat

put list

Output:

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

SETL

program knuth_shuffle;
    setrandom(0);

    array := [1..10];
    print("Before shuffling:", array);
    shuffle(array);
    print("After shuffling: ", array);

    proc shuffle(rw tup);
        loop for i in [1..#tup-1] do
            j := random [i+1..#tup];
            [tup(i), tup(j)] := [tup(j), tup(i)];
        end loop;
    end proc;
end program;

Output:

Before shuffling: [1 2 3 4 5 6 7 8 9 10]
After shuffling:  [7 8 1 10 2 5 6 9 4 3]

Sidef

func knuth_shuffle(a) {
    for i (a.len ^.. 1) {
        var j = i.irand
        a[i, j] = a[j, i]
    }
    return a
}

say knuth_shuffle(@(1..10))

Output:

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

Smalltalk

Works with: GNU 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
    ]      
  ]
].

Testing

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

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<i = i + 1> span(' ') = :s(sa1)f(return)
s2a_end

*       # Array -> string
        define('a2s(a)i') :(a2s_end)
a2s     a2s = a2s a<i = i + 1> ' ' :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

Output:

1 2 3 4 5 6 7 8 9 10 ->
2 10 4 9 1 5 6 8 7 3

SparForte

As a structured script.

#!/usr/local/bin/spar
pragma annotate( summary, "shuffle" );
pragma annotate( description, "Implement the Knuth shuffle (aka the" );
pragma annotate( description, "Fisher-Yates-Durstenfeld shuffle)" );
pragma annotate( description, "for an integer array (or, if possible, an array of any" );
pragma annotate( description, "type). The Knuth shuffle is used to create a random" );
pragma annotate( description, "permutation of an array." );
pragma annotate( description, "Note: spar has a built-in arrays.shuffle() function that does this." );
pragma annotate( see_also, "http://rosettacode.org/wiki/Knuth_shuffle" );
pragma annotate( author, "Ken O. Burtch" );
pragma license( unrestricted );

pragma restriction( no_external_commands );

procedure shuffle is

  subtype array_element_type is string;
  type magic_items is array(1..3) of array_element_type;

  a : magic_items := ( "bell", "book", "candle" );
  t : array_element_type;
  k : integer;

begin

  for i in reverse arrays.first( a ) .. arrays.last( a )-1 loop
    k := integer( numerics.rnd( i+1 ) ) - 1 + arrays.first(a);
    t := a(i);
    a(i) := a(k);
    a(k) := t;
  end loop;

  for i in arrays.first( a ) .. arrays.last( a ) loop
    ? a(i);
  end loop;

end shuffle;

Output:

$ spar shuffle
bell
candle
book

$ spar shuffle
candle
bell
book

Stata

mata
function shuffle(a) {
	n = length(a)
	r = runiformint(1,1,1,1..n)
	for (i=n; i>=2; i--) {
		j = r[i]
		x = a[i]
		a[i] = a[j]
		a[j] = x
	}
	return(a)
}

shuffle(1..10)
end

Output

        1    2    3    4    5    6    7    8    9   10
    +---------------------------------------------------+
  1 |   8   10    9    1    7    2    6    4    3    5  |
    +---------------------------------------------------+

Swift

Version that works in Swift 5.x and probably above. This version works for any mutable bidirectional collection although O(n) time complexity can only be guaranteed for a RandomAccessCollection where the index meets the Apple requirements for O(1) access to elements.

Also has the advantage that it implemented the algorithm as written at the top of this page i.e. it counts down from the end and picks the random element from the part of the array that has not yet been traversed.

extension BidirectionalCollection where Self: MutableCollection
{
	mutating func shuffleInPlace()
	{
		var index = self.index(before: self.endIndex)
		while index != self.startIndex
		{
			// Note the use of ... below. This makes the current element eligible for being selected
			let randomInt = Int.random(in: 0 ... self.distance(from: startIndex, to: index))
			let randomIndex = self.index(startIndex, offsetBy: randomInt)
			self.swapAt(index, randomIndex)
			index = self.index(before: index)
		}
	}
}

var a = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
a.shuffleInPlace()
print(a)

Output:

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

Simple version (any Swift version): Extend Array with shuffle methods; using arc4random_uniform from C stdlib:

import func Darwin.arc4random_uniform

extension Array {
    
    func shuffle() -> Array {
        
        var result = self; result.shuffleInPlace(); return result
    }
    
    mutating func shuffleInPlace() {
        
        for i in 1 ..< count { swap(&self[i], &self[Int(arc4random_uniform(UInt32(i+1)))]) }
    }
    
}

// Swift 2.0:
print([1, 2, 3, 4, 5, 6, 7, 8, 9, 10].shuffle())
// Swift 1.x:
//println([1, 2, 3, 4, 5, 6, 7, 8, 9, 10].shuffle())

Output:

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

Generic version (any Swift version): While the above code is generic in that it works with arrays of any element type, we can use generic global functions to define shuffling for any mutable collection with random-access index type which is far more generic than the above code:

import func Darwin.arc4random_uniform

func shuffleInPlace<T: MutableCollectionType where T.Index: RandomAccessIndexType>(inout collection: T) {
    
    let i0 = collection.startIndex
    
    for i in i0.successor() ..< collection.endIndex {
        
        let j = i0.advancedBy(numericCast(
                    arc4random_uniform(numericCast(
                        i0.distanceTo()
                    )+1)
                ))
        
        swap(&collection[i], &collection[j])
    }
}

func shuffle<T: MutableCollectionType where T.Index: RandomAccessIndexType>(collection: T) -> T {
    
    var result = collection
    
    shuffleInPlace(&result)
    
    return result
}

// Swift 2.0:
print(shuffle([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))
// Swift 1.x:
//println(shuffle([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))

Output:

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

Works with: Swift version 2.0

While the above solutions work with Swift 2.0 as they are, we can use Swift 2.0's Protocol Oriented Programming features to add shuffling methods to any mutable collection that has a random-access index:

import func Darwin.arc4random_uniform

// Define a protocol for shuffling:

protocol Shufflable {
    
    @warn_unused_result (mutable_variant="shuffleInPlace")
    func shuffle() -> Self
    
    mutating func shuffleInPlace()
    
}

// Provide a generalized implementation of the shuffling protocol for any mutable collection with random-access index:

extension Shufflable where Self: MutableCollectionType, Self.Index: RandomAccessIndexType {
    
    func shuffle() -> Self {
        
        var result = self
        
        result.shuffleInPlace()
        
        return result
    }
    
    mutating func shuffleInPlace() {
        
        let i0 = startIndex
        
        for i in i0+1 ..< endIndex {
            
            let j = i0.advancedBy(numericCast(
                        arc4random_uniform(numericCast(
                            i0.distanceTo(i)
                        )+1)
                    ))

            swap(&self[i], &self[j])
        }
    }
    
}

// Declare Array's conformance to Shufflable:

extension Array: Shufflable 
    { /* Implementation provided by Shufflable protocol extension */ }

print([1, 2, 3, 4, 5, 6, 7, 8, 9, 10].shuffle())

Output:

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

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

As a test of skewing (an indicator of a poor implementation) this code was used:

% 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

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

Transd

#lang transd

MainModule: {
    // Define an abstract type Vec to make the shuffling
    // function polymorphic
    Vec: typedef(Lambda<:Data Bool>(λ d :Data() 
        (starts-with (_META_type d) "Vector<"))),

    kshuffle: (λ v Vec() locals: rnd 0 
        (for n in Range( (- (size v) 1) 0) do
            (= rnd (randr (to-Int n)))
            (with tmp (cp (get v n))
                (set-el v n (get v rnd))
                (set-el v rnd tmp))
        )
        (lout v)
    ),
	_start: (λ 
        (with v [10,20,30,40,50,60,70,80,90,100]
            (lout "Original:\n" v)
            (lout "Shuffled:")
            (kshuffle v))
        (lout "")
        (with v ["A","B","C","D","E","F","G","H"]
            (lout "Original:\n" v)
            (lout "Shuffled:")
            (kshuffle (cp v))
            // Transd has a built-in function that performs the same
            // kind of random shuffle
            (lout "Built-in shuffle:")
            (lout (shuffle v)))
    )
}

Output:

Original:
[10, 20, 30, 40, 50, 60, 70, 80, 90, 100]
Shuffled:
[20, 60, 100, 80, 70, 10, 50, 90, 40, 30]

Original:
["A", "B", "C", "D", "E", "F", "G", "H"]
Shuffled:
["G", "A", "D", "B", "F", "E", "C", "H"]
Built-in shuffle:
["A", "E", "C", "H", "G", "F", "B", "D"]

TUSCRIPT

$$ MODE TUSCRIPT
oldnumbers=newnumbers="",range=20
LOOP nr=1,#range
 oldnumbers=APPEND(oldnumbers,nr)
ENDLOOP

PRINT "before ",oldnumbers

LOOP r=#range,1,-1
 RANDNR=RANDOM_NUMBERS (1,#r,1)
 shuffle=SELECT (oldnumbers,#randnr,oldnumbers)
 newnumbers=APPEND(newnumbers,shuffle)
ENDLOOP

PRINT "after  ",newnumbers

Output:

before 1'2'3'4'5'6'7'8'9'10'11'12'13'14'15'16'17'18'19'20
after  7'16'13'11'1'9'15'4'18'14'3'12'17'8'19'20'6'5'2'10

uBasic/4tH

PRINT "before:"
FOR L = 0 TO 51
    @(L) = L
    PRINT @(L); " ";
NEXT
 
FOR L = 51 TO 0 STEP -1
    C = RND(L + 1)
    IF C # L THEN 
      PUSH @(C), L, @(L), C
      GOSUB 100
    ENDIF
NEXT
 
PRINT : PRINT "after:"
FOR L = 0 TO 51
    PRINT @(L); " ";
NEXT
PRINT
END

100 @(POP()) = POP() : @(POP()) = POP() : RETURN

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

Uiua

Works with: Uiua version 0.10.0-dev.1

Build pairs of indexes to be swapped then apply these as a fold.

Knuth ← ∧(⍜⊏⇌)≡(⊟⌊×⚂.)⇌↘1⇡⧻.
Knuth ⇡10

Typical output:

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

UNIX Shell

Works with: ksh93

Works with: pdksh

# Shuffle array[@].
function shuffle {
	integer i j t

	((i = ${#array[@]}))
	while ((i > 1)); do
		((j = RANDOM))                 # 0 <= j < 32768
		((j < 32768 % i)) && continue  # no modulo bias
		((j %= i))                     # 0 <= j < i

		((i -= 1))
		((t = array[i]))
		((array[i] = array[j]))
		((array[j] = t))
	done
}

# Test program.
set -A array 11 22 33 44 55 66 77 88 99 110
shuffle
echo "${array[@]}"

Ursala

This function works on lists of any type and length, including character strings.

shuffle = @iNX ~&l->r ^jrX/~&l ~&lK8PrC

test program:

#cast %s

example = shuffle 'abcdefghijkl'

Output:

'keacfjlbdigh'

VBA

Private Sub Knuth(Optional ByRef a As Variant)
    Dim t As Variant, i As Integer
    If Not IsMissing(a) Then
        For i = UBound(a) To LBound(a) + 1 Step -1
            j = Int((UBound(a) - LBound(a) + 1) * Rnd + LBound(a))
            t = a(i)
            a(i) = a(j)
            a(j) = t
        Next i
    End If
End Sub
Public Sub program()
    Dim b As Variant, c As Variant, d As Variant, e As Variant
    Randomize
    'imagine an empty array on this line
    b = [{10}]
    c = [{10, 20}]
    d = [{10, 20, 30}]
    e = [{11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22}]
    f = [{"This ", "is ", "a ", "test"}]
    Debug.Print "Before:"
    Knuth 'feeding an empty array ;)
    Debug.Print "After: "
    Debug.Print "Before:";
    For Each i In b: Debug.Print i;: Next i: Debug.Print
    Knuth b
    Debug.Print "After: ";
    For Each i In b: Debug.Print i;: Next i: Debug.Print
    Debug.Print "Before:";
    For Each i In c: Debug.Print i;: Next i: Debug.Print
    Knuth c
    Debug.Print "After: ";
    For Each i In c: Debug.Print i;: Next i: Debug.Print
    Debug.Print "Before:";
    For Each i In d: Debug.Print i;: Next i: Debug.Print
    Knuth d
    Debug.Print "After: ";
    For Each i In d: Debug.Print i;: Next i: Debug.Print
    Debug.Print "Before:";
    For Each i In e: Debug.Print i;: Next i: Debug.Print
    Knuth e
    Debug.Print "After: ";
    For Each i In e: Debug.Print i;: Next i: Debug.Print
    Debug.Print "Before:";
    For Each i In f: Debug.Print i;: Next i: Debug.Print
    Knuth f
    Debug.Print "After: ";
    For Each i In f: Debug.Print i;: Next i: Debug.Print
End Sub

Output:

Before:

After: Before: 10 After: 10 Before: 10 20 After: 10 20 Before: 10 20 30 After: 20 10 30 Before: 11 12 13 14 15 16 17 18 19 20 21 22 After: 22 12 15 20 19 11 13 21 16 17 14 18 Before:This is a test After: a This testis

VBScript

Implementation

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

Invocation

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, ", " )

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.

// 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)

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

V (Vlang)

Updated to Vlang version 0.2.2

import rand
import rand.seed

fn shuffle(mut arr []int) {
    for i := arr.len - 1; i >= 0; i-- {
        j := rand.intn(i + 1)
        arr[i], arr[j] = arr[j], arr[i]
    }
    println('After Shuffle: $arr')
}

fn main() {
    seed_array := seed.time_seed_array(2)
    rand.seed(seed_array)
    mut arr := [6, 9, 1, 4]
    println('Input: $arr')
    shuffle(mut arr)
    shuffle(mut arr)
    println('Output: $arr')
}

Output:

Input: [6, 9, 1, 4]
After Shuffle: [6, 1, 4, 9]
After Shuffle: [4, 9, 1, 6]
Output: [4, 9, 1, 6]

Wren

import "random" for Random

var rand = Random.new()

var knuthShuffle = Fn.new { |a|
    var i = a.count - 1
    while (i >= 1) {
        var j = rand.int(i + 1)
        var t = a[i]
        a[i] = a[j]
        a[j] = t
        i = i - 1
    }
}

var tests = [ [], [10], [10, 20], [10, 20, 30] ]
for (a in tests) {
    var b = a.toList // store original order
    knuthShuffle.call(a)
    System.print("%(b) -> %(a)")
}

Output:

Sample run:

[] -> []
[10] -> [10]
[10, 20] -> [20, 10]
[10, 20, 30] -> [30, 10, 20]

XPL0

proc Shuffle(Array, Items, BytesPerItem);
int  Array, Items, BytesPerItem;
int  I, J;
char Temp(8);
[for I:= Items-1 downto 1 do
    [J:= Ran(I+1);      \range [0..I]
    CopyMem(Temp, Array+I*BytesPerItem, BytesPerItem);
    CopyMem(Array+I*BytesPerItem, Array+J*BytesPerItem, BytesPerItem);
    CopyMem(Array+J*BytesPerItem, Temp, BytesPerItem);
    ];
];

string 0;       \use zero-terminated strings
int A;  char B;  real C;
int I;
[A:= [1, 2, 3, 4, 5];
Shuffle(A, 5, 4 \bytes per int\);
for I:= 0 to 5-1 do
    [IntOut(0, A(I));  ChOut(0, ^ )];
CrLf(0);
B:= "12345";
Shuffle(B, 5, 1 \byte per char\);
for I:= 0 to 5-1 do
    [ChOut(0, B(I));  ChOut(0, ^ )];
CrLf(0);
C:= [1., 2., 3., 4., 5.];
Shuffle(addr C(0), 5, 8 \bytes per real\);
for I:= 0 to 5-1 do
    [RlOut(0, C(I));  ChOut(0, ^ )];
CrLf(0);
A:= [10];
Shuffle(A, 1, 4 \bytes per int\);
for I:= 0 to 1-1 do
    [IntOut(0, A(I));  ChOut(0, ^ )];
CrLf(0);
]

Output:

2 4 1 5 3 
1 3 4 5 2 
    5.00000     4.00000     2.00000     1.00000     3.00000 
10

Yabasic

// Rosetta Code problem: https://www.rosettacode.org/wiki/Ramsey%27s_theorem
// by Jjuanhdez, 06/2022

dim array(52)
for i = 1 to arraysize(array(),1) : array(i) = i : next i

print "Starting array"
for i = 1 to arraysize(array(),1)
    print array(i) using "####";
next i

KnuthShuffle(array())

print "\n\nAfter Knuth shuffle downwards"
for i = 1 to arraysize(array(),1)
    print array(i) using "####";
next i
print
end

sub KnuthShuffle(a())
    local i, j, t, lb, ub
    lb = 1
    ub = arraysize(a(),1) - lb 
    
    for i = lb to ub
        j = round(ran(i +1))
        t = a(lb + i)
        a(lb + i) = a(lb + j)
        a(lb + j) = t
    next i
end sub

zkl

Two versions, imperative and functional, same results. xs has to be a mutable list.

fcn kshuffle(xs){
   foreach i in ([xs.len()-1..1,-1]){ xs.swap(i,(0).random(0,i+1)) } 
   xs
}
fcn kshufflep(xs){
   [xs.len()-1..1,-1].pump(Void,'wrap(i){ xs.swap(i,(0).random(0,i+1)) })
   xs
}

var ns=(1).pump(10,List).copy() // [1..10] made mutable
kshuffle(ns)  //-->L(6,3,8,2,4,5,10,9,1,7)

ns="this is a test foo bar hoho".split(" ").copy();
kshufflep(ns)  //-->L("a","bar","hoho","foo","test","is","this")

When the array address is known before runtime

Iteration

Functional composition

Standard Version

One Implementation

Icon and Unicon

ES5

ES6

Mutating in-place swap

Non-mutating swap

Mathematica /Wolfram Language

version 1

version 2

version 1

version 2

Original Fisher-Yates version

Knuth variation

Short version

version 0, card pips

version 1, card names

version 2