Sorting algorithms/Merge sort

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< Sorting algorithms(Redirected from Merge sort)
Task
Sorting algorithms/Merge sort
You are encouraged to solve this task according to the task description, using any language you may know.

The   merge sort   is a recursive sort of order   n*log(n).

It is notable for having a worst case and average complexity of   O(n*log(n)),   and a best case complexity of   O(n)   (for pre-sorted input).

The basic idea is to split the collection into smaller groups by halving it until the groups only have one element or no elements   (which are both entirely sorted groups).

Then merge the groups back together so that their elements are in order.

This is how the algorithm gets its   divide and conquer   description.


Task

Write a function to sort a collection of integers using the merge sort.


The merge sort algorithm comes in two parts:

   a sort function     and 
   a merge function 

The functions in pseudocode look like this:

function mergesort(m)
   var list left, right, result
   if length(m) ≤ 1
       return m
   else
       var middle = length(m) / 2
       for each x in m up to middle - 1
           add x to left
       for each x in m at and after middle
           add x to right
       left = mergesort(left)
       right = mergesort(right)
       if last(left) ≤ first(right) 
          append right to left
          return left
       result = merge(left, right)
       return result

function merge(left,right)
   var list result
   while length(left) > 0 and length(right) > 0
       if first(left) ≤ first(right)
           append first(left) to result
           left = rest(left)
       else
           append first(right) to result
           right = rest(right)
   if length(left) > 0 
       append rest(left) to result
   if length(right) > 0 
       append rest(right) to result
   return result


See also


Note:   better performance can be expected if, rather than recursing until   length(m) ≤ 1,   an insertion sort is used for   length(m)   smaller than some threshold larger than   1.   However, this complicates the example code, so it is not shown here.

11l[edit]

Translation of: Python
F merge(left, right)
   [Int] result
   V left_idx = 0
   V right_idx = 0
   L left_idx < left.len & right_idx < right.len
      I left[left_idx] <= right[right_idx]
         result.append(left[left_idx])
         left_idx++
      E
         result.append(right[right_idx])
         right_idx++

   I left_idx < left.len
      result.extend(left[left_idx ..])
   I right_idx < right.len
      result.extend(right[right_idx ..])
   R result

F merge_sort(m)
   I m.len <= 1
      R m

   V middle = m.len I/ 2
   V left = m[0.<middle]
   V right = m[middle..]

   left = merge_sort(left)
   right = merge_sort(right)
   R Array(merge(left, right))

V arr = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0]
print(merge_sort(arr))
Output:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

360 Assembly[edit]

Translation of: BBC BASIC

The program uses ASM structured macros and two ASSIST macros (XDECO, XPRNT) to keep the code as short as possible.

*      Merge sort                  19/06/2016
MAIN   CSECT
       STM     R14,R12,12(R13)     save caller's registers
       LR      R12,R15             set R12 as base register
       USING   MAIN,R12            notify assembler
       LA      R11,SAVEXA          get the address of my savearea
       ST      R13,4(R11)          save caller's save area pointer
       ST      R11,8(R13)          save my save area pointer
       LR      R13,R11             set R13 to point to my save area
       LA      R1,1                1
       LA      R2,NN               hbound(a)
       BAL     R14,SPLIT           call split(1,hbound(a))
       LA      RPGI,PG             pgi=0
       LA      RI,1                i=1
       DO WHILE=(C,RI,LE,=A(NN))   do i=1 to hbound(a)
         LR    R1,RI                 i
         SLA   R1,2                  .
         L     R2,A-4(R1)            a(i)
         XDECO R2,XDEC               edit a(i)
         MVC   0(4,RPGI),XDEC+8      output a(i) 
         LA    RPGI,4(RPGI)          pgi=pgi+4
         LA    RI,1(RI)              i=i+1
       ENDDO   ,                   end do
       XPRNT   PG,80               print buffer
       L       R13,SAVEXA+4        restore caller's savearea address
       LM      R14,R12,12(R13)     restore caller's registers
       XR      R15,R15             set return code to 0
       BR      R14                 return to caller
*      split(istart,iend)          ------recursive---------------------
SPLIT  STM     R14,R12,12(R13)     save all registers
       LR      R9,R1               save R1
       LA      R1,72               amount of storage required
       GETMAIN RU,LV=(R1)          allocate storage for stack
       USING   STACK,R10           make storage addressable
       LR      R10,R1              establish stack addressability
       LA      R11,SAVEXB          get the address of my savearea
       ST      R13,4(R11)          save caller's save area pointer
       ST      R11,8(R13)          save my save area pointer
       LR      R13,R11             set R13 to point to my save area
       LR      R1,R9               restore R1
       LR      RSTART,R1           istart=R1
       LR      REND,R2             iend=R2
       IF CR,REND,EQ,RSTART THEN   if iend=istart
         B     RETURN                return
       ENDIF   ,                   end if
       BCTR    R2,0                iend-1
       IF C,R2,EQ,RSTART THEN      if iend-istart=1
         LR    R1,REND               iend
         SLA   R1,2                  .
         L     R2,A-4(R1)            a(iend)
         LR    R1,RSTART             istart
         SLA   R1,2                  .
         L     R3,A-4(R1)            a(istart)
         IF CR,R2,LT,R3 THEN         if a(iend)<a(istart)
           LR  R1,RSTART               istart
           SLA R1,2                    .
           LA  R2,A-4(R1)              @a(istart)
           LR  R1,REND                 iend
           SLA R1,2                    .
           LA  R3,A-4(R1)              @a(iend)
           MVC TEMP,0(R2)              temp=a(istart)
           MVC 0(4,R2),0(R3)           a(istart)=a(iend)
           MVC 0(4,R3),TEMP            a(iend)=temp
         ENDIF ,                     end if
         B     RETURN                return
       ENDIF   ,                   end if 
       LR      RMIDDL,REND         iend
       SR      RMIDDL,RSTART       iend-istart
       SRA     RMIDDL,1            (iend-istart)/2
       AR      RMIDDL,RSTART       imiddl=istart+(iend-istart)/2
       LR      R1,RSTART           istart
       LR      R2,RMIDDL           imiddl
       BAL     R14,SPLIT           call split(istart,imiddl)
       LA      R1,1(RMIDDL)        imiddl+1
       LR      R2,REND             iend
       BAL     R14,SPLIT           call split(imiddl+1,iend)
       LR      R1,RSTART           istart
       LR      R2,RMIDDL           imiddl
       LR      R3,REND             iend
       BAL     R14,MERGE           call merge(istart,imiddl,iend)
RETURN L       R13,SAVEXB+4        restore caller's savearea address
       XR      R15,R15             set return code to 0        
       LA      R0,72               amount of storage to free
       FREEMAIN A=(R10),LV=(R0)    free allocated storage
       L       R14,12(R13)         restore caller's return address
       LM      R2,R12,28(R13)      restore registers R2 to R12
       BR      R14                 return to caller
       DROP    R10                 base no longer needed
*      merge(jstart,jmiddl,jend)   ------------------------------------
MERGE  STM     R1,R3,JSTART        jstart=r1,jmiddl=r2,jend=r3
       SR      R2,R1               jmiddl-jstart
       LA      RBS,2(R2)           bs=jmiddl-jstart+2
       LA      RI,1                i=1
       LR      R3,RBS              bs
       BCTR    R3,0                bs-1
       DO WHILE=(CR,RI,LE,R3)      do i=0 to bs-1
         L     R2,JSTART             jstart
         AR    R2,RI                 jstart+i
         SLA   R2,2                  .
         L     R2,A-8(R2)            a(jstart+i-1)
         LR    R1,RI                 i
         SLA   R1,2                  .
         ST    R2,B-4(R1)            b(i)=a(jstart+i-1)
         LA    RI,1(RI)              i=i+1
       ENDDO   ,                   end do
       LA      RI,1                i=1
       L       RJ,JMIDDL           j=jmiddl
       LA      RJ,1(RJ)            j=jmiddl+1
       L       RK,JSTART           k=jstart
       DO UNTIL=(CR,RI,EQ,RBS,OR,  do until i=bs or                    X
               C,RJ,GT,JEND)                j>jend  
         LR    R1,RI                 i
         SLA   R1,2                  .
         L     R4,B-4(R1)            r4=b(i)
         LR    R1,RJ                 j
         SLA   R1,2                  .
         L     R3,A-4(R1)            r3=a(j)
         LR    R9,RK                 k
         SLA   R9,2                  r9 for a(k)
         IF CR,R4,LE,R3 THEN         if b(i)<=a(j)
           ST  R4,A-4(R9)              a(k)=b(i)
           LA  RI,1(RI)                i=i+1 
         ELSE  ,                     else
           ST  R3,A-4(R9)              a(k)=a(j)
           LA  RJ,1(RJ)                j=j+1
         ENDIF ,                     end if
         LA    RK,1(RK)              k=k+1
       ENDDO   ,                   end do  
       DO WHILE=(CR,RI,LT,RBS)     do while i<bs 
         LR    R1,RI                 i
         SLA   R1,2                  .
         L     R2,B-4(R1)            b(i)
         LR    R1,RK                 k
         SLA   R1,2                  .
         ST    R2,A-4(R1)            a(k)=b(i)
         LA    RI,1(RI)              i=i+1
         LA    RK,1(RK)              k=k+1
       ENDDO   ,                   end do
       BR      R14                 return to caller
*      ------- ------------------  ------------------------------------
       LTORG   
SAVEXA DS      18F                 savearea of main
NN     EQU     ((B-A)/L'A)         number of items
A      DC F'4',F'65',F'2',F'-31',F'0',F'99',F'2',F'83',F'782',F'1'
       DC F'45',F'82',F'69',F'82',F'104',F'58',F'88',F'112',F'89',F'74'
B      DS      (NN/2+1)F           merge sort static storage
TEMP   DS      F                   for swap
JSTART DS      F                   jstart 
JMIDDL DS      F                   jmiddl
JEND   DS      F                   jend
PG     DC      CL80' '             buffer
XDEC   DS      CL12                for edit
STACK  DSECT                       dynamic area
SAVEXB DS      18F                 " savearea of mergsort (72 bytes)
       YREGS
RI     EQU     6                   i
RJ     EQU     7                   j
RK     EQU     8                   k
RSTART EQU     6                   istart
REND   EQU     7                   i
RMIDDL EQU     8                   i
RPGI   EQU     3                   pgi
RBS    EQU     0                   bs
       END     MAIN
Output:
 -31   0   1   2   2   4  45  58  65  69  74  82  82  83  88  89  99 104 112 782

AArch64 Assembly[edit]

Works with: as version Raspberry Pi 3B version Buster 64 bits
/* ARM assembly AARCH64 Raspberry PI 3B */
/*  program mergeSort64.s  */
 
/*******************************************/
/* Constantes file                         */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeConstantesARM64.inc"

/*********************************/
/* Initialized data              */
/*********************************/
.data
szMessSortOk:       .asciz "Table sorted.\n"
szMessSortNok:      .asciz "Table not sorted !!!!!.\n"
sMessResult:        .asciz "Value  : @ \n"
szCarriageReturn:   .asciz "\n"
 
.align 4
TableNumber:      .quad   1,3,11,6,2,5,9,10,8,4,7
#TableNumber:     .quad   10,9,8,7,6,-5,4,3,2,1
                 .equ NBELEMENTS, (. - TableNumber) / 8 
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConv:       .skip 24
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main 
main:                                              // entry of program 
    ldr x0,qAdrTableNumber                         // address number table
    mov x1,0                                       // first element
    mov x2,NBELEMENTS                              // number of élements 
    bl mergeSort
    ldr x0,qAdrTableNumber                         // address number table
    bl displayTable
 
    ldr x0,qAdrTableNumber                         // address number table
    mov x1,NBELEMENTS                              // number of élements 
    bl isSorted                                    // control sort
    cmp x0,1                                       // sorted ?
    beq 1f                                    
    ldr x0,qAdrszMessSortNok                       // no !! error sort
    bl affichageMess
    b 100f
1:                                                 // yes
    ldr x0,qAdrszMessSortOk
    bl affichageMess
100:                                               // standard end of the program 
    mov x0,0                                       // return code
    mov x8,EXIT                                    // request to exit program
    svc 0                                          // perform the system call
 
qAdrsZoneConv:            .quad sZoneConv
qAdrszCarriageReturn:     .quad szCarriageReturn
qAdrsMessResult:          .quad sMessResult
qAdrTableNumber:          .quad TableNumber
qAdrszMessSortOk:         .quad szMessSortOk
qAdrszMessSortNok:        .quad szMessSortNok
/******************************************************************/
/*     control sorted table                                   */ 
/******************************************************************/
/* x0 contains the address of table */
/* x1 contains the number of elements  > 0  */
/* x0 return 0  if not sorted   1  if sorted */
isSorted:
    stp x2,lr,[sp,-16]!             // save  registers
    stp x3,x4,[sp,-16]!             // save  registers
    mov x2,0
    ldr x4,[x0,x2,lsl 3]
1:
    add x2,x2,1
    cmp x2,x1
    bge 99f
    ldr x3,[x0,x2, lsl 3]
    cmp x3,x4
    blt 98f
    mov x4,x3
    b 1b
98:
    mov x0,0                       // not sorted
    b 100f
99:
    mov x0,1                       // sorted
100:
    ldp x3,x4,[sp],16              // restaur  2 registers
    ldp x2,lr,[sp],16              // restaur  2 registers
    ret                            // return to address lr x30
/******************************************************************/
/*         merge                                              */ 
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains first start index
/* r2 contains second start index */
/* r3 contains the last index   */ 
merge:
    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
    str x8,[sp,-16]!
    mov x5,x2                  // init index x2->x5 
1:                             // begin loop first section
    ldr x6,[x0,x1,lsl 3]       // load value first section index r1
    ldr x7,[x0,x5,lsl 3]       // load value second section index r5
    cmp x6,x7
    ble 4f                     // <=  -> location first section OK
    str x7,[x0,x1,lsl 3]       // store value second section in first section
    add x8,x5,1
    cmp x8,x3                  // end second section ?
    ble 2f
    str x6,[x0,x5,lsl 3]
    b 4f                       // loop
2:                             // loop insert element part 1 into part 2
    sub x4,x8,1
    ldr x7,[x0,x8,lsl 3]       // load value 2
    cmp x6,x7                  // value < 
    bge 3f
    str x6,[x0,x4,lsl 3]       // store value 
    b 4f                       // loop
3:
    str x7,[x0,x4,lsl 3]       // store value 2
    add x8,x8,1
    cmp x8,x3                  // end second section ?
    ble 2b                     // no loop 
    sub x8,x8,1
    str x6,[x0,x8,lsl 3]       // store value 1
4:
    add x1,x1,1
    cmp x1,x2                  // end first section ?
    blt 1b

100:
    ldr x8,[sp],16             // restaur 1 register
    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                        // return to address lr x30
/******************************************************************/
/*      merge sort                                                */ 
/******************************************************************/
/* x0 contains the address of table */
/* x1 contains the index of first element */
/* x2 contains the number of element */
mergeSort:
    stp x3,lr,[sp,-16]!    // save  registers
    stp x4,x5,[sp,-16]!    // save  registers
    stp x6,x7,[sp,-16]!    // save  registers
    cmp x2,2               // end ?
    blt 100f
    lsr x4,x2,1            // number of element of each subset
    add x5,x4,1
    tst x2,#1              // odd ?
    csel x4,x5,x4,ne
    mov x5,x1              // save first element
    mov x6,x2              // save number of element
    mov x7,x4              // save number of element of each subset
    mov x2,x4
    bl mergeSort
    mov x1,x7              // restaur number of element of each subset
    mov x2,x6              // restaur  number of element
    sub x2,x2,x1
    mov x3,x5              // restaur first element
    add x1,x1,x3              // + 1
    bl mergeSort           // sort first subset
    mov x1,x5              // restaur first element
    mov x2,x7              // restaur number of element of each subset
    add x2,x2,x1
    mov x3,x6              // restaur  number of element
    add x3,x3,x1 
    sub x3,x3,1              // last index
    bl merge
100:
    ldp x6,x7,[sp],16          // restaur  2 registers
    ldp x4,x5,[sp],16          // restaur  2 registers
    ldp x3,lr,[sp],16          // restaur  2 registers
    ret                        // return to address lr x30

/******************************************************************/
/*      Display table elements                                */ 
/******************************************************************/
/* x0 contains the address of table */
displayTable:
    stp x1,lr,[sp,-16]!              // save  registers
    stp x2,x3,[sp,-16]!              // save  registers
    mov x2,x0                        // table address
    mov x3,0
1:                                   // loop display table
    ldr x0,[x2,x3,lsl 3]
    ldr x1,qAdrsZoneConv
    bl conversion10S                  // décimal conversion
    ldr x0,qAdrsMessResult
    ldr x1,qAdrsZoneConv
    bl strInsertAtCharInc            // insert result at // character
    bl affichageMess                 // display message
    add x3,x3,1
    cmp x3,NBELEMENTS - 1
    ble 1b
    ldr x0,qAdrszCarriageReturn
    bl affichageMess
    mov x0,x2
100:
    ldp x2,x3,[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[edit]

(defun split (xys)
   (if (endp (rest xys))
       (mv xys nil)
       (mv-let (xs ys)
               (split (rest (rest xys)))
          (mv (cons (first xys) xs)
              (cons (second xys) ys)))))

(defun mrg (xs ys)
   (declare (xargs :measure (+ (len xs) (len ys))))
   (cond ((endp xs) ys)
         ((endp ys) xs)
         ((< (first xs) (first ys))
          (cons (first xs) (mrg (rest xs) ys)))
         (t (cons (first ys) (mrg xs (rest ys))))))

(defthm split-shortens
   (implies (consp (rest xs))
            (mv-let (ys zs)
                    (split xs)
               (and (< (len ys) (len xs))
                    (< (len zs) (len xs))))))

(defun msort (xs)
     (declare (xargs
            :measure (len xs)
            :hints (("Goal"
                     :use ((:instance split-shortens))))))
   (if (endp (rest xs))
       xs
       (mv-let (ys zs)
               (split xs)
          (mrg (msort ys)
               (msort zs)))))

Action![edit]

Action! language does not support recursion. Therefore an iterative approach has been proposed.

DEFINE MAX_COUNT="100"

PROC PrintArray(INT ARRAY a INT size)
  INT i

  Put('[)
  FOR i=0 TO size-1
  DO
    IF i>0 THEN Put(' ) FI
    PrintI(a(i))
  OD
  Put(']) PutE()
RETURN

PROC Merge(INT ARRAY a INT first,mid,last)
  INT ARRAY left(MAX_COUNT),right(MAX_COUNT)
  INT leftSize,rightSize,i,j,k
  
  leftSize=mid-first+1
  rightSize=last-mid
 
  FOR i=0 TO leftSize-1
  DO
    left(i)=a(first+i)
  OD
  FOR i=0 TO rightSize-1
  DO
    right(i)=a(mid+1+i)
  OD 
  i=0 j=0
  k=first
  WHILE i<leftSize AND j<rightSize
  DO
    IF left(i)<=right(j) THEN
      a(k)=left(i)
      i==+1
    ELSE
      a(k)=right(j)
      j==+1
    FI
    k==+1
  OD
 
  WHILE i<leftSize
  DO
    a(k)=left(i)
    i==+1 k==+1
  OD
 
  WHILE j<rightSize
  DO
    a(k)=right(j)
    j==+1 k==+1
  OD
RETURN

PROC MergeSort(INT ARRAY a INT size)
  INT currSize,first,mid,last

  currSize=1
  WHILE currSize<size
  DO
    first=0
    WHILE first<size-1
    DO
      mid=first+currSize-1
      IF mid>size-1 THEN
        mid=size-1
      FI
      last=first+2*currSize-1
      IF last>size-1 THEN
        last=size-1
      FI
      Merge(a,first,mid,last);

      first==+2*currSize
    OD
    currSize==*2
  OD
RETURN

PROC Test(INT ARRAY a INT size)
  PrintE("Array before sort:")
  PrintArray(a,size)
  MergeSort(a,size)
  PrintE("Array after sort:")
  PrintArray(a,size)
  PutE()
RETURN

PROC Main()
  INT ARRAY
    a(10)=[1 4 65535 0 3 7 4 8 20 65530],
    b(21)=[10 9 8 7 6 5 4 3 2 1 0
      65535 65534 65533 65532 65531
      65530 65529 65528 65527 65526],
    c(8)=[101 102 103 104 105 106 107 108],
    d(12)=[1 65535 1 65535 1 65535 1
      65535 1 65535 1 65535]
  
  Test(a,10)
  Test(b,21)
  Test(c,8)
  Test(d,12)
RETURN
Output:

Screenshot from Atari 8-bit computer

Array before sort:
[1 4 -1 0 3 7 4 8 20 -6]
Array after sort:
[-6 -1 0 1 3 4 4 7 8 20]

Array before sort:
[10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10]
Array after sort:
[-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10]

Array before sort:
[101 102 103 104 105 106 107 108]
Array after sort:
[101 102 103 104 105 106 107 108]

Array before sort:
[1 -1 1 -1 1 -1 1 -1 1 -1 1 -1]
Array after sort:
[-1 -1 -1 -1 -1 -1 1 1 1 1 1 1]

ActionScript[edit]

function mergesort(a:Array)
{
	//Arrays of length 1 and 0 are always sorted
	if(a.length <= 1) return a;
	else
	{
		var middle:uint = a.length/2;
		//split the array into two
		var left:Array = new Array(middle);
		var right:Array = new Array(a.length-middle);
		var j:uint = 0, k:uint = 0;
		//fill the left array
		for(var i:uint = 0; i < middle; i++)
			left[j++]=a[i];
		//fill the right array
		for(i = middle; i< a.length; i++)
			right[k++]=a[i];
		//sort the arrays
		left = mergesort(left);
		right = mergesort(right);
		//If the last element of the left array is less than or equal to the first
		//element of the right array, they are in order and don't need to be merged
		if(left[left.length-1] <= right[0])
			return left.concat(right);
		a = merge(left, right);
		return a;
	}
}

function merge(left:Array, right:Array)
{
	var result:Array = new Array(left.length + right.length);
	var j:uint = 0, k:uint = 0, m:uint = 0;
	//merge the arrays in order
	while(j < left.length && k < right.length)
	{
		if(left[j] <= right[k])
			result[m++] = left[j++];
		else
			result[m++] = right[k++];
	}
	//If one of the arrays has remaining entries that haven't been merged, they
	//will be greater than the rest of the numbers merged so far, so put them on the
	//end of the array.
	for(; j < left.length; j++)
		result[m++] = left[j];
	for(; k < right.length; k++)
		result[m++] = right[k];
	return result;
}

Ada[edit]

This example creates a generic package for sorting arrays of any type. Ada allows array indices to be any discrete type, including enumerated types which are non-numeric. Furthermore, numeric array indices can start at any value, positive, negative, or zero. The following code handles all the possible variations in index types.

generic
   type Element_Type is private;
   type Index_Type is (<>);
   type Collection_Type is array(Index_Type range <>) of Element_Type;
   with function "<"(Left, Right : Element_Type) return Boolean is <>;

package Mergesort is
   function Sort(Item : Collection_Type) return Collection_Type;
end MergeSort;
package body Mergesort is
   
   -----------
   -- Merge --
   -----------
   
   function Merge(Left, Right : Collection_Type) return Collection_Type is
      Result : Collection_Type(Left'First..Right'Last);
      Left_Index : Index_Type := Left'First;
      Right_Index : Index_Type := Right'First;
      Result_Index : Index_Type := Result'First;
   begin
      while Left_Index <= Left'Last and Right_Index <= Right'Last loop
         if Left(Left_Index) <= Right(Right_Index) then
            Result(Result_Index) := Left(Left_Index);
            Left_Index := Index_Type'Succ(Left_Index); -- increment Left_Index
         else
            Result(Result_Index) := Right(Right_Index);
            Right_Index := Index_Type'Succ(Right_Index); -- increment Right_Index
         end if;
         Result_Index := Index_Type'Succ(Result_Index); -- increment Result_Index
      end loop;
      if Left_Index <= Left'Last then
         Result(Result_Index..Result'Last) := Left(Left_Index..Left'Last);
      end if;
      if Right_Index <= Right'Last then
         Result(Result_Index..Result'Last) := Right(Right_Index..Right'Last);
      end if;
      return Result;
   end Merge;
   
   ----------
   -- Sort --
   ----------

   function Sort (Item : Collection_Type) return Collection_Type is
      Result : Collection_Type(Item'range);
      Middle : Index_Type;
   begin
      if Item'Length <= 1 then
         return Item;
      else
         Middle := Index_Type'Val((Item'Length / 2) + Index_Type'Pos(Item'First));
         declare
            Left : Collection_Type(Item'First..Index_Type'Pred(Middle));
            Right : Collection_Type(Middle..Item'Last);
         begin
            for I in Left'range loop
               Left(I) := Item(I);
            end loop;
            for I in Right'range loop
               Right(I) := Item(I);
            end loop;
            Left := Sort(Left);
            Right := Sort(Right);
            Result := Merge(Left, Right);
         end;
         return Result;
      end if;
   end Sort;

end Mergesort;

The following code provides an usage example for the generic package defined above.

with Ada.Text_Io; use Ada.Text_Io;
with Mergesort; 

procedure Mergesort_Test is
   type List_Type is array(Positive range <>) of Integer;
   package List_Sort is new Mergesort(Integer, Positive, List_Type);
   procedure Print(Item : List_Type) is
   begin
      for I in Item'range loop
         Put(Integer'Image(Item(I)));
      end loop;
      New_Line;
   end Print;
   
   List : List_Type := (1, 5, 2, 7, 3, 9, 4, 6);
begin
   Print(List);
   Print(List_Sort.Sort(List));
end Mergesort_Test;
Output:
 1 5 2 7 3 9 4 6
 1 2 3 4 5 6 7 9

ALGOL 68[edit]

Translation of: python

Below are two variants of the same routine. If copying the DATA type to a different memory location is expensive, then the optimised version should be used as the DATA elements are handled indirectly.

MODE DATA = CHAR;

PROC merge sort = ([]DATA m)[]DATA: (
    IF LWB m >= UPB m THEN
        m
    ELSE
        INT middle = ( UPB m + LWB m ) OVER 2;
        []DATA left = merge sort(m[:middle]);
        []DATA right = merge sort(m[middle+1:]);
        flex merge(left, right)[AT LWB m]
    FI
);

# FLEX version: A demonstration of FLEX for manipulating arrays #
PROC flex merge = ([]DATA in left, in right)[]DATA:(
    [UPB in left + UPB in right]DATA result;
    FLEX[0]DATA left := in left;
    FLEX[0]DATA right := in right;

    FOR index TO UPB result DO
        # change the direction of this comparison to change the direction of the sort #
        IF LWB right > UPB right THEN
            result[index:] := left; 
            stop iteration
        ELIF LWB left > UPB left THEN
            result[index:] := right;
            stop iteration
        ELIF left[1] <= right[1] THEN
            result[index] := left[1];
            left := left[2:]
        ELSE
            result[index] := right[1];
            right := right[2:]
        FI
    OD;
stop iteration:
    result
);

[32]CHAR char array data := "big fjords vex quick waltz nymph";
print((merge sort(char array data), new line));
Output:
     abcdefghiijklmnopqrstuvwxyz

Optimised version:

  1. avoids FLEX array copies and manipulations
  2. avoids type DATA memory copies, useful in cases where DATA is a large STRUCT
PROC opt merge sort = ([]REF DATA m)[]REF DATA: (
    IF LWB m >= UPB m THEN
        m
    ELSE
        INT middle = ( UPB m + LWB m ) OVER 2;
        []REF DATA left = opt merge sort(m[:middle]);
        []REF DATA right = opt merge sort(m[middle+1:]);
        opt merge(left, right)[AT LWB m]
    FI
);

PROC opt merge = ([]REF DATA left, right)[]REF DATA:(
    [UPB left - LWB left + 1 + UPB right - LWB right + 1]REF DATA result;
    INT index left:=LWB left, index right:=LWB right;

    FOR index TO UPB result DO
        # change the direction of this comparison to change the direction of the sort #
        IF index right > UPB right THEN
            result[index:] := left[index left:]; 
            stop iteration
        ELIF index left > UPB left THEN
            result[index:] := right[index right:];
            stop iteration
        ELIF left[index left] <= right[index right] THEN
            result[index] := left[index left]; index left +:= 1
        ELSE
            result[index] := right[index right]; index right +:= 1
        FI
    OD;
stop iteration:
    result
);

# create an array of pointers to the data being sorted #
[UPB char array data]REF DATA data; FOR i TO UPB char array data DO data[i] := char array data[i] OD;

[]REF CHAR result = opt merge sort(data);
FOR i TO UPB result DO print((result[i])) OD; print(new line)
Output:
     abcdefghiijklmnopqrstuvwxyz

AppleScript[edit]

(*
    In-place, iterative binary merge sort
    Merge sort algorithm: John von Neumann, 1945.
    
    Convenience terminology used here:
        run: one of two adjacent source-list ranges containing ordered items for merging.
        block: range in the destination list to which two runs are merged.
*)
on mergeSort(theList, l, r) -- Sort items l thru r of theList.
    set listLength to (count theList)
    if (listLength < 2) then return
    -- Convert negative and/or transposed range indices.
    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 object containing the input list and the sort range indices.
    script main
        property lst : theList
        property l : missing value
        property r : missing value
    end script
    set {main's l, main's r} to {l, r}
    
    -- Just swap adjacent items as necessary on the first pass.
    -- (Short insertion sorts would be better, to create larger initial runs.)
    repeat with j from (l + 1) to r by 2
        set i to j - 1
        set lv to main's lst's item i
        set rv to main's lst's item j
        if (lv > rv) then
            set main's lst's item i to rv
            set main's lst's item j to lv
        end if
    end repeat
    set rangeLength to r - l + 1
    if (rangeLength < 3) then return -- That's all if fewer than three items to sort.
    
    -- Script object to alternate with the one above as the source and destination for the
    -- merges. Its list need only contain the items from the sort range as ordered so far.
    script aux
        property lst : main's lst's items l thru r
        property l : 1
        property r : rangeLength
    end script
    
    -- Work out how many merging passes will be needed and set the script objects' initial
    -- source and destination roles so that the final pass will merge back to the original list.
    set passesToDo to 0
    set blockSize to 2
    repeat while (blockSize < rangeLength)
        set passesToDo to passesToDo + 1
        set blockSize to blockSize + blockSize
    end repeat
    set {srce, dest} to {{main, aux}, {aux, main}}'s item (passesToDo mod 2 + 1)
    
    -- Do the remaining passes, doubling the run and block sizes on each pass.
    -- (The end set in each pass will usually be truncated.)
    set blockSize to 2
    repeat passesToDo times -- Per pass.
        set runSize to blockSize
        set blockSize to blockSize + blockSize
        set k to (dest's l) - 1 -- Destination traversal index.
        
        repeat with leftStart from srce's l to srce's r by blockSize -- Per merge.
            set blockEnd to k + blockSize
            if (blockEnd comes after dest's r) then set blockEnd to dest's r
            set i to leftStart -- Left run traversal index.
            set leftEnd to leftStart + runSize - 1
            if (leftEnd comes before srce's r) then
                set j to leftEnd + 1 -- Right run traversal index.
                set rightEnd to leftEnd + runSize
                if (rightEnd comes after srce's r) then set rightEnd to srce's r
                -- Merge process:
                set lv to srce's lst's item i
                set rv to srce's lst's item j
                repeat with k from (k + 1) to blockEnd
                    if (lv > rv) then
                        set dest's lst's item k to rv
                        if (j = rightEnd) then exit repeat -- Right run used up.
                        set j to j + 1
                        set rv to srce's lst's item j
                    else
                        set dest's lst's item k to lv
                        if (i = leftEnd) then -- Left run used up.
                            set i to j
                            exit repeat
                        end if
                        set i to i + 1
                        set lv to srce's lst's item i
                    end if
                end repeat
            end if
            -- Use up the remaining items from the not-yet-exhausted run.
            repeat with k from (k + 1) to blockEnd
                set dest's lst's item k to srce's lst's item i
                set i to i + 1
            end repeat
        end repeat -- Per merge.
        
        -- Switch source and destination scripts for the next pass.
        tell srce
            set srce to dest
            set dest to it
        end tell
    end repeat -- Per pass.
    
    return -- nothing
end mergeSort
property sort : mergeSort

-- Demo:
local aList
set aList to {22, 15, 98, 82, 22, 4, 58, 70, 80, 38, 49, 48, 46, 54, 93, 8, 54, 2, 72, 84, 86, 76, 53, 37, 90}
sort(aList, 1, -1) -- Sort items 1 thru -1 of aList.
return aList
Output:
{2, 4, 8, 15, 22, 22, 37, 38, 46, 48, 49, 53, 54, 54, 58, 70, 72, 76, 80, 82, 84, 86, 90, 93, 98}

ARM Assembly[edit]

Works with: as version Raspberry Pi
/* ARM assembly Raspberry PI  */
/*  program mergeSort.s  */
 
 /* REMARK 1 : this program use routines in a include file 
   see task Include a file language arm assembly 
   for the routine affichageMess conversion10 
   see at end of this program the instruction include */
/* for constantes see task include a file in arm assembly */
/************************************/
/* Constantes                       */
/************************************/
.include "../constantes.inc"

/*********************************/
/* Initialized data              */
/*********************************/
.data
szMessSortOk:       .asciz "Table sorted.\n"
szMessSortNok:      .asciz "Table not sorted !!!!!.\n"
sMessResult:        .asciz "Value  : @ \n"
szCarriageReturn:   .asciz "\n"
 
.align 4
#TableNumber:      .int   1,11,3,6,2,5,9,10,8,4,7
TableNumber:       .int   10,9,8,7,6,5,4,3,2,1
                   .equ NBELEMENTS, (. - TableNumber) / 4
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConv:            .skip 24
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main 
main:                                              @ entry of program 
 
    ldr r0,iAdrTableNumber                         @ address number table
    mov r1,#0                                      @ first element
    mov r2,#NBELEMENTS                             @ number of élements 
    bl mergeSort
    ldr r0,iAdrTableNumber                         @ address number table
    bl displayTable
 
    ldr r0,iAdrTableNumber                         @ address number table
    mov r1,#NBELEMENTS                             @ number of élements 
    bl isSorted                                    @ control sort
    cmp r0,#1                                      @ sorted ?
    beq 1f                                    
    ldr r0,iAdrszMessSortNok                       @ no !! error sort
    bl affichageMess
    b 100f
1:                                                 @ yes
    ldr r0,iAdrszMessSortOk
    bl affichageMess
100:                                               @ standard end of the program 
    mov r0, #0                                     @ return code
    mov r7, #EXIT                                  @ request to exit program
    svc #0                                         @ perform the system call
 
iAdrszCarriageReturn:     .int szCarriageReturn
iAdrsMessResult:          .int sMessResult
iAdrTableNumber:          .int TableNumber
iAdrszMessSortOk:         .int szMessSortOk
iAdrszMessSortNok:        .int szMessSortNok
/******************************************************************/
/*     control sorted table                                   */ 
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the number of elements  > 0  */
/* r0 return 0  if not sorted   1  if sorted */
isSorted:
    push {r2-r4,lr}                                    @ save registers
    mov r2,#0
    ldr r4,[r0,r2,lsl #2]
1:
    add r2,#1
    cmp r2,r1
    movge r0,#1
    bge 100f
    ldr r3,[r0,r2, lsl #2]
    cmp r3,r4
    movlt r0,#0
    blt 100f
    mov r4,r3
    b 1b
100:
    pop {r2-r4,lr}
    bx lr                                              @ return 
    
/******************************************************************/
/*         merge                                              */ 
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains first start index
/* r2 contains second start index */
/* r3 contains the last index   */ 
merge:
    push {r1-r8,lr}               @ save registers
    mov r5,r2                     @ init index r2->r5 
1:                                @ begin loop first section
    ldr r6,[r0,r1,lsl #2]         @ load value first section index r1
    ldr r7,[r0,r5,lsl #2]         @ load value second section index r5
    cmp r6,r7
    ble 3f                        @ <=  -> location first section OK
    str r7,[r0,r1,lsl #2]         @ store value second section in first section
    add r8,r5,#1
    cmp r8,r3                     @ end second section ?
    strgt r6,[r0,r5,lsl #2]
    bgt 3f                        @ loop
2:                                @ loop insert element part 1 into part 2
    sub r4,r8,#1
    ldr r7,[r0,r8,lsl #2]         @ load value 2
    cmp r6,r7                     @ value < 
    strlt r6,[r0,r4,lsl #2]       @ store value 
    blt 3f
    str r7,[r0,r4,lsl #2]         @ store value 2
    add r8,#1
    cmp r8,r3                     @ end second section ?
    ble 2b                        @ no loop 
    sub r8,#1
    str r6,[r0,r8,lsl #2]         @ store value 1
3:
    add r1,#1
    cmp r1,r2                     @ end first section ?
    blt 1b

100:
    pop {r1-r8,lr}
    bx lr                          @ return 
/******************************************************************/
/*      merge sort                                                */ 
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the index of first element */
/* r2 contains the number of element */
mergeSort:
    push {r3-r7,lr}           @ save registers
    cmp r2,#2
    blt 100f
    lsr r4,r2,#1             @ number of element of each subset
    tst r2,#1
    addne r4,#1
    mov r5,r1              @ save first element
    mov r6,r2              @ save number of element
    mov r7,r4              @ save number of element of each subset
    mov r2,r4
    bl mergeSort
    mov r1,r7              @ restaur number of element of each subset
    mov r2,r6              @ restaur  number of element
    sub r2,r1
    mov r3,r5              @ restaur first element
    add r1,r3              @ + 1
    bl mergeSort           @ sort first subset
    mov r1,r5              @ restaur first element
    mov r2,r7              @ restaur number of element of each subset
    add r2,r1
    mov r3,r6              @ restaur  number of element
    add r3,r1 
    sub r3,#1              @ last index
    bl merge
100:
    pop {r3-r7,lr}
    bx lr                  @ return 
 
/******************************************************************/
/*      Display table elements                                */ 
/******************************************************************/
/* r0 contains the address of table */
displayTable:
    push {r0-r3,lr}                                    @ save registers
    mov r2,r0                                          @ table address
    mov r3,#0
1:                                                     @ loop display table
    ldr r0,[r2,r3,lsl #2]
    ldr r1,iAdrsZoneConv                               @ 
    bl conversion10S                                    @ décimal conversion 
    ldr r0,iAdrsMessResult
    ldr r1,iAdrsZoneConv                               @ insert conversion
    bl strInsertAtCharInc
    bl affichageMess                                   @ display message
    add r3,#1
    cmp r3,#NBELEMENTS - 1
    ble 1b
    ldr r0,iAdrszCarriageReturn
    bl affichageMess
    mov r0,r2
100:
    pop {r0-r3,lr}
    bx lr
iAdrsZoneConv:           .int sZoneConv
/***************************************************/
/*      ROUTINES INCLUDE                           */
/***************************************************/
.include "../affichage.inc"

Astro[edit]

fun mergesort(m):
    if m.lenght <= 1: return m
    let middle = floor m.lenght / 2
    let left = merge(m[:middle])
    let right = merge(m[middle-1:]);

fun merge(left, right):
    let result = []
    while not (left.isempty or right.isempty):
        if left[1] <= right[1]:
            result.push! left.shift!()
        else:
            result.push! right.shift!()
    result.push! left.push! right

let arr = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0]
print mergesort arr

ATS[edit]

A mergesort for linear lists[edit]

This algorithm modifies the links in the list, rather than allocate new cons-pairs. It requires no garbage collector.

(*------------------------------------------------------------------*)
(* Mergesort in ATS2, for linear lists.                             *)
(*------------------------------------------------------------------*)

#include "share/atspre_staload.hats"

staload UN = "prelude/SATS/unsafe.sats"

#define NIL list_vt_nil ()
#define ::  list_vt_cons

(*------------------------------------------------------------------*)

(* Destructive stable merge. *)
extern fun {a : vt@ype}
list_vt_merge {m, n : int}
              (lst1 : list_vt (a, m),
               lst2 : list_vt (a, n))
    :<!wrt> list_vt (a, m + n)

(* Order predicate for list_vt_merge. You have to implement this to
   suit your needs. *)
extern fun {a : vt@ype}
list_vt_merge$lt : (&a, &a) -<> bool

(* Destructive stable mergesort. *)
extern fun {a : vt@ype}
list_vt_mergesort {n   : int}
                  (lst : list_vt (a, n))
    :<!wrt> list_vt (a, n)

(* Order predicate for list_vt_mergesort. You have to implement this
   to suit your needs. *)
extern fun {a : vt@ype}
list_vt_mergesort$lt : (&a, &a) -<> bool

(*------------------------------------------------------------------*)

implement {a}
list_vt_merge {m, n} (lst1, lst2) =
  let
    macdef lt = list_vt_merge$lt<a>

    fun
    loop {m, n       : nat} .<m + n>.
         (lst1       : list_vt (a, m),
          lst2       : list_vt (a, n),
          lst_merged : &List_vt a? >> list_vt (a, m + n))
        :<!wrt> void =
      case+ lst1 of
      | ~ NIL => lst_merged := lst2
      | @ elem1 :: tail1 =>
        begin
          case+ lst2 of
          | ~ NIL =>
            let
              prval () = fold@ lst1
            in
              lst_merged := lst1
            end
          | @ elem2 :: tail2 =>
            if ~(elem2 \lt elem1) then
              let
                val () = lst_merged := lst1
                prval () = fold@ lst2
                val () = loop (tail1, lst2, tail1)
                prval () = fold@ lst_merged
              in
              end
            else
              let
                val () = lst_merged := lst2
                prval () = fold@ lst1
                val () = loop (lst1, tail2, tail2)
                prval () = fold@ lst_merged
              in
              end
        end

    prval () = lemma_list_vt_param lst1 (* Proves 0 <= m. *)
    prval () = lemma_list_vt_param lst2 (* Proves 0 <= n. *)
    prval () = prop_verify {0 <= m} ()
    prval () = prop_verify {0 <= n} ()

    var lst_merged : List_vt a?
    val () = loop {m, n} (lst1, lst2, lst_merged)
  in
    lst_merged
  end

(*------------------------------------------------------------------*)

implement {a}
list_vt_mergesort {n} lst =
  let
    implement
    list_vt_merge$lt<a> (x, y) =
      list_vt_mergesort$lt<a> (x, y)

    (* You can make SMALL larger than 1 and write small_sort as a fast
       stable sort for small lists. *)
    #define SMALL 1
    fn
    small_sort {m   : pos | m <= SMALL}
               (lst : list_vt (a, m),
                m   : int m)
        :<!wrt> list_vt (a, m) =
      lst

    fun
    recurs {m   : pos} .<m>.
           (lst : list_vt (a, m),
            m   : int m)
        :<!wrt> list_vt (a, m) =
      if m <= SMALL then
        small_sort (lst, m)
      else
        let
          prval () = prop_verify {2 <= m} ()
          val i = m / 2
          val @(lst1, lst2) = list_vt_split_at<a> (lst, i)
          val lst1 = recurs (lst1, i)
          val lst2 = recurs (lst2, m - i)
        in
          list_vt_merge<a> (lst1, lst2)
        end

    prval () = lemma_list_vt_param lst (* Proves 0 <= n. *)
    prval () = prop_verify {0 <= n} ()
  in
    case+ lst of
    | NIL => lst
    | _ :: _ => recurs (lst, length lst)
  end

(*------------------------------------------------------------------*)

extern fun
list_vt_mergesort_int {n   : int}
                      (lst : list_vt (int, n))
    :<!wrt> list_vt (int, n)

implement
list_vt_mergesort_int {n} lst =
  let
    implement
    list_vt_mergesort$lt<int> (x, y) =
      x < y
  in
    list_vt_mergesort<int> {n} lst
  end

implement
main0 () =
  let
    val lst = $list_vt (22, 15, 98, 82, 22, 4, 58, 70, 80, 38, 49,
                        48, 46, 54, 93, 8, 54, 2, 72, 84, 86, 76,
                        53, 37, 90)
    val () = println! ("before : ", $UN.castvwtp1{List int} lst)
    val lst = list_vt_mergesort_int lst
    val () = println! ("after  : ", $UN.castvwtp1{List int} lst)
  in
    list_vt_free<int> lst
  end

(*------------------------------------------------------------------*)
Output:
$ patscc -O3 -DATS_MEMALLOC_LIBC mergesort_task_for_list_vt.dats && ./a.out
before : 22, 15, 98, 82, 22, 4, 58, 70, 80, 38, 49, 48, 46, 54, 93, 8, 54, 2, 72, 84, 86, 76, 53, 37, 90
after  : 2, 4, 8, 15, 22, 22, 37, 38, 46, 48, 49, 53, 54, 54, 58, 70, 72, 76, 80, 82, 84, 86, 90, 93, 98

Footnote: Rather than directly write a mergesort for "ordinary" non-linear lists, I would write a routine to do the following:

  • make a copy of the list;
  • cast the copy to a linear list;
  • sort the linear list;
  • cast the result to non-linear list, and return the casted result.


This way, new cons-pairs are allocated only once.

The same thing can be done in other languages, of course. An interesting thing about this ATS implementation, though, is it proves the result is of the same length as the input. It does not, however, prove that the result satisfies the order predicate.

A mergesort for non-linear lists of integers, guaranteeing a sorted result[edit]

The following program not only sorts a list of integers, but verifies that the result is sorted. It is the simplest implementation I could think of that does that. It works by having a special kind of list that can be consed only in sorted order.

The length of the result also is verified. However, there is no proof that the result contains the same data as the input.

//--------------------------------------------------------------------
//
//  A mergesort for 32-bit signed integers.
//
//--------------------------------------------------------------------

#include "share/atspre_staload.hats"

(*------------------------------------------------------------------*)

#define ENTIER_MAX 2147483647

(* We do not include the most negative two's-complement number. *)
stadef entier (i : int) = ~ENTIER_MAX <= i && i <= ENTIER_MAX
sortdef entier          = {i : int | entier i}

typedef entier (i : int) = [entier i] int i
typedef entier           = [i : entier] entier i

datatype sorted_entier_list (int, int) =
| sorted_entier_list_nil (0, ENTIER_MAX)
| {n : nat}
  {i, j : entier | ~(j < i)}
  sorted_entier_list_cons (n + 1, i) of
    (entier i, sorted_entier_list (n, j))
typedef sorted_entier_list (n : int) =
  [i : entier] sorted_entier_list (n, i)
typedef sorted_entier_list =
  [n : int] sorted_entier_list n

infixr ( :: ) :::
#define NIL  list_nil ()
#define ::   list_cons
#define SNIL sorted_entier_list_nil ()
#define :::  sorted_entier_list_cons

(*------------------------------------------------------------------*)

extern prfn
lemma_sorted_entier_list_param
          {n   : int}
          (lst : sorted_entier_list n)
    :<prf> [0 <= n] void

extern fn
sorted_entier_list_length
          {n   : int}
          (lst : sorted_entier_list n)
    :<> [0 <= n] int n

extern fn
sorted_entier_list_merge
          {m, n : int}
          {i, j : entier}
          (lst1 : sorted_entier_list (m, i),
           lst2 : sorted_entier_list (n, j))
    :<> sorted_entier_list (m + n, min (i, j))

extern fn
entier_list_mergesort
          {n   : int}
          (lst : list (entier, n)) (* An ordinary list. *)
    :<!wrt> sorted_entier_list n

extern fn
sorted_entier_list2list
          {n   : int}
          (lst : sorted_entier_list n)
    :<> list (entier, n)

overload length with sorted_entier_list_length
overload merge with sorted_entier_list_merge
overload mergesort with entier_list_mergesort
overload to_list with sorted_entier_list2list

(*------------------------------------------------------------------*)

primplement
lemma_sorted_entier_list_param {n} lst =
  case+ lst of
  | SNIL => ()
  | _ ::: _ => ()

implement
sorted_entier_list_length {n} lst =
  (* This implementation is tail-recursive. *)
  let
    fun
    count {m   : nat | m <= n} .<n - m>.
          (lst : sorted_entier_list (n - m),
           m   : int m)
        :<> [0 <= n] int n =
      case+ lst of
      | SNIL => m
      | _ ::: tail => count {m + 1} (tail, succ m)

    prval () = lemma_sorted_entier_list_param lst
  in
    count (lst, 0)
  end

implement
sorted_entier_list_merge (lst1, lst2) =
  (* This implementation is *NOT* tail recursive. It will use O(m+n)
     stack space. *)
  let
    fun
    recurs {m, n : nat}
           {i, j : entier} .<m + n>.
           (lst1 : sorted_entier_list (m, i),
            lst2 : sorted_entier_list (n, j))
        :<> sorted_entier_list (m + n, min (i, j)) =
      case+ lst1 of
      | SNIL => lst2
      | i ::: tail1 =>
        begin
          case+ lst2 of
          | SNIL => lst1
          | j ::: tail2 =>
            if ~(j < i) then
              i ::: recurs (tail1, lst2)
            else
              j ::: recurs (lst1, tail2)
        end

    prval () = lemma_sorted_entier_list_param lst1
    prval () = lemma_sorted_entier_list_param lst2
  in
    recurs (lst1, lst2)
  end

implement
entier_list_mergesort lst =
  let
    fun
    recurs {m   : nat} .<m>.
           (lst : list (entier, m),
            m   : int m)
        :<!wrt> sorted_entier_list m =
      if m = 1 then
        let
          val+ head :: NIL = lst
        in
          head ::: SNIL
        end
      else if m = 0 then
        SNIL
      else
        let
          val m_left = m \g1int_ndiv 2
          val m_right = m - m_left
          val @(left, right) = list_split_at (lst, m_left)
          val left = recurs (list_vt2t left, m_left)
          and right = recurs (right, m_right)
        in
          left \merge right
        end

    prval () = lemma_list_param lst
  in
    recurs (lst, length lst)
  end

implement
sorted_entier_list2list lst =
  (* This implementation is *NOT* tail recursive. It will use O(n)
     stack space. *)
  let
    fun
    recurs {n   : nat} .<n>.
           (lst : sorted_entier_list n)
        :<> list (entier, n) =
      case+ lst of
      | SNIL => NIL
      | head ::: tail => head :: recurs tail

    prval () = lemma_sorted_entier_list_param lst
  in
    recurs lst
  end

(*------------------------------------------------------------------*)

fn
print_Int_list
          {n   : int}
          (lst : list (Int, n))
    : void =
  let
    fun
    loop {n   : nat} .<n>.
         (lst : list (Int, n))
        : void =
      case+ lst of
      | NIL => ()
      | head :: tail =>
        begin
          print! (" ");
          print! (head);
          loop tail
        end
    prval () = lemma_list_param lst
  in
    loop lst
  end

implement
main0 () =
  let
    val example_list =
      $list (22, 15, 98, 82, 22, 4, 58, 70, 80, 38, 49, 48, 46, 54,
             93, 8, 54, 2, 72, 84, 86, 76, 53, 37, 90)
    val sorted_list = mergesort example_list
  in
    print! ("unsorted  ");
    print_Int_list example_list;
    println! ();
    print! ("sorted    ");
    print_Int_list (to_list sorted_list);
    println! ()
  end

(*------------------------------------------------------------------*)
Output:
patscc -O3 -DATS_MEMALLOC_GCBDW mergesort_task_verified.dats -lgc && ./a.out
unsorted   22 15 98 82 22 4 58 70 80 38 49 48 46 54 93 8 54 2 72 84 86 76 53 37 90
sorted     2 4 8 15 22 22 37 38 46 48 49 53 54 54 58 70 72 76 80 82 84 86 90 93 98

Postscript. One might try adding a line such as

val x = 3 ::: 2 ::: SNIL

to the program and see that the compiler will report it as erroneous, on grounds that "2 is not less than 3" is unsatisfied.

AutoHotkey_L[edit]

AutoHotkey_L has true array support and can dynamically grow and shrink its arrays at run time. This version of Merge Sort only needs n locations to sort. AHK forum post

#NoEnv

Test := []
Loop 100 {
    Random n, 0, 999
    Test.Insert(n)
}
Result := MergeSort(Test)
Loop % Result.MaxIndex() {
    MsgBox, 1, , % Result[A_Index]
    IfMsgBox Cancel
        Break
}
Return


/*
    Function MergeSort
        Sorts an array by first recursively splitting it down to its
        individual elements and then merging those elements in their
        correct order.
       
    Parameters
        Array   The array to be sorted
       
    Returns
        The sorted array
*/
MergeSort(Array)
    {
        ; Return single element arrays
        If (! Array.HasKey(2))
            Return Array

        ; Split array into Left and Right halfs
        Left := [], Right := [], Middle := Array.MaxIndex() // 2
        Loop % Middle
            Right.Insert(Array.Remove(Middle-- + 1)), Left.Insert(Array.Remove(1))
        If (Array.MaxIndex())
            Right.Insert(Array.Remove(1))
       
        Left := MergeSort(Left), Right := MergeSort(Right)

        ; If all the Right values are greater than all the
        ; Left values, just append Right at the end of Left.
        If (Left[Left.MaxIndex()] <= Right[1]) {
            Loop % Right.MaxIndex()
                Left.Insert(Right.Remove(1))
            Return Left
        }
        ; Loop until one of the arrays is empty
        While(Left.MaxIndex() and Right.MaxIndex())
            Left[1] <= Right[1] ? Array.Insert(Left.Remove(1))
                                : Array.Insert(Right.Remove(1))

        Loop % Left.MaxIndex()
            Array.Insert(Left.Remove(1))

        Loop % Right.MaxIndex()
            Array.Insert(Right.Remove(1))
           
        Return Array
    }

AutoHotkey[edit]

Contributed by Laszlo on the ahk forum

MsgBox % MSort("")
MsgBox % MSort("xxx")
MsgBox % MSort("3,2,1")
MsgBox % MSort("dog,000000,cat,pile,abcde,1,zz,xx,z")

MSort(x) {                                                  ; Merge-sort of a comma separated list
   If (2 > L:=Len(x))
       Return x                                             ; empty or single item lists are sorted
   StringGetPos p, x, `,, % "L" L//2                        ; Find middle comma
   Return Merge(MSort(SubStr(x,1,p)), MSort(SubStr(x,p+2))) ; Split, Sort, Merge
}

Len(list) {
   StringReplace t, list,`,,,UseErrorLevel                  ; #commas -> ErrorLevel
   Return list="" ? 0 : ErrorLevel+1
}

Item(list,ByRef p) {                                        ; item at position p, p <- next position
   Return (p := InStr(list,",",0,i:=p+1)) ? SubStr(list,i,p-i) : SubStr(list,i)
}

Merge(list0,list1) {                                        ; Merge 2 sorted lists
   IfEqual list0,, Return list1
   IfEqual list1,, Return list0
   i0 := Item(list0,p0:=0)
   i1 := Item(list1,p1:=0)
   Loop  {
      i := i0>i1
      list .= "," i%i%                                      ; output smaller
      If (p%i%)
         i%i% := Item(list%i%,p%i%)                         ; get next item from processed list
      Else {
         i ^= 1                                             ; list is exhausted: attach rest of other
         Return SubStr(list "," i%i% (p%i% ? "," SubStr(list%i%,p%i%+1) : ""), 2)
      }
   }
}

BBC BASIC[edit]

DEFPROC_MergeSort(Start%,End%)
REM *****************************************************************
REM This procedure Merge Sorts the chunk of data% bounded by
REM Start% & End%.
REM *****************************************************************

LOCAL Middle%
IF End%=Start% ENDPROC

IF End%-Start%=1 THEN
   IF data%(End%)<data%(Start%) THEN
      SWAP data%(Start%),data%(End%)
   ENDIF
   ENDPROC
ENDIF

Middle%=Start%+(End%-Start%)/2

PROC_MergeSort(Start%,Middle%)
PROC_MergeSort(Middle%+1,End%)
PROC_Merge(Start%,Middle%,End%)

ENDPROC
:
DEF PROC_Merge(Start%,Middle%,End%)

LOCAL fh_size%
fh_size% = Middle%-Start%+1

FOR I%=0 TO fh_size%-1
  fh%(I%)=data%(Start%+I%)
NEXT I%

I%=0
J%=Middle%+1
K%=Start%

REPEAT
  IF fh%(I%) <= data%(J%) THEN
    data%(K%)=fh%(I%)
    I%+=1
    K%+=1
  ELSE
    data%(K%)=data%(J%)
    J%+=1
    K%+=1
  ENDIF
UNTIL I%=fh_size% OR J%>End%

WHILE I% < fh_size%
  data%(K%)=fh%(I%)
  I%+=1
  K%+=1
ENDWHILE

ENDPROC

Usage would look something like this example which sorts a series of 1000 random integers:

REM Example of merge sort usage.
Size%=1000

S1%=Size%/2

DIM data%(Size%)
DIM fh%(S1%)

FOR I%=1 TO Size%
  data%(I%)=RND(100000)
NEXT

PROC_MergeSort(1,Size%)

END

BCPL[edit]

get "libhdr"

let mergesort(A, n) be if n >= 2
$(  let m = n / 2
    mergesort(A, m)
    mergesort(A+m, n-m)
    merge(A, n, m)
$)
and merge(A, n, m) be
$(  let i, j = 0, m
    let x = getvec(n)
    for k=0 to n-1
        x!k := A!valof
            test j~=n & (i=m | A!j < A!i)
            $(  j := j + 1
                resultis j - 1
            $)
            else 
            $(  i := i + 1
                resultis i - 1
            $)
    for i=0 to n-1 do a!i := x!i
    freevec(x)
$)

let write(s, A, len) be
$(  writes(s)
    for i=0 to len-1 do writed(A!i, 4)
    wrch('*N')
$)
    
let start() be
$(  let array = table 4,65,2,-31,0,99,2,83,782,1
    let length = 10    
    write("Before: ", array, length)
    mergesort(array, length)
    write("After:  ", array, length)
$)
Output:
Before:    4  65   2 -31   0  99   2  83 782   1
After:   -31   0   1   2   2   4  65  83  99 782

C[edit]

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

void merge (int *a, int n, int m) {
    int i, j, k;
    int *x = malloc(n * sizeof (int));
    for (i = 0, j = m, k = 0; k < n; k++) {
        x[k] = j == n      ? a[i++]
             : i == m      ? a[j++]
             : a[j] < a[i] ? a[j++]
             :               a[i++];
    }
    for (i = 0; i < n; i++) {
        a[i] = x[i];
    }
    free(x);
}

void merge_sort (int *a, int n) {
    if (n < 2)
        return;
    int m = n / 2;
    merge_sort(a, m);
    merge_sort(a + m, n - m);
    merge(a, n, m);
}

int main () {
    int a[] = {4, 65, 2, -31, 0, 99, 2, 83, 782, 1};
    int n = sizeof a / sizeof a[0];
    int i;
    for (i = 0; i < n; i++)
        printf("%d%s", a[i], i == n - 1 ? "\n" : " ");
    merge_sort(a, n);
    for (i = 0; i < n; i++)
        printf("%d%s", a[i], i == n - 1 ? "\n" : " ");
    return 0;
}
Output:
4 65 2 -31 0 99 2 83 782 1
-31 0 1 2 2 4 65 83 99 782

Non-recursive variant:

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

/* x and y are sorted, copy nx+ny sorted values to r */
void merge(int nx, int*x, int ny, int*y, int*r) {
    int i= 0, j= 0, k= 0;
    while (i<nx && j<ny) {
        int a= x[i], b= y[j];
        if (a<b) {
            r[k++]= a;
            i++;
        } else {
            r[k++]= b;
            j++;
        }
    }
    if (i<nx) {
        memcpy(r+k, i+x, (nx-i)*sizeof (int));
    } else if (j<ny) {
        memcpy(r+k, j+y, (ny-j)*sizeof (int));
    }
}

void mergesort(int ny, int *y) {
    int stride= 1, mid, *r= y, *t, *x= malloc(ny*sizeof (int));
    while (stride < ny) {
        stride= 2*(mid= stride);
        for (int i= 0; i<ny; i+= stride) {
            int lim= mid;
            if (i+stride >= ny) {
                if (i+mid >= ny) {
                    memcpy(i+x, i+y, (ny-i)*sizeof (int));
                    continue;
                }
                lim= ny-(i+mid);
            }
            merge(mid, i+y, lim, i+mid+y, i+x);
        }
        t= x; x= y; y=t;
    }
    if (y!=r) {
        memcpy(r, y, ny*sizeof(int));
        x= y;
    }
    free(x);
}

int main () {
    int a[] = {4, 65, 2, -31, 0, 99, 2, 83, 782, 1};
    int n = sizeof a / sizeof a[0];
    int i;
    for (i = 0; i < n; i++)
        printf("%d%s", a[i], i == n - 1 ? "\n" : " ");
    mergesort(n, a);
    for (i = 0; i < n; i++)
        printf("%d%s", a[i], i == n - 1 ? "\n" : " ");
    return 0;
}
Output:
4 65 2 -31 0 99 2 83 782 1
-31 0 1 2 2 4 65 83 99 782

C#[edit]

Works with: C# version 3.0+
namespace RosettaCode {
  using System;

  public class MergeSort<T> where T : IComparable {
    #region Constants
    public const UInt32 INSERTION_LIMIT_DEFAULT = 12;
    public const Int32 MERGES_DEFAULT = 6;
    #endregion

    #region Properties
    public UInt32 InsertionLimit { get; }
    protected UInt32[] Positions { get; set; }

    private Int32 merges;
    public Int32 Merges {
      get { return merges; }
      set {
        // A minimum of 2 merges are required
        if (value > 1)
          merges = value;
        else
          throw new ArgumentOutOfRangeException($"value = {value} must be greater than one", nameof(Merges));

        if (Positions == null || Positions.Length != merges)
          Positions = new UInt32[merges];
      }
    }
    #endregion

    #region Constructors
    public MergeSort(UInt32 insertionLimit, Int32 merges) {
      InsertionLimit = insertionLimit;
      Merges = merges;
    }

    public MergeSort()
      : this(INSERTION_LIMIT_DEFAULT, MERGES_DEFAULT) {
    }
    #endregion

    #region Sort Methods
    public void Sort(T[] entries) {
      // Allocate merge buffer
      var entries2 = new T[entries.Length];
      Sort(entries, entries2, 0, entries.Length - 1);
    }

    // Top-Down K-way Merge Sort
    public void Sort(T[] entries1, T[] entries2, Int32 first, Int32 last) {
      var length = last + 1 - first;
      if (length < 2) return;      
      if (length < Merges || length < InsertionLimit) {
        InsertionSort<T>.Sort(entries1, first, last);
        return;
      }

      var left = first;
      var size = ceiling(length, Merges);
      for (var remaining = length; remaining > 0; remaining -= size, left += size) {
        var right = left + Math.Min(remaining, size) - 1;
        Sort(entries1, entries2, left, right);
      }

      Merge(entries1, entries2, first, last);
      Array.Copy(entries2, first, entries1, first, length);
    }
    #endregion

    #region Merge Methods
    public void Merge(T[] entries1, T[] entries2, Int32 first, Int32 last) {
      Array.Clear(Positions, 0, Merges);
      // This implementation has a quadratic time dependency on the number of merges
      for (var index = first; index <= last; index++)
        entries2[index] = remove(entries1, first, last);
    }

    private T remove(T[] entries, Int32 first, Int32 last) {
      T entry = default;
      Int32? found = default;
      var length = last + 1 - first;

      var index = 0;
      var left = first;
      var size = ceiling(length, Merges);
      for (var remaining = length; remaining > 0; remaining -= size, left += size, index++) {
        var position = Positions[index];
        if (position < Math.Min(remaining, size)) {
          var next = entries[left + position];
          if (!found.HasValue || entry.CompareTo(next) > 0) {
            found = index;
            entry = next;
          }
        }
      }

      // Remove entry
      Positions[found.Value]++;
      return entry;
    }
    #endregion

    #region Math Methods
    private static Int32 ceiling(Int32 numerator, Int32 denominator) {
      return (numerator + denominator - 1) / denominator;
    }
    #endregion
  }

  #region Insertion Sort
  static class InsertionSort<T> where T : IComparable {
    public static void Sort(T[] entries, Int32 first, Int32 last) {
      for (var next = first + 1; next <= last; next++)
        insert(entries, first, next);
    }

    /// <summary>Bubble next entry up to its sorted location, assuming entries[first:next - 1] are already sorted.</summary>
    private static void insert(T[] entries, Int32 first, Int32 next) {
      var entry = entries[next];
      while (next > first && entries[next - 1].CompareTo(entry) > 0)
        entries[next] = entries[--next];
      entries[next] = entry;
    }
  }
  #endregion
}

Example:

  using Sort;
  using System;

  class Program {
    static void Main(String[] args) {
      var entries = new Int32[] { 7, 5, 2, 6, 1, 4, 2, 6, 3 };
      var sorter = new MergeSort<Int32>();
      sorter.Sort(entries);
      Console.WriteLine(String.Join(" ", entries));
    }
  }
Output:
1 2 2 3 4 5 6 6 7

C++[edit]

#include <iterator>
#include <algorithm> // for std::inplace_merge
#include <functional> // for std::less

template<typename RandomAccessIterator, typename Order>
 void mergesort(RandomAccessIterator first, RandomAccessIterator last, Order order)
{
  if (last - first > 1)
  {
    RandomAccessIterator middle = first + (last - first) / 2;
    mergesort(first, middle, order);
    mergesort(middle, last, order);
    std::inplace_merge(first, middle, last, order);
  }
}

template<typename RandomAccessIterator>
 void mergesort(RandomAccessIterator first, RandomAccessIterator last)
{
  mergesort(first, last, std::less<typename std::iterator_traits<RandomAccessIterator>::value_type>());
}

Clojure[edit]

Translation of: Haskell
(defn merge [left right]
  (cond (nil? left) right
        (nil? right) left
        :else (let [[l & *left] left
                    [r & *right] right]
                (if (<= l r) (cons l (merge *left right))
                             (cons r (merge left *right))))))

(defn merge-sort [list]
  (if (< (count list) 2)
    list
    (let [[left right] (split-at (/ (count list) 2) list)]
      (merge (merge-sort left) (merge-sort right)))))

COBOL[edit]

Cobol cannot do recursion, so this version simulates recursion. The working storage is therefore pretty complex, so I have shown the whole program, not just the working procedure division parts.

       IDENTIFICATION DIVISION.
       PROGRAM-ID.                      MERGESORT.
       AUTHOR.                          DAVE STRATFORD.
       DATE-WRITTEN.                    APRIL 2010.
       INSTALLATION.                    HEXAGON SYSTEMS LIMITED.
      ******************************************************************
      *                            MERGE SORT                          *
      *  The Merge sort uses a completely different paradigm, one of   *
      * divide and conquer, to many of the other sorts. The data set   *
      * is split into smaller sub sets upon which are sorted and then  *
      * merged together to form the final sorted data set.             *
      *  This version uses the recursive method. Split the data set in *
      * half and perform a merge sort on each half. This in turn splits*
      * each half again and again until each set is just one or 2 items*
      * long. A set of one item is already sorted so is ignored, a set *
      * of two is compared and swapped as necessary. The smaller data  *
      * sets are then repeatedly merged together to eventually form the*
      * full, sorted, set.                                             *
      *  Since cobol cannot do recursion this module only simulates it *
      * so is not as fast as a normal recursive version would be.      *
      *  Scales very well to larger data sets, its relative complexity *
      * means it is not suited to sorting smaller data sets: use an    *
      * Insertion sort instead as the Merge sort is a stable sort.     *
      ******************************************************************

       ENVIRONMENT DIVISION.
       CONFIGURATION SECTION.
       SOURCE-COMPUTER.                 ICL VME.
       OBJECT-COMPUTER.                 ICL VME.

       INPUT-OUTPUT SECTION.
       FILE-CONTROL.
           SELECT FA-INPUT-FILE  ASSIGN FL01.
           SELECT FB-OUTPUT-FILE ASSIGN FL02.

       DATA DIVISION.
       FILE SECTION.
       FD  FA-INPUT-FILE.
       01  FA-INPUT-REC.
         03  FA-DATA                    PIC 9(6).

       FD  FB-OUTPUT-FILE.
       01  FB-OUTPUT-REC                PIC 9(6).

       WORKING-STORAGE SECTION.
       01  WA-IDENTITY.
         03  WA-PROGNAME                PIC X(10) VALUE "MERGESORT".
         03  WA-VERSION                 PIC X(6) VALUE "000001".

       01  WB-TABLE.
         03  WB-ENTRY                   PIC 9(8) COMP SYNC OCCURS 100000
                                                 INDEXED BY WB-IX-1
                                                            WB-IX-2.

       01  WC-VARS.
         03  WC-SIZE                    PIC S9(8) COMP SYNC.
         03  WC-TEMP                    PIC S9(8) COMP SYNC.
         03  WC-START                   PIC S9(8) COMP SYNC.
         03  WC-MIDDLE                  PIC S9(8) COMP SYNC.
         03  WC-END                     PIC S9(8) COMP SYNC.

       01  WD-FIRST-HALF.
         03  WD-FH-MAX                  PIC S9(8) COMP SYNC.
         03  WD-ENTRY                   PIC 9(8) COMP SYNC OCCURS 50000
                                                 INDEXED BY WD-IX.

       01  WF-CONDITION-FLAGS.
         03  WF-EOF-FLAG                PIC X.
           88  END-OF-FILE              VALUE "Y".
         03  WF-EMPTY-FILE-FLAG         PIC X.
           88  EMPTY-FILE               VALUE "Y".

       01  WS-STACK.
      * This stack is big enough to sort a list of 1million items.
         03  WS-STACK-ENTRY OCCURS 20 INDEXED BY WS-STACK-TOP.
           05  WS-START                 PIC S9(8) COMP SYNC.
           05  WS-MIDDLE                PIC S9(8) COMP SYNC.
           05  WS-END                   PIC S9(8) COMP SYNC.
           05  WS-FS-FLAG               PIC X.
             88  FIRST-HALF             VALUE "F".
             88  SECOND-HALF            VALUE "S".
             88  WS-ALL                 VALUE "A".
           05  WS-IO-FLAG               PIC X.
             88  WS-IN                  VALUE "I".
             88  WS-OUT                 VALUE "O".

       PROCEDURE DIVISION.
       A-MAIN SECTION.
       A-000.
           PERFORM B-INITIALISE.

           IF NOT EMPTY-FILE
              PERFORM C-PROCESS.

           PERFORM D-FINISH.

       A-999.
           STOP RUN.

       B-INITIALISE SECTION.
       B-000.
           DISPLAY "*** " WA-PROGNAME " VERSION "
                          WA-VERSION " STARTING ***".

           MOVE ALL "N" TO WF-CONDITION-FLAGS.
           OPEN INPUT FA-INPUT-FILE.
           SET WB-IX-1 TO 0.

           READ FA-INPUT-FILE AT END MOVE "Y" TO WF-EOF-FLAG
                                                 WF-EMPTY-FILE-FLAG.

           PERFORM BA-READ-INPUT UNTIL END-OF-FILE.

           CLOSE FA-INPUT-FILE.

           SET WC-SIZE TO WB-IX-1.

       B-999.
           EXIT.

       BA-READ-INPUT SECTION.
       BA-000.
           SET WB-IX-1 UP BY 1.
           MOVE FA-DATA TO WB-ENTRY(WB-IX-1).

           READ FA-INPUT-FILE AT END MOVE "Y" TO WF-EOF-FLAG.

       BA-999.
           EXIT.

       C-PROCESS SECTION.
       C-000.
           DISPLAY "SORT STARTING".

           MOVE 1           TO WS-START(1).
           MOVE WC-SIZE     TO WS-END(1).
           MOVE "F"         TO WS-FS-FLAG(1).
           MOVE "I"         TO WS-IO-FLAG(1).
           SET WS-STACK-TOP TO 2.

           PERFORM E-MERGE-SORT UNTIL WS-OUT(1).

           DISPLAY "SORT FINISHED".

       C-999.
           EXIT.

       D-FINISH SECTION.
       D-000.
           OPEN OUTPUT FB-OUTPUT-FILE.
           SET WB-IX-1 TO 1.

           PERFORM DA-WRITE-OUTPUT UNTIL WB-IX-1 > WC-SIZE.

           CLOSE FB-OUTPUT-FILE.

           DISPLAY "*** " WA-PROGNAME " FINISHED ***".

       D-999.
           EXIT.

       DA-WRITE-OUTPUT SECTION.
       DA-000.
           WRITE FB-OUTPUT-REC FROM WB-ENTRY(WB-IX-1).
           SET WB-IX-1 UP BY 1.

       DA-999.
           EXIT.

      ******************************************************************
       E-MERGE-SORT SECTION.
      *=====================                                           *
      * This section controls the simulated recursion.                 *
      ******************************************************************
       E-000.
           IF WS-OUT(WS-STACK-TOP - 1)
              GO TO E-010. 

           MOVE WS-START(WS-STACK-TOP - 1) TO WC-START.
           MOVE WS-END(WS-STACK-TOP - 1)   TO WC-END.

      * First check size of part we are dealing with.
           IF WC-END - WC-START = 0
      * Only 1 number in range, so simply set for output, and move on
              MOVE "O" TO WS-IO-FLAG(WS-STACK-TOP - 1)
              GO TO E-010.

           IF WC-END - WC-START = 1
      * 2 numbers, so compare and swap as necessary. Set for output
              MOVE "O" TO WS-IO-FLAG(WS-STACK-TOP - 1)
              IF WB-ENTRY(WC-START) > WB-ENTRY(WC-END)
                 MOVE WB-ENTRY(WC-START) TO WC-TEMP
                 MOVE WB-ENTRY(WC-END) TO WB-ENTRY(WC-START)
                 MOVE WC-TEMP TO WB-ENTRY(WC-END)
                 GO TO E-010
              ELSE
                 GO TO E-010.

      * More than 2, so split and carry on down
           COMPUTE WC-MIDDLE = ( WC-START + WC-END ) / 2.

           MOVE WC-START  TO WS-START(WS-STACK-TOP).
           MOVE WC-MIDDLE TO WS-END(WS-STACK-TOP).
           MOVE "F"       TO WS-FS-FLAG(WS-STACK-TOP).
           MOVE "I"       TO WS-IO-FLAG(WS-STACK-TOP).
           SET WS-STACK-TOP UP BY 1.

           GO TO E-999.

       E-010.
           SET WS-STACK-TOP DOWN BY 1.

           IF SECOND-HALF(WS-STACK-TOP)
              GO TO E-020.

           MOVE WS-START(WS-STACK-TOP - 1) TO WC-START.
           MOVE WS-END(WS-STACK-TOP - 1)   TO WC-END.
           COMPUTE WC-MIDDLE = ( WC-START + WC-END ) / 2 + 1.

           MOVE WC-MIDDLE TO WS-START(WS-STACK-TOP).
           MOVE WC-END    TO WS-END(WS-STACK-TOP).
           MOVE "S"       TO WS-FS-FLAG(WS-STACK-TOP).
           MOVE "I"       TO WS-IO-FLAG(WS-STACK-TOP).
           SET WS-STACK-TOP UP BY 1.

           GO TO E-999.

       E-020.
           MOVE WS-START(WS-STACK-TOP - 1) TO WC-START.
           MOVE WS-END(WS-STACK-TOP - 1)   TO WC-END.
           COMPUTE WC-MIDDLE = ( WC-START + WC-END ) / 2.
           PERFORM H-PROCESS-MERGE.
           MOVE "O" TO WS-IO-FLAG(WS-STACK-TOP - 1).

       E-999.
           EXIT.

      ******************************************************************
       H-PROCESS-MERGE SECTION.
      *========================                                        *
      * This section identifies which data is to be merged, and then   *
      * merges the two data streams into a single larger data stream.  *
      ******************************************************************
       H-000.
           INITIALISE WD-FIRST-HALF.
           COMPUTE WD-FH-MAX = WC-MIDDLE - WC-START + 1.
           SET WD-IX                        TO 1.

           PERFORM HA-COPY-OUT VARYING WB-IX-1 FROM WC-START BY 1
                               UNTIL WB-IX-1 > WC-MIDDLE.

           SET WB-IX-1 TO WC-START.
           SET WB-IX-2 TO WC-MIDDLE.
           SET WB-IX-2 UP BY 1.
           SET WD-IX   TO 1.
          
           PERFORM HB-MERGE UNTIL WD-IX > WD-FH-MAX OR WB-IX-2 > WC-END.

           PERFORM HC-COPY-BACK UNTIL WD-IX > WD-FH-MAX.

       H-999.
           EXIT.

       HA-COPY-OUT SECTION.
       HA-000.
           MOVE WB-ENTRY(WB-IX-1) TO WD-ENTRY(WD-IX).
           SET WD-IX UP BY 1.

       HA-999.
           EXIT.

       HB-MERGE SECTION.
       HB-000.
           IF WB-ENTRY(WB-IX-2) < WD-ENTRY(WD-IX)
              MOVE WB-ENTRY(WB-IX-2) TO WB-ENTRY(WB-IX-1)
              SET WB-IX-2            UP BY 1
           ELSE
              MOVE WD-ENTRY(WD-IX) TO WB-ENTRY(WB-IX-1)
              SET WD-IX            UP BY 1.

           SET WB-IX-1 UP BY 1.

       HB-999.
           EXIT.

       HC-COPY-BACK SECTION.
       HC-000.
           MOVE WD-ENTRY(WD-IX) TO WB-ENTRY(WB-IX-1).
           SET WD-IX            UP BY 1.
           SET WB-IX-1          UP BY 1.

       HC-999.
           EXIT.

CoffeeScript[edit]

# This is a simple version of mergesort that returns brand-new arrays.
# A more sophisticated version would do more in-place optimizations.
merge_sort = (arr) ->
  if arr.length <= 1
    return (elem for elem in arr)
  m = Math.floor(arr.length / 2)
  arr1 = merge_sort(arr.slice 0, m)
  arr2 = merge_sort(arr.slice m)
  result = []
  p1 = p2 = 0
  while true
    if p1 >= arr1.length
      if p2 >= arr2.length
        return result 
      result.push arr2[p2]
      p2 += 1
    else if p2 >= arr2.length or arr1[p1] < arr2[p2]
      result.push arr1[p1]
      p1 += 1
    else
      result.push arr2[p2]
      p2 += 1

do ->
  console.log merge_sort [2,4,6,8,1,3,5,7,9,10,11,0,13,12]
Output:
> coffee mergesort.coffee 
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]

Common Lisp[edit]

(defun merge-sort (result-type sequence predicate)
   (let ((split (floor (length sequence) 2)))
     (if (zerop split)
       (copy-seq sequence)
       (merge result-type (merge-sort result-type (subseq sequence 0 split) predicate)
                          (merge-sort result-type (subseq sequence split)   predicate)
                          predicate))))

merge is a standard Common Lisp function.

> (merge-sort 'list (list 1 3 5 7 9 8 6 4 2) #'<)
(1 2 3 4 5 6 7 8 9)

Crystal[edit]

Translation of: Ruby
def merge_sort(a : Array(Int32)) : Array(Int32)
  return a if a.size <= 1
  m = a.size // 2
  lt = merge_sort(a[0 ... m])
  rt = merge_sort(a[m .. -1])
  return merge(lt, rt)
end
 
def merge(lt : Array(Int32), rt : Array(Int32)) : Array(Int32)
  result = Array(Int32).new
  until lt.empty? || rt.empty?
    result << (lt.first < rt.first ? lt.shift : rt.shift)
  end
  return result + lt + rt
end
 
a = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0]
puts merge_sort(a) # => [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

Curry[edit]

Copied from Curry: Example Programs

-- merge sort: sorting two lists by merging the sorted first
-- and second half of the list

sort :: ([a] -> [a] -> [a] -> Success) -> [a] -> [a] -> Success

sort merge xs ys =
   if length xs < 2 then ys =:= xs
   else sort merge (firsthalf xs) us
        & sort merge (secondhalf xs) vs
        & merge us vs ys
   where us,vs free


intMerge :: [Int] -> [Int] -> [Int] -> Success

intMerge []     ys     zs =  zs =:= ys
intMerge (x:xs) []     zs =  zs =:= x:xs
intMerge (x:xs) (y:ys) zs =
   if (x > y) then intMerge (x:xs) ys us & zs =:= y:us
              else intMerge xs (y:ys) vs & zs =:= x:vs
   where us,vs free
  
firsthalf  xs = take (length xs `div` 2) xs
secondhalf xs = drop (length xs `div` 2) xs



goal1 xs = sort intMerge [3,1,2] xs
goal2 xs = sort intMerge [3,1,2,5,4,8] xs
goal3 xs = sort intMerge [3,1,2,5,4,8,6,7,2,9,1,4,3] xs

D[edit]

Arrays only, not in-place.

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

T[] mergeSorted(T)(in T[] D) /*pure nothrow @safe*/ {
    if (D.length < 2)
        return D.dup;
    return [D[0 .. $ / 2].mergeSorted, D[$ / 2 .. $].mergeSorted]
           .nWayUnion.array;
}

void main() {
    [3, 4, 2, 5, 1, 6].mergeSorted.writeln;
}

Alternative Version[edit]

This in-place version allocates the auxiliary memory on the stack, making life easier for the garbage collector, but with risk of stack overflow (same output):

import std.stdio, std.algorithm, core.stdc.stdlib, std.exception,
       std.range;

void mergeSort(T)(T[] data) if (hasSwappableElements!(typeof(data))) {
    immutable L = data.length;
    if (L < 2) return;
    T* ptr = cast(T*)alloca(L * T.sizeof);
    enforce(ptr != null);
    ptr[0 .. L] = data[];
    mergeSort(ptr[0 .. L/2]);
    mergeSort(ptr[L/2 .. L]);
    [ptr[0 .. L/2], ptr[L/2 .. L]].nWayUnion().copy(data);
}

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

Dart[edit]

void main() {
  MergeSortInDart sampleSort = MergeSortInDart();

  List<int> theResultingList = sampleSort.sortTheList([54, 89, 125, 47899, 32, 61, 42, 895647, 215, 345, 6, 21, 2, 78]);

  print('Here\'s the sorted list: ${theResultingList}');
}

/////////////////////////////////////

class MergeSortInDart {

  List<int> sortedList;

  // In Dart we often put helper functions at the bottom.
  // You could put them anywhere, we just like it this way
  // for organizational purposes. It's nice to be able to
  // read them in the order they're called.

  // Start here
  List<int> sortTheList(List<int> sortThis){
    // My parameters are listed vertically for readability. Dart
    // doesn't care how you list them, vertically or horizontally.
    sortedList = mSort(
      sortThis,
      sortThis.sublist(0, sortThis.length),
      sortThis.length,
    );
    return sortThis;
  }

  mSort(
    List<int> sortThisList,
    List<int> tempList,
    int thisListLength) {

    if (thisListLength == 1) {
      return;
    }

    // In Dart using ~/ is more efficient than using .floor()
    int middle = (thisListLength ~/ 2);

    // If you use something in a try/on/catch/finally block then
    // be sure to declare it outside the block (for scope)
    List<int> tempLeftList;

    // This was used for troubleshooting. It was left here to show
    // how a basic block try/on can be better than a debugPrint since
    // it won't print unless there's a problem.
    try {
      tempLeftList = tempList.sublist(0, middle);
    } on RangeError {
      print(
          'tempLeftList length = ${tempList.length}, thisListLength '
            'was supposedly $thisListLength and Middle was $middle');
    }

    // If you see "myList.getRange(x,y)" that's a sign the code is
    // from Dart 1 and needs to be updated. It's "myList.sublist" in Dart 2
    List<int> tempRightList = tempList.sublist(middle);

    // Left side.
    mSort(
      tempLeftList,
      sortThisList.sublist(0, middle),
      middle,
    );

    // Right side.
    mSort(
      tempRightList,
      sortThisList.sublist(middle),
      sortThisList.length - middle,
    );

    // Merge it.
    dartMerge(
      tempLeftList,
      tempRightList,
      sortThisList,
    );
  }

  dartMerge(
    List<int> leftSide,
    List<int> rightSide,
    List<int> sortThisList,
    ) {
    int index = 0;
    int elementValue;

    // This should be human readable.
    while (leftSide.isNotEmpty && rightSide.isNotEmpty) {
      if (rightSide[0] < leftSide[0]) {
        elementValue = rightSide[0];
        rightSide.removeRange(0, 1);
      } else {
        elementValue = leftSide[0];
        leftSide.removeRange(0, 1);
      }
      sortThisList[index++] = elementValue;
    }

    while (leftSide.isNotEmpty) {
      elementValue = leftSide[0];
      leftSide.removeRange(0, 1);
      sortThisList[index++] = elementValue;
    }

    while (rightSide.isNotEmpty) {
      elementValue = rightSide[0];
      rightSide.removeRange(0, 1);
      sortThisList[index++] = elementValue;
    }
    sortedList = sortThisList;
  }
}

Delphi[edit]

See Pascal.

E[edit]

def merge(var xs :List, var ys :List) {
    var result := []
    while (xs =~ [x] + xr && ys =~ [y] + yr) {
        if (x <= y) {
            result with= x
            xs := xr
        } else {
            result with= y
            ys := yr
        }
    }
    return result + xs + ys
}

def sort(list :List) {
    if (list.size() <= 1) { return list }
    def split := list.size() // 2
    return merge(sort(list.run(0, split)),
                 sort(list.run(split)))
}

EasyLang[edit]

func sort . d[] .
  len tmp[] len d[]
  sz = 1
  while sz < len d[]
    swap tmp[] d[]
    left = 1
    while left < len d[]
      # merge
      mid = left + sz - 1
      if mid > len d[]
        mid = len d[]
      .
      right = mid + sz
      if right > len d[]
        right = len d[]
      .
      l = left
      r = mid + 1
      for i = left to right
        if r > right or l <= mid and tmp[l] < tmp[r]
          d[i] = tmp[l]
          l += 1
        else
          d[i] = tmp[r]
          r += 1
        .
      .
      left += sz + sz
    .
    sz += sz
  .
.
data[] = [ 29 4 72 44 55 26 27 77 92 5 ]
call sort data[]
print data[]

Eiffel[edit]

class
	MERGE_SORT [G -> COMPARABLE]

create
	sort

feature

	sort (ar: ARRAY [G])
			-- Sorted array in ascending order.
		require
			ar_not_empty: not ar.is_empty
		do
			create sorted_array.make_empty
			mergesort (ar, 1, ar.count)
			sorted_array := ar
		ensure
			sorted_array_not_empty: not sorted_array.is_empty
			sorted: is_sorted (sorted_array, 1, sorted_array.count)
		end

	sorted_array: ARRAY [G]

feature {NONE}

	mergesort (ar: ARRAY [G]; l, r: INTEGER)
			-- Sorting part of mergesort.
		local
			m: INTEGER
		do
			if l < r then
				m := (l + r) // 2
				mergesort (ar, l, m)
				mergesort (ar, m + 1, r)
				merge (ar, l, m, r)
			end
		end

	merge (ar: ARRAY [G]; l, m, r: INTEGER)
			-- Merge part of mergesort.
		require
			positive_index_l: l >= 1
			positive_index_m: m >= 1
			positive_index_r: r >= 1
			ar_not_empty: not ar.is_empty
		local
			merged: ARRAY [G]
			h, i, j, k: INTEGER
		do
			i := l
			j := m + 1
			k := l
			create merged.make_filled (ar [1], 1, ar.count)
			from
			until
				i > m or j > r
			loop
				if ar.item (i) <= ar.item (j) then
					merged.force (ar.item (i), k)
					i := i + 1
				elseif ar.item (i) > ar.item (j) then
					merged.force (ar.item (j), k)
					j := j + 1
				end
				k := k + 1
			end
			if i > m then
				from
					h := j
				until
					h > r
				loop
					merged.force (ar.item (h), k + h - j)
					h := h + 1
				end
			elseif j > m then
				from
					h := i
				until
					h > m
				loop
					merged.force (ar.item (h), k + h - i)
					h := h + 1
				end
			end
			from
				h := l
			until
				h > r
			loop
				ar.item (h) := merged.item (h)
				h := h + 1
			end
		ensure
			is_partially_sorted: is_sorted (ar, l, r)
		end

	is_sorted (ar: ARRAY [G]; l, r: INTEGER): BOOLEAN
			-- Is 'ar' sorted in ascending order?
		require
			ar_not_empty: not ar.is_empty
			l_in_range: l >= 1
			r_in_range: r <= ar.count
		local
			i: INTEGER
		do
			Result := True
			from
				i := l
			until
				i = r
			loop
				if ar [i] > ar [i + 1] then
					Result := False
				end
				i := i + 1
			end
		end

end

Test:

class
	APPLICATION

create
	make

feature

	make
		do
			test := <<2, 5, 66, -2, 0, 7>>
			io.put_string ("unsorted" + "%N")
			across
				test as ar
			loop
				io.put_string (ar.item.out + "%T")
			end
			io.put_string ("%N" + "sorted" + "%N")
			create merge.sort (test)
			across
				merge.sorted_array as ar
			loop
				io.put_string (ar.item.out + "%T")
			end
		end

	test: ARRAY [INTEGER]

	merge: MERGE_SORT [INTEGER]

end
Output:
unsorted
2 5 66 -2 0 7
sorted
-2 0 2 5 7 66

Elixir[edit]

defmodule Sort do
  def merge_sort(list) when length(list) <= 1, do: list
  def merge_sort(list) do
    {left, right} = Enum.split(list, div(length(list), 2))
    :lists.merge( merge_sort(left), merge_sort(right))
  end
end

Example:

iex(10)> Sort.merge_sort([5,3,9,4,1,6,8,2,7])
[1, 2, 3, 4, 5, 6, 7, 8, 9]

Erlang[edit]

Below are two versions. Both take advantage of built-in Erlang functions, lists:split and list:merge. The multi-process version spawns a new process each time it splits. This was slightly faster on a test system with only two cores, so it may not be the best implementation, however it does illustrate how easy it can be to add multi-threaded/process capabilities to a program.

Single-threaded version:

mergeSort(L) when length(L) == 1 -> L;
mergeSort(L) when length(L) > 1 ->
    {L1, L2} = lists:split(length(L) div 2, L),
    lists:merge(mergeSort(L1), mergeSort(L2)).

Multi-process version:

pMergeSort(L) when length(L) == 1 -> L;
pMergeSort(L) when length(L) > 1 ->
    {L1, L2} = lists:split(length(L) div 2, L),
    spawn(mergesort, pMergeSort2, [L1, self()]),
    spawn(mergesort, pMergeSort2, [L2, self()]),
    mergeResults([]).

pMergeSort2(L, Parent) when length(L) == 1 -> Parent ! L;
pMergeSort2(L, Parent) when length(L) > 1 ->
    {L1, L2} = lists:split(length(L) div 2, L),
    spawn(mergesort, pMergeSort2, [L1, self()]),
    spawn(mergesort, pMergeSort2, [L2, self()]),
    Parent ! mergeResults([]).


another multi-process version (number of processes == number of processor cores):

merge_sort(List) -> m(List, erlang:system_info(schedulers)).

m([L],_) -> [L]; 
m(L, N) when N > 1  -> 
    {L1,L2} = lists:split(length(L) div 2, L),
    {Parent, Ref} = {self(), make_ref()},
    spawn(fun()-> Parent ! {l1, Ref, m(L1, N-2)} end), 
    spawn(fun()-> Parent ! {l2, Ref, m(L2, N-2)} end), 
    {L1R, L2R} = receive_results(Ref, undefined, undefined),
    lists:merge(L1R, L2R);
m(L, _) -> {L1,L2} = lists:split(length(L) div 2, L), lists:merge(m(L1, 0), m(L2, 0)).

receive_results(Ref, L1, L2) ->
    receive
        {l1, Ref, L1R} when L2 == undefined -> receive_results(Ref, L1R, L2);
        {l2, Ref, L2R} when L1 == undefined -> receive_results(Ref, L1, L2R);
        {l1, Ref, L1R} -> {L1R, L2};
        {l2, Ref, L2R} -> {L1, L2R}
    after 5000 -> receive_results(Ref, L1, L2)
    end.

ERRE[edit]

PROGRAM MERGESORT_DEMO

! Example of merge sort usage.

CONST SIZE%=100,S1%=50

DIM DTA%[SIZE%],FH%[S1%],STACK%[20,2]


PROCEDURE MERGE(START%,MIDDLE%,ENDS%)

LOCAL FHSIZE%

  FHSIZE%=MIDDLE%-START%+1

  FOR I%=0 TO FHSIZE%-1 DO
     FH%[I%]=DTA%[START%+I%]
  END FOR

  I%=0
  J%=MIDDLE%+1
  K%=START%

  REPEAT
    IF FH%[I%]<=DTA%[J%] THEN
        DTA%[K%]=FH%[I%]
        I%=I%+1
        K%=K%+1
      ELSE
        DTA%[K%]=DTA%[J%]
        J%=J%+1
        K%=K%+1
    END IF
  UNTIL I%=FHSIZE% OR J%>ENDS%

  WHILE I%<FHSIZE% DO
     DTA%[K%]=FH%[I%]
     I%=I%+1
     K%=K%+1
  END WHILE

END PROCEDURE

PROCEDURE MERGE_SORT(LEV->LEV)

! *****************************************************************
! This procedure Merge Sorts the chunk of DTA% bounded by
! Start% & Ends%.
! *****************************************************************

   LOCAL MIDDLE%

   IF ENDS%=START% THEN LEV=LEV-1 EXIT PROCEDURE END IF

   IF ENDS%-START%=1 THEN
      IF DTA%[ENDS%]<DTA%[START%] THEN
         SWAP(DTA%[START%],DTA%[ENDS%])
      END IF
      LEV=LEV-1
      EXIT PROCEDURE
   END IF

   MIDDLE%=START%+(ENDS%-START%)/2

   STACK%[LEV,0]=START%  STACK%[LEV,1]=ENDS%  STACK%[LEV,2]=MIDDLE%
   START%=START%  ENDS%=MIDDLE%
   MERGE_SORT(LEV+1->LEV)
   START%=STACK%[LEV,0]  ENDS%=STACK%[LEV,1]  MIDDLE%=STACK%[LEV,2]

   STACK%[LEV,0]=START%  STACK%[LEV,1]=ENDS%  STACK%[LEV,2]=MIDDLE%
   START%=MIDDLE%+1  ENDS%=ENDS%
   MERGE_SORT(LEV+1->LEV)
   START%=STACK%[LEV,0]  ENDS%=STACK%[LEV,1]  MIDDLE%=STACK%[LEV,2]

   MERGE(START%,MIDDLE%,ENDS%)

   LEV=LEV-1
END PROCEDURE

BEGIN
  FOR I%=1 TO SIZE% DO
     DTA%[I%]=RND(1)*10000
  END FOR

  START%=1  ENDS%=SIZE%
  MERGE_SORT(0->LEV)

  FOR I%=1 TO SIZE% DO
     WRITE("#####";DTA%[I%];)
  END FOR
  PRINT
END PROGRAM

Euphoria[edit]

function merge(sequence left, sequence right)
    sequence result
    result = {}
    while length(left) > 0 and length(right) > 0 do
        if compare(left[1], right[1]) <= 0 then
            result = append(result, left[1])
            left = left[2..$]
        else
            result = append(result, right[1])
            right = right[2..$]
        end if
    end while
    return result & left & right
end function

function mergesort(sequence m)
    sequence left, right
    integer middle
    if length(m) <= 1 then
        return m
    else
        middle = floor(length(m)/2)
        left = mergesort(m[1..middle])
        right = mergesort(m[middle+1..$])
        if compare(left[$], right[1]) <= 0 then
            return left & right
        elsif compare(right[$], left[1]) <= 0 then
            return right & left
        else
            return merge(left, right)
        end if
    end if
end function

constant s = rand(repeat(1000,10))
? s
? mergesort(s)
Output:
{385,599,284,650,457,804,724,300,434,722}
{284,300,385,434,457,599,650,722,724,804}

F#[edit]

let split list =
    let rec aux l acc1 acc2 =
        match l with
            | [] -> (acc1,acc2)
            | [x] -> (x::acc1,acc2)
            | x::y::tail ->
                aux tail (x::acc1) (y::acc2)
    in aux list [] []

let rec merge l1 l2 =
    match (l1,l2) with
        | (x,[]) -> x
        | ([],y) -> y
        | (x::tx,y::ty) ->
            if x <= y then x::merge tx l2
            else y::merge l1 ty
let rec mergesort list = 
    match list with
        | [] -> []
        | [x] -> [x]
        | _ -> let (l1,l2) = split list
               in merge (mergesort l1) (mergesort l2)

Factor[edit]

: mergestep ( accum seq1 seq2 -- accum seq1 seq2 )
2dup [ first ] bi@ <
[ [ [ first ] [ rest-slice ] bi [ suffix ] dip ] dip ]
[ [ first ] [ rest-slice ] bi [ swap [ suffix ] dip ] dip ]
if ;

: merge ( seq1 seq2 -- merged )
[ { } ] 2dip
[ 2dup [ length 0 > ] bi@ and ]
[ mergestep ] while
append append ;

: mergesort ( seq -- sorted )
dup length 1 >
[ dup length 2 / floor [ head ] [ tail ] 2bi [ mergesort ] bi@ merge ]
[ ] if ;
( scratchpad ) { 4 2 6 5 7 1 3 } mergesort .
{ 1 2 3 4 5 6 7 }

Forth[edit]

This is an in-place mergesort which works on arrays of integers.

: merge-step ( right mid left -- right mid+ left+ )
  over @ over @ < if
    over @ >r
    2dup - over dup cell+ rot move
    r> over !
    >r cell+ 2dup = if rdrop dup else r> then
  then cell+ ;
: merge ( right mid left -- right left )
  dup >r begin 2dup > while merge-step repeat 2drop r> ;

: mid ( l r -- mid ) over - 2/ cell negate and + ;

: mergesort ( right left -- right left )
  2dup cell+ <= if exit then
  swap 2dup mid recurse rot recurse merge ;
  
: sort ( addr len -- )  cells over + swap mergesort 2drop ;

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

: .array ( addr len -- ) 0 do dup i cells + @ . loop drop ;

test 10 2dup sort .array       \ 0 1 2 3 4 5 6 7 8 9

Fortran[edit]

Works with: Fortran version 95 and later and with both free or fixed form syntax.
      program TestMergeSort
        implicit none
        integer, parameter :: N = 8
        integer :: A(N) = (/ 1, 5, 2, 7, 3, 9, 4, 6 /)
        integer :: work((size(A) + 1) / 2)
        write(*,'(A,/,10I3)')'Unsorted array :',A
        call MergeSort(A, work)
        write(*,'(A,/,10I3)')'Sorted array :',A
      contains

      subroutine merge(A, B, C)
        implicit none
! The targe attribute is necessary, because A .or. B might overlap with C.
        integer, target, intent(in) :: A(:), B(:)
        integer, target, intent(inout) :: C(:)
        integer :: i, j, k

        if (size(A) + size(B) > size(C)) stop(1)

        i = 1; j = 1
        do k = 1, size(C)
          if (i <= size(A) .and. j <= size(B)) then
            if (A(i) <= B(j)) then
              C(k) = A(i)
              i = i + 1
            else
              C(k) = B(j)
              j = j + 1
            end if
          else if (i <= size(A)) then
            C(k) = A(i)
            i = i + 1
          else if (j <= size(B)) then
            C(k) = B(j)
            j = j + 1
          end if
        end do
      end subroutine merge

      subroutine swap(x, y)
        implicit none
        integer, intent(inout) :: x, y
        integer :: tmp
        tmp = x; x = y; y = tmp
      end subroutine

      recursive subroutine MergeSort(A, work)
        implicit none
        integer, intent(inout) :: A(:)
        integer, intent(inout) :: work(:)
        integer :: half
        half = (size(A) + 1) / 2
        if (size(A) < 2) then
          continue
        else if (size(A) == 2) then
          if (A(1) > A(2)) then
            call swap(A(1), A(2))
          end if
        else
          call MergeSort(A( : half), work)
          call MergeSort(A(half + 1 :), work)
          if (A(half) > A(half + 1)) then
            work(1 : half) = A(1 : half)
            call merge(work(1 : half), A(half + 1:), A)
          endif
        end if
      end subroutine MergeSort
      end program TestMergeSort

FreeBASIC[edit]

Uses 'top down' C-like algorithm in Wikipedia article:

' FB 1.05.0 Win64

Sub copyArray(a() As Integer, iBegin As Integer, iEnd As Integer, b() As Integer)
  Redim b(iBegin To iEnd - 1) As Integer
  For k As Integer = iBegin To iEnd - 1
    b(k) = a(k)
  Next
End Sub

' Left source half is  a(iBegin  To iMiddle-1).
' Right source half is a(iMiddle To iEnd-1).
' Result is            b(iBegin  To iEnd-1).
Sub topDownMerge(a() As Integer, iBegin As Integer, iMiddle As Integer, iEnd As Integer, b() As Integer)
  Dim i As Integer = iBegin
  Dim j As Integer = iMiddle
    
  ' While there are elements in the left or right runs...
  For k As Integer = iBegin To iEnd - 1 
  ' If left run head exists and is <= existing right run head.
    If i < iMiddle AndAlso (j >= iEnd OrElse a(i) <= a(j)) Then
      b(k) = a(i)
      i += 1
    Else
      b(k) = a(j)
      j += 1    
    End If
  Next 
End Sub

' Sort the given run of array a() using array b() as a source.
' iBegin is inclusive; iEnd is exclusive (a(iEnd) is not in the set).
Sub topDownSplitMerge(b() As Integer, iBegin As Integer, iEnd As Integer, a() As Integer)
  If (iEnd - iBegin) < 2 Then Return  '' If run size = 1, consider it sorted
  ' split the run longer than 1 item into halves
  Dim iMiddle As Integer = (iEnd + iBegin) \ 2  '' iMiddle = mid point
  ' recursively sort both runs from array a() into b()
  topDownSplitMerge(a(), iBegin,  iMiddle, b())  '' sort the left  run
  topDownSplitMerge(a(), iMiddle, iEnd, b())     '' sort the right run
  ' merge the resulting runs from array b() into a()
  topDownMerge(b(), iBegin, iMiddle, iEnd, a())
End Sub

' Array a() has the items to sort; array b() is a work array (empty initially).      
Sub topDownMergeSort(a() As Integer, b() As Integer, n As Integer)
  copyArray(a(), 0, n, b())  '' duplicate array a() into b()           
  topDownSplitMerge(b(), 0, n, a())  '' sort data from b() into a()
End Sub

Sub printArray(a() As Integer)
  For i As Integer = LBound(a) To UBound(a)
    Print Using "####"; a(i);
  Next
  Print
End Sub

Dim a(0 To 9) As Integer = {4, 65, 2, -31, 0, 99, 2, 83, 782, 1}

Dim b() As Integer
Print "Unsorted : ";
printArray(a())
topDownMergeSort a(), b(), 10
Print "Sorted   : ";
printArray(a())
Print
Dim a2(0 To 8) As Integer = {7, 5, 2, 6, 1, 4, 2, 6, 3}
Erase b
Print "Unsorted : ";
printArray(a2())
topDownMergeSort a2(), b(), 9
Print "Sorted   : ";
printArray(a2())
Print
Print "Press any key to quit"
Sleep
Output:
Unsorted :    4  65   2 -31   0  99   2  83 782   1
Sorted   :  -31   0   1   2   2   4  65  83  99 782

Unsorted :    7   5   2   6   1   4   2   6   3
Sorted   :    1   2   2   3   4   5   6   6   7

FunL[edit]

def
  sort( [] )          =  []
  sort( [x] )         =  [x]
  sort( xs )          =
    val (l, r) = xs.splitAt( xs.length()\2 )
    merge( sort(l), sort(r) )

  merge( [], xs )     =  xs
  merge( xs, [] )     =  xs
  merge( x:xs, y:ys )
    | x <= y          =  x : merge( xs, y:ys )
    | otherwise       =  y : merge( x:xs, ys )
    
println( sort([94, 37, 16, 56, 72, 48, 17, 27, 58, 67]) )
println( sort(['Sofía', 'Alysha', 'Sophia', 'Maya', 'Emma', 'Olivia', 'Emily']) )
Output:
[16, 17, 27, 37, 48, 56, 58, 67, 72, 94]
[Alysha, Emily, Emma, Maya, Olivia, Sofía, Sophia]

Go[edit]

package main

import "fmt"

var a = []int{170, 45, 75, -90, -802, 24, 2, 66}
var s = make([]int, len(a)/2+1) // scratch space for merge step

func main() {
    fmt.Println("before:", a)
    mergeSort(a)
    fmt.Println("after: ", a)
}

func mergeSort(a []int) {
    if len(a) < 2 {
        return
    }
    mid := len(a) / 2
    mergeSort(a[:mid])
    mergeSort(a[mid:])
    if a[mid-1] <= a[mid] {
        return
    }
    // merge step, with the copy-half optimization
    copy(s, a[:mid])
    l, r := 0, mid
    for i := 0; ; i++ {
        if s[l] <= a[r] {
            a[i] = s[l]
            l++
            if l == mid {
                break
            }
        } else {
            a[i] = a[r]
            r++
            if r == len(a) {
                copy(a[i+1:], s[l:mid])
                break
            }
        }
    }
    return
}

Groovy[edit]

This is the standard algorithm, except that in the looping phase of the merge we work backwards through the left and right lists to construct the merged list, to take advantage of the Groovy List.pop() method. However, this results in a partially merged list in reverse sort order; so we then reverse it to put in back into correct order. This could play havoc with the sort stability, but we compensate by picking aggressively from the right list (ties go to the right), rather than aggressively from the left as is done in the standard algorithm.

def merge = { List left, List right ->
    List mergeList = []
    while (left && right) {
        print "."
        mergeList << ((left[-1] > right[-1]) ? left.pop() : right.pop())
    }
    mergeList = mergeList.reverse()
    mergeList = left + right + mergeList
}

def mergeSort;
mergeSort = { List list ->

    def n = list.size()
    if (n < 2) return list
    
    def middle = n.intdiv(2)
    def left = [] + list[0..<middle]
    def right = [] + list[middle..<n]
    left = mergeSort(left)
    right = mergeSort(right)
    
    if (left[-1] <= right[0]) return left + right
    
    merge(left, right)
}

Test:

println (mergeSort([23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78,4]))
println (mergeSort([88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70,12,7,1]))
println ()
println (mergeSort([10, 10.0, 10.00, 1]))
println (mergeSort([10, 10.00, 10.0, 1]))
println (mergeSort([10.0, 10, 10.00, 1]))
println (mergeSort([10.0, 10.00, 10, 1]))
println (mergeSort([10.00, 10, 10.0, 1]))
println (mergeSort([10.00, 10.0, 10, 1]))

The presence of decimal and integer versions of the same numbers, demonstrates, but of course does not prove, that the sort remains stable.

Output:
.............................................................[4, 12, 14, 23, 24, 24, 31, 35, 38, 46, 51, 57, 57, 58, 76, 78, 89, 92, 95, 97, 99]
....................................................................[0, 1, 4, 5, 7, 8, 12, 14, 18, 20, 31, 33, 44, 62, 70, 73, 75, 76, 78, 81, 82, 84, 88]

....[1, 10, 10.0, 10.00]
....[1, 10, 10.00, 10.0]
....[1, 10.0, 10, 10.00]
....[1, 10.0, 10.00, 10]
....[1, 10.00, 10, 10.0]
....[1, 10.00, 10.0, 10]

Tail recursion version[edit]

It is possible to write a version based on tail recursion, similar to that written in Haskell, OCaml or F#. This version also takes into account stack overflow problems induced by recursion for large lists using closure trampolines:

split = { list ->
    list.collate((list.size()+1)/2 as int)
}

merge = { left, right, headBuffer=[] ->
    if(left.size() == 0) headBuffer+right
    else if(right.size() == 0) headBuffer+left
    else if(left.head() <= right.head()) merge.trampoline(left.tail(), right, headBuffer+left.head())
    else merge.trampoline(right.tail(), left, headBuffer+right.head())
}.trampoline()

mergesort = { List list ->
    if(list.size() < 2) list
    else merge(split(list).collect {mergesort it})
}

assert mergesort((500..1)) == (1..500)
assert mergesort([5,4,6,3,1,2]) == [1,2,3,4,5,6]
assert mergesort([3,3,1,4,6,78,9,1,3,5]) == [1,1,3,3,3,4,5,6,9,78]

which uses List.collate(), alternatively one could write a purely recursive split() closure as:

split = { list, left=[], right=[] ->
    if(list.size() <2) [list+left, right]
    else split.trampoline(list.tail().tail(), [list.head()]+left,[list.tail().head()]+right)
}.trampoline()

Haskell[edit]

Splitting in half in the middle like the normal merge sort does would be inefficient on the singly-linked lists used in Haskell (since you would have to do one pass just to determine the length, and then another half-pass to do the splitting). Instead, the algorithm here splits the list in half in a different way -- by alternately assigning elements to one list and the other. That way we (lazily) construct both sublists in parallel as we traverse the original list. Unfortunately, under this way of splitting we cannot do a stable sort.

merge []         ys                   = ys
merge xs         []                   = xs
merge xs@(x:xt) ys@(y:yt) | x <= y    = x : merge xt ys
                          | otherwise = y : merge xs yt

split (x:y:zs) = let (xs,ys) = split zs in (x:xs,y:ys)
split [x]      = ([x],[])
split []       = ([],[])

mergeSort []  = []
mergeSort [x] = [x]
mergeSort xs  = let (as,bs) = split xs
                in merge (mergeSort as) (mergeSort bs)

Alternatively, we can use bottom-up mergesort. This starts with lots of tiny sorted lists, and repeatedly merges pairs of them, building a larger and larger sorted list

mergePairs (sorted1 : sorted2 : sorteds) = merge sorted1 sorted2 : mergePairs sorteds
mergePairs sorteds = sorteds

mergeSortBottomUp list = mergeAll (map (\x -> [x]) list)

mergeAll [sorted] = sorted
mergeAll sorteds = mergeAll (mergePairs sorteds)

The standard library's sort function in GHC takes a similar approach to the bottom-up code, the differece being that, instead of starting with lists of size one, which are sorted by default, it detects runs in original list and uses those:

sort = sortBy compare
sortBy cmp = mergeAll . sequences
  where
    sequences (a:b:xs)
      | a `cmp` b == GT = descending b [a]  xs
      | otherwise       = ascending  b (a:) xs
    sequences xs = [xs]

    descending a as (b:bs)
      | a `cmp` b == GT = descending b (a:as) bs
    descending a as bs  = (a:as): sequences bs

    ascending a as (b:bs)
      | a `cmp` b /= GT = ascending b (\ys -> as (a:ys)) bs
    ascending a as bs   = as [a]: sequences bs

In this code, mergeAll, mergePairs, and merge are as above, except using the specialized cmp function in merge.

Icon and Unicon[edit]

procedure main()                                                         #: demonstrate various ways to sort a list and string 
   demosort(mergesort,[3, 14, 1, 5, 9, 2, 6, 3],"qwerty")
end

procedure mergesort(X,op,lower,upper)                                    #: return sorted list ascending(or descending)
local middle

   if /lower := 1 then {                                                 # top level call setup
      upper := *X   
      op := sortop(op,X)                                                 # select how and what we sort
      }
	  
   if upper ~= lower then {                                              # sort all sections with 2 or more elements
      X := mergesort(X,op,lower,middle := lower + (upper - lower) / 2)
      X := mergesort(X,op,middle+1,upper)
   
      if op(X[middle+1],X[middle]) then                                  # @middle+1 < @middle merge if halves reversed
         X := merge(X,op,lower,middle,upper)
   }	  
   return X                                                              
end

procedure merge(X,op,lower,middle,upper)                                 # merge two list sections within a larger list
local p1,p2,add

   p1 := lower
   p2 := middle + 1
   add := if type(X) ~== "string" then put else "||"                     # extend X, strings require X := add (until ||:= is invocable)
 
   while p1 <= middle & p2 <= upper do 
      if op(X[p1],X[p2]) then {                                          # @p1 < @p2
         X := add(X,X[p1])                                               # extend X temporarily (rather than use a separate temporary list)
         p1 +:= 1
         }
      else {
         X := add(X,X[p2])                                               # extend X temporarily
         p2 +:= 1
         }
		 
   while X := add(X,X[middle >= p1]) do p1 +:= 1                         # and rest of lower or ...
   while X := add(X,X[upper  >= p2]) do p2 +:= 1                         # ... upper trailers if any 
   
   if type(X) ~== "string" then                                          # pull section's sorted elements from extension
      every X[upper to lower by -1] := pull(X)
   else	  
      (X[lower+:(upper-lower+1)] := X[0-:(upper-lower+1)])[0-:(upper-lower+1)] := ""
   
   return X 
end

Note: This example relies on the supporting procedures 'sortop', and 'demosort' in Bubble Sort. The full demosort exercises the named sort of a list with op = "numeric", "string", ">>" (lexically gt, descending),">" (numerically gt, descending), a custom comparator, and also a string.

Output:
Abbreviated sample
Sorting Demo using procedure mergesort
  on list : [ 3 14 1 5 9 2 6 3 ]
    with op = &null:         [ 1 2 3 3 5 6 9 14 ]   (0 ms)
  ...
  on string : "qwerty"
    with op = &null:         "eqrtwy"   (0 ms)

Io[edit]

List do (
    merge := method(lst1, lst2,
        result := list()
        while(lst1 isNotEmpty or lst2 isNotEmpty,
            if(lst1 first <= lst2 first) then(
                result append(lst1 removeFirst)
            ) else (
                result append(lst2 removeFirst)
            )
        )
    result)

    mergeSort := method(
        if (size > 1) then(
            half_size := (size / 2) ceil
            return merge(slice(0, half_size) mergeSort,
                         slice(half_size, size) mergeSort)
        ) else (return self)
    )

    mergeSortInPlace := method(
        copy(mergeSort)
    )
)

lst := list(9, 5, 3, -1, 15, -2)
lst mergeSort println # ==> list(-2, -1, 3, 5, 9, 15)
lst mergeSortInPlace println # ==> list(-2, -1, 3, 5, 9, 15)

Isabelle[edit]

theory Mergesort
  imports Main
begin

fun merge :: "int list ⇒ int list ⇒ int list" where
  "merge [] ys = ys"
| "merge xs [] = xs"
| "merge (x#xs) (y#ys) = (if x ≤ y
                          then x # merge xs (y#ys)
                          else y # merge (x # xs) ys)"

textexample:
lemma "merge [1,3,6] [1,2,5,8] = [1,1,2,3,5,6,8]" by simp

lemma merge_set: "set (merge xs ys) = set xs ∪ set ys"
  by(induction xs ys rule: merge.induct) auto

lemma merge_sorted:
  "sorted xs ⟹ sorted ys ⟹ sorted (merge xs ys)"
proof(induction xs ys rule: merge.induct)
  case (1 ys)
  then show "sorted (merge [] ys)" by simp
next
  case (2 x xs)
  then show "sorted (merge (x # xs) [])" by simp
next
  case (3 x xs y ys)
  assume premx: "sorted (x # xs)"
     and premy: "sorted (y # ys)"
     and IHx: "x ≤ y ⟹ sorted xs ⟹ sorted (y # ys) ⟹
                 sorted (merge xs (y # ys))"
     and IHy: "¬ x ≤ y ⟹ sorted (x # xs) ⟹ sorted ys ⟹
                 sorted (merge (x # xs) ys)"
  then show "sorted (merge (x # xs) (y # ys))"
  proof(cases "x ≤ y")
    case True
    with premx IHx premy have IH: "sorted (merge xs (y # ys))" by simp
    from x  y premx premy merge_set have
      "∀z ∈ set (merge xs (y # ys)). x ≤ z" by fastforce
    with x  y IH show "sorted (merge (x # xs) (y # ys))" by(simp)
  next
    case False
    with premy IHy premx have IH: "sorted (merge (x # xs) ys)" by simp
    from ‹¬x  y premx premy merge_set have
      "∀z ∈ set (merge (x # xs) ys). y ≤ z" by fastforce
    with ‹¬x  y IH show "sorted (merge (x # xs) (y # ys))" by(simp)
  qed
qed

fun mergesort :: "int list ⇒ int list" where
  "mergesort [] = []"
| "mergesort [x] = [x]"
| "mergesort xs = merge (mergesort (take (length xs div 2) xs))
                        (mergesort (drop (length xs div 2) xs))"

theorem mergesort_set: "set xs = set (mergesort xs)"
proof(induction xs rule: mergesort.induct)
  case 1
  show "set [] = set (mergesort [])" by simp
next
  case (2 x)
  show "set [x] = set (mergesort [x])" by simp
next
  case (3 x1 x2 xs)
  from 3 have IH_simplified_take:
    "set (mergesort (x1 # take (length xs div 2) (x2 # xs))) =
     insert x1 (set (take (length xs div 2) (x2 # xs)))"
  and IH_simplified_drop:
    "set (mergesort (drop (length xs div 2) (x2 # xs))) = 
     set (drop (length xs div 2) (x2 # xs))" by simp+

  have "(set (take n as) ∪ set (drop n as)) = set as"
    for n and as::"int list"
  proof -
    from set_append[of "take n as" "drop n as"] have
      "(set (take n as) ∪ set (drop n as)) =
       set (take n as @ drop n as)" by simp
    moreover have
      "set (take n as @ drop n as) =
       set as" using append_take_drop_id by simp
    ultimately show ?thesis by simp
  qed
  hence "(set (take (length xs div 2) (x2 # xs)) ∪
        set (drop (length xs div 2) (x2 # xs))) =
        set (x2 # xs)"by(simp)
  with IH_simplified_take IH_simplified_drop show
    "set (x1 # x2 # xs) = set (mergesort (x1 # x2 # xs))"
    by(simp add: merge_set)
qed

theorem mergesort_sorted: "sorted (mergesort xs)"
  by(induction xs rule: mergesort.induct) (simp add: merge_sorted)+

textexample:
lemma "mergesort [42, 5, 1, 3, 67, 3, 9, 0, 33, 32] =
                 [0, 1, 3, 3, 5, 9, 32, 33, 42, 67]" by simp
end

J[edit]

Generally, this task should be accomplished in J using /:~. Here we take an approach that's more comparable with the other examples on this page.

Recursive Solution

mergesort=: {{
  if. 2>#y do. y return.end.
  middle=. <.-:#y
  X=. mergesort middle{.y
  Y=. mergesort middle}.y
  X merge Y
}}

merge=: {{ r=. y#~ i=. j=. 0
  while. (i<#x)*(j<#y) do. a=. i{x [b=. j{y
    if. a<b do. r=. r,a [i=. i+1
       else.    r=. r,b [j=. j+1 end.
  end.
  if. i<#x do. r=. r, i}.x end.
  if. j<#y do. r=. r, j}.y end.
}}

Non-Recursive Solution

(This uses the same merge):

mergesort=: {{  r=. y [  stride=. 1
  while. stride < #r do. stride=. 2*mid=. stride
    r=. ;(-stride) (mid&}. <@merge (mid<.#) {.])\ r
  end.
}}

Example use:

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

But use J's /:~ if you really need this function.

   (/:~ -: mergesort) ?~?10000
1

Java[edit]

Works with: Java version 1.5+
import java.util.List;
import java.util.ArrayList;
import java.util.Iterator;

public class Merge{
    public static <E extends Comparable<? super E>> List<E> mergeSort(List<E> m){
        if(m.size() <= 1) return m;

        int middle = m.size() / 2;
        List<E> left = m.subList(0, middle);
        List<E> right = m.subList(middle, m.size());

        right = mergeSort(right);
        left = mergeSort(left);
        List<E> result = merge(left, right);

        return result;
    }

    public static <E extends Comparable<? super E>> List<E> merge(List<E> left, List<E> right){
        List<E> result = new ArrayList<E>();
        Iterator<E> it1 = left.iterator();
        Iterator<E> it2 = right.iterator();

	E x = it1.next();
	E y = it2.next();
        while (true){
            //change the direction of this comparison to change the direction of the sort
            if(x.compareTo(y) <= 0){
		result.add(x);
		if(it1.hasNext()){
		    x = it1.next();
		}else{
		    result.add(y);
		    while(it2.hasNext()){
			result.add(it2.next());
		    }
		    break;
		}
	    }else{
		result.add(y);
		if(it2.hasNext()){
		    y = it2.next();
		}else{
		    result.add(x);
		    while (it1.hasNext()){
			result.add(it1.next());
		    }
		    break;
		}
	    }
        }
        return result;
    }
}

JavaScript[edit]

function merge(left, right, arr) {
  var a = 0;

  while (left.length && right.length) {
    arr[a++] = (right[0] < left[0]) ? right.shift() : left.shift();
  }
  while (left.length) {
    arr[a++] = left.shift();
  }
  while (right.length) {
    arr[a++] = right.shift();
  }
}

function mergeSort(arr) {
  var len = arr.length;

  if (len === 1) { return; }

  var mid = Math.floor(len / 2),
      left = arr.slice(0, mid),
      right = arr.slice(mid);

  mergeSort(left);
  mergeSort(right);
  merge(left, right, arr);
}

var arr = [1, 5, 2, 7, 3, 9, 4, 6, 8];
mergeSort(arr); // arr will now: 1, 2, 3, 4, 5, 6, 7, 8, 9

// here is improved faster version, also often faster than QuickSort!

function mergeSort2(a) {
  if (a.length <= 1) return
  const mid = Math.floor(a.length / 2), left = a.slice(0, mid), right = a.slice(mid)
  mergeSort2(left)
  mergeSort2(right)
  let ia = 0, il = 0, ir = 0
  while (il < left.length && ir < right.length)
    a[ia++] = left[il] < right[ir] ? left[il++] : right[ir++]
  while (il < left.length)
    a[ia++] = left[il++]
  while (ir < right.length)
    a[ia++] = right[ir++]
}

jq[edit]

The sort function defined here will sort any JSON array.

# Input: [x,y] -- the two arrays to be merged
# If x and y are sorted as by "sort", then the result will also be sorted:
def merge:
  def m:  # state: [x, y, array]  (array being the answer)
    .[0] as $x
    | .[1] as $y
    | if   0 == ($x|length) then .[2] + $y
      elif 0 == ($y|length) then .[2] + $x
      else
        (if $x[0] <= $y[0] then [$x[1:], $y,     .[2] + [$x[0] ]] 
         else                   [$x,     $y[1:], .[2] + [$y[0] ]]
         end) | m
      end;
   [.[0], .[1], []] | m;

def merge_sort:
  if length <= 1 then .
  else
    (length/2 |floor) as $len
    | . as $in
    | [ ($in[0:$len] | merge_sort), ($in[$len:] | merge_sort) ] | merge
  end;

Example:

( [1, 3, 8, 9, 0, 0, 8, 7, 1, 6],
  [170, 45, 75, 90, 2, 24, 802, 66],
  [170, 45, 75, 90, 2, 24, -802, -66] )
| (merge_sort == sort)
Output:
true
true
true

Julia[edit]

Works with: Julia version 0.6
function mergesort(arr::Vector)
    if length(arr)  1 return arr end
    mid = length(arr) ÷ 2
    lpart = mergesort(arr[1:mid])
    rpart = mergesort(arr[mid+1:end])
    rst = similar(arr)
    i = ri = li = 1
    @inbounds while li  length(lpart) && ri  length(rpart)
        if lpart[li]  rpart[ri]
            rst[i] = lpart[li]
            li += 1
        else
            rst[i] = rpart[ri]
            ri += 1
        end
        i += 1
    end
    if li  length(lpart)
        copy!(rst, i, lpart, li)
    else
        copy!(rst, i, rpart, ri)
    end
    return rst
end

v = rand(-10:10, 10)
println("# unordered: $v\n -> ordered: ", mergesort(v))
Output:
# unordered: [8, 6, 7, 1, -1, 0, -4, 7, -7, 0]
 -> ordered: [-7, -4, -1, 0, 0, 1, 6, 7, 7, 8]

Kotlin[edit]

fun mergeSort(list: List<Int>): List<Int> {
    if (list.size <= 1) {
        return list
    }

    val left = mutableListOf<Int>()
    val right = mutableListOf<Int>()

    val middle = list.size / 2
    list.forEachIndexed { index, number ->
        if (index < middle) {
            left.add(number)
        } else {
            right.add(number)
        }
    }

    fun merge(left: List<Int>, right: List<Int>): List<Int> = mutableListOf<Int>().apply {
        var indexLeft = 0
        var indexRight = 0

        while (indexLeft < left.size && indexRight < right.size) {
            if (left[indexLeft] <= right[indexRight]) {
                add(left[indexLeft])
                indexLeft++
            } else {
                add(right[indexRight])
                indexRight++
            }
        }

        while (indexLeft < left.size) {
            add(left[indexLeft])
            indexLeft++
        }

        while (indexRight < right.size) {
            add(right[indexRight])
            indexRight++
        }
    }

    return merge(mergeSort(left), mergeSort(right))
}

fun main(args: Array<String>) {
    val numbers = listOf(5, 2, 3, 17, 12, 1, 8, 3, 4, 9, 7)
    println("Unsorted: $numbers")
    println("Sorted: ${mergeSort(numbers)}")
}
Output:
Unsorted: [5, 2, 3, 17, 12, 1, 8, 3, 4, 9, 7]
Sorted:   [1, 2, 3, 3, 4, 5, 7, 8, 9, 12, 17]

Lambdatalk[edit]

A close translation from Picolisp. In lambdatalk lists are implemented as dynamical arrays with list-like functions, cons is A.addfirst!, car is A.first, cdr is A.rest, nil is A.new and so on.

{def alt
 {lambda {:list}
  {if {A.empty? :list}
   then {A.new}
   else {A.addfirst! {A.first :list}
                     {alt {A.rest {A.rest :list}}}} }}}
-> alt

{def merge
 {lambda {:l1 :l2}
  {if {A.empty? :l2}
   then :l1
   else {if {< {A.first :l1} {A.first :l2}}
   then {A.addfirst! {A.first :l1} {merge :l2 {A.rest :l1}}}
   else {A.addfirst! {A.first :l2} {merge :l1 {A.rest :l2}}} }}}}
-> merge

{def mergesort
 {lambda {:list}
  {if {A.empty? {A.rest :list}}
   then :list
   else {merge {mergesort {alt :list}}
               {mergesort {alt {A.rest :list}}}} }}}
-> mergesort

{mergesort {A.new 8 1 5 3 9 0 2 7 6 4}}
-> [0,1,2,3,4,5,6,7,8,9]

Liberty BASIC[edit]

    itemCount = 20
    dim A(itemCount)
    dim tmp(itemCount)    'merge sort needs additionally same amount of storage

    for i = 1 to itemCount
        A(i) = int(rnd(1) * 100)
    next i

    print "Before Sort"
    call printArray itemCount

    call mergeSort 1,itemCount

    print "After Sort"
    call printArray itemCount
end

'------------------------------------------
sub mergeSort start, theEnd
    if theEnd-start < 1 then exit sub
    if theEnd-start = 1 then
        if A(start)>A(theEnd) then
            tmp=A(start)
            A(start)=A(theEnd)
            A(theEnd)=tmp
        end if
        exit sub
    end if
    middle = int((start+theEnd)/2)
    call mergeSort start, middle
    call mergeSort middle+1, theEnd
    call merge start, middle, theEnd
end sub

sub merge start, middle, theEnd
    i = start: j = middle+1: k = start
    while i<=middle OR j<=theEnd
        select case
        case i<=middle AND j<=theEnd
            if A(i)<=A(j) then
                tmp(k)=A(i)
                i=i+1
            else
                tmp(k)=A(j)
                j=j+1
            end if
            k=k+1
        case i<=middle
            tmp(k)=A(i)
            i=i+1
            k=k+1
        case else    'j<=theEnd
            tmp(k)=A(j)
            j=j+1
            k=k+1
        end select
    wend

    for i = start to theEnd
        A(i)=tmp(i)
    next
end sub

'===========================================
sub printArray itemCount
    for i = 1 to itemCount
        print using("###", A(i));
    next i
    print
end sub

[edit]

Works with: UCB Logo
to split :size :front :list
  if :size < 1 [output list :front :list]
  output split :size-1 (lput first :list :front) (butfirst :list)
end

to merge :small :large
  if empty? :small [output :large]
  ifelse lessequal? first :small first :large ~
    [output fput first :small merge butfirst :small :large] ~
    [output fput first :large merge butfirst :large :small]
end

to mergesort :list
  localmake "half split (count :list) / 2 [] :list
  if empty? first :half [output :list]
  output merge mergesort first :half mergesort last :half
end

Logtalk[edit]

msort([], []) :- !.
msort([X], [X]) :- !.
msort([X, Y| Xs], Ys) :-
    split([X, Y| Xs], X1s, X2s),
    msort(X1s, Y1s),
    msort(X2s, Y2s),
    merge(Y1s, Y2s, Ys).

split([], [], []).
split([X| Xs], [X| Ys], Zs) :-
    split(Xs, Zs, Ys).

merge([X| Xs], [Y| Ys], [X| Zs]) :-
    X @=< Y, !,
    merge(Xs, [Y| Ys], Zs).
merge([X| Xs], [Y| Ys], [Y| Zs]) :-
    X @> Y, !,
    merge([X | Xs], Ys, Zs).
merge([], Xs, Xs) :- !.
merge(Xs, [], Xs).

Lua[edit]

local function merge(left_container, left_container_begin, left_container_end, right_container, right_container_begin, right_container_end, result_container, result_container_begin, comparator)
	while left_container_begin <= left_container_end do
		if right_container_begin > right_container_end then
			for i = left_container_begin, left_container_end do
				result_container[result_container_begin] = left_container[i]
				result_container_begin = result_container_begin + 1
			end

			return
		end

		if comparator(right_container[right_container_begin], left_container[left_container_begin]) then
			result_container[result_container_begin] = right_container[right_container_begin]
			right_container_begin = right_container_begin + 1
		else
			result_container[result_container_begin] = left_container[left_container_begin]
			left_container_begin = left_container_begin + 1
		end

		result_container_begin = result_container_begin + 1
	end

	for i = right_container_begin, right_container_end do
		result_container[result_container_begin] = right_container[i]
		result_container_begin = result_container_begin + 1
	end
end

local function mergesort_impl(container, container_begin, container_end, comparator)
	local range_length = (container_end - container_begin) + 1
	if range_length < 2 then return end
	local copy = {}
	local copy_len = 0

	for it = container_begin, container_end do
		copy_len = copy_len + 1
		copy[copy_len] = container[it]
	end

	local middle = bit.rshift(range_length, 1) -- or math.floor(range_length / 2)
	mergesort_impl(copy, 1, middle, comparator)
	mergesort_impl(copy, middle + 1, copy_len, comparator)
	merge(copy, 1, middle, copy, middle + 1, copy_len, container, container_begin, comparator)
end

local function mergesort_default_comparator(a, b)
	return a < b
end

function table.mergesort(container, comparator)
	if not comparator then
		comparator = mergesort_default_comparator
	end

	mergesort_impl(container, 1, #container, comparator)
end
function getLower(a,b)
  local i,j=1,1
  return function() 
    if not b[j] or a[i] and a[i]<b[j] then
      i=i+1; return a[i-1]
    else
      j=j+1; return b[j-1]
    end
  end  
end

function merge(a,b)
  local res={}
  for v in getLower(a,b) do res[#res+1]=v end
  return res
end

function mergesort(list)
  if #list<=1 then return list end
  local s=math.floor(#list/2)
  return merge(mergesort{unpack(list,1,s)}, mergesort{unpack(list,s+1)})
end

Lucid[edit]

[1]

msort(a) = if iseod(first next a) then a else merge(msort(b0),msort(b1)) fi
  where
   p = false fby not p;
   b0 = a whenever p;
   b1 = a whenever not p;
   just(a) = ja
      where
         ja = a fby if iseod ja then eod else next a fi;
      end;
   merge(x,y) = if takexx then xx else yy fi
     where
      xx = (x) upon takexx;
      yy = (y) upon not takexx;
      takexx = if iseod(yy) then true elseif
                  iseod(xx) then false else xx <= yy fi;
     end;
  end;

M2000 Interpreter[edit]

module checkit {
	\\ merge sort
	group merge {
		function sort(right as stack) {
			if len(right)<=1 then =right : exit
			left=.sort(stack up right, len(right) div 2 )
			right=.sort(right)
			\\ stackitem(right) is same as stackitem(right,1)
			if stackitem(left, len(left))<=stackitem(right) then
				\\ !left take items from left for merging
				\\ so after this left and right became empty stacks
				=stack:=!left, !right
				exit
			end if
			=.merge(left, right)
		}
		function sortdown(right as stack) {
			if len(right)<=1 then =right : exit
			left=.sortdown(stack up right, len(right) div 2 )
			right=.sortdown(right)
			if stackitem(left, len(left))>stackitem(right) then
				=stack:=!left, !right : exit
			end if
			=.mergedown(left, right)
		}
		\\ left and right are pointers to stack objects
		\\ here we pass by value the pointer not the data
		function merge(left as stack, right as stack) {			
			result=stack
			while len(left) > 0 and len(right) > 0
				if stackitem(left,1) <= stackitem(right) then
					result=stack:=!result, !(stack up left, 1)
				else
					result=stack:=!result, !(stack up right, 1)
				end if
			end while
			if len(right) > 0 then  result=stack:= !result,!right
			if len(left) > 0 then result=stack:= !result,!left
			=result
		}
		function mergedown(left as stack, right as stack) {			
			result=stack
			while len(left) > 0 and len(right) > 0
				if stackitem(left,1) > stackitem(right) then
					result=stack:=!result, !(stack up left, 1)
				else
					result=stack:=!result, !(stack up right, 1)
				end if
			end while
			if len(right) > 0 then  result=stack:= !result,!right
			if len(left) > 0 then result=stack:= !result,!left
			=result
		}
	}
	k=stack:=7, 5, 2, 6, 1, 4, 2, 6, 3
	print merge.sort(k)
	print len(k)=0   ' we have to use merge.sort(stack(k)) to pass a copy of k
	
	\\ input array  (arr is a pointer to array)
	arr=(10,8,9,7,5,6,2,3,0,1)
	\\ stack(array pointer) return a stack with a copy of array items
	\\ array(stack pointer) return an array, empty the stack
	
	arr2=array(merge.sort(stack(arr)))
	Print type$(arr2)
	Dim a()
	\\ a() is an array as a value, so we just copy arr2 to a()
	a()=arr2
	\\ to prove we add 1 to each element of arr2
	arr2++
	Print a()  ' 0,1,2,3,4,5,6,7,8,9
	Print arr2  ' 1,2,3,4,5,6,7,8,9,11
	p=a()  ' we get a pointer
	\\ a() has a double pointer inside
	\\ so a() get just the inner pointer
	a()=array(merge.sortdown(stack(p)))
	\\ so now p (which use the outer pointer)
	\\ still points to a()
	print p   ' p point to a()
	
}
checkit

Maple[edit]

merge := proc(arr, left, mid, right)
	local i, j, k, n1, n2, L, R;
	n1 := mid-left+1: 
	n2 := right-mid:
	L := Array(1..n1):
	R := Array(1..n2):
	for i from 0 to n1-1 do
		L(i+1) :=arr(left+i):
	end do:
	for j from 0 to n2-1 do
		R(j+1) := arr(mid+j+1):
	end do:
	i := 1:
	j := 1:
	k := left:
	while(i <= n1 and j <= n2) do
		if (L[i] <= R[j]) then
			arr[k] := L[i]:
			i++:
		else
			arr[k] := R[j]:
			j++:
		end if:
		k++:
	end do:
	while(i <= n1) do
		arr[k] := L[i]:
		i++:
		k++:
	end do:
	while(j <= n2) do
		arr[k] := R[j]:
		j++:
		k++:
	end do:
end proc:
arr := Array([17,3,72,0,36,2,3,8,40,0]);
mergeSort(arr,1,numelems(arr)):
arr;
Output:
[0,0,2,3,3,8,17,36,40,72]

Mathematica / Wolfram Language[edit]

Works with: Mathematica version 7.0
MergeSort[m_List] := Module[{middle},
  If[Length[m] >= 2,
   middle = Ceiling[Length[m]/2];
   Apply[Merge, 
    Map[MergeSort, Partition[m, middle, middle, {1, 1}, {}]]],
   m
   ]
  ]
  
Merge[left_List, right_List] := Module[
  {leftIndex = 1, rightIndex = 1},
  Table[
   Which[
    leftIndex > Length[left], right[[rightIndex++]],
    rightIndex > Length[right], left[[leftIndex++]],
    left[[leftIndex]] <= right[[rightIndex]], left[[leftIndex++]],
    True, right[[rightIndex++]]],
   {Length[left] + Length[right]}]
  ]

MATLAB[edit]

function list = mergeSort(list)

    if numel(list) <= 1
        return
    else
        middle = ceil(numel(list) / 2);
        left = list(1:middle);
        right = list(middle+1:end);
        
        left = mergeSort(left);
        right = mergeSort(right);
        
        if left(end) <= right(1)
            list = [left right];
            return
        end
        
        %merge(left,right)
        counter = 1;
        while (numel(left) > 0) && (numel(right) > 0)
            if(left(1) <= right(1))
                list(counter) = left(1);
                left(1) = [];
            else
                list(counter) = right(1);
                right(1) = [];
            end           
            counter = counter + 1;   
        end

        if numel(left) > 0
            list(counter:end) = left;
        elseif numel(right) > 0
            list(counter:end) = right;
        end
        %end merge        
    end %if
end %mergeSort

Sample Usage:

>> mergeSort([4 3 1 5 6 2])

ans =

     1     2     3     4     5     6

Maxima[edit]

merge(a, b) := block(
   [c: [ ], i: 1, j: 1, p: length(a), q: length(b)],
   while i <= p and j <= q do (
      if a[i] < b[j] then (
         c: endcons(a[i], c),
         i: i + 1
      ) else (
         c: endcons(b[j], c),
         j: j + 1
      )
   ),
   if i > p then append(c, rest(b, j - 1)) else append(c, rest(a, i - 1))
)$

mergesort(u) := block(
   [n: length(u), k, a, b],
   if n <= 1 then u else (
      a: rest(u, k: quotient(n, 2)),
      b: rest(u, k - n),
      merge(mergesort(a), mergesort(b))
   )
)$

MAXScript[edit]

fn mergesort arr =
(
	local left = #()
	local right = #()
	local result = #()
	if arr.count < 2 then return arr
	else
	(
		local mid = arr.count/2
		for i = 1 to mid do
		(
			append left arr[i]
		)
		for i = (mid+1) to arr.count do
		(
			append right arr[i]
		)
		left = mergesort left
		right = mergesort right
		if left[left.count] <= right[1] do
		(
			join left right
			return left
		)
		result = _merge left right
		return result
	)
)

fn _merge a b =
(
	local result = #()
	while a.count > 0 and b.count > 0 do
	(
		if a[1] <= b[1] then
		(
			append result a[1] 
			a = for i in 2 to a.count collect a[i]
		)
		else
		(
			append result b[1]
			b = for i in 2 to b.count collect b[i]
		)
	)
	if a.count > 0 do
	(
		join result a
	)
	if b.count > 0 do
	(
		join result b
	)
	return result
)

Output:

a = for i in 1 to 15 collect random -5 20
#(-3, 13, 2, -2, 13, 9, 17, 7, 16, 19, 0, 0, 20, 18, 1)
mergeSort a
#(-3, -2, 0, 0, 1, 2, 7, 9, 13, 13, 16, 17, 18, 19, 20)

Mercury[edit]

This version of a sort will sort a list of any type for which there is an ordering predicate defined. Both a function form and a predicate form are defined here with the function implemented in terms of the predicate. Some of the ceremony has been elided.

:- module merge_sort.

:- interface.

:- import_module list.

:- type split_error ---> split_error.

:- func merge_sort(list(T)) = list(T).
:- pred merge_sort(list(T)::in, list(T)::out) is det.

:- implementation.

:- import_module int, exception.

merge_sort(U) = S :- merge_sort(U, S).
 
merge_sort(U, S) :- merge_sort(list.length(U), U, S).
 
:- pred merge_sort(int::in, list(T)::in, list(T)::out) is det.
merge_sort(L, U, S) :-
    ( L > 1 ->
        H = L // 2,
        ( split(H, U, F, B) ->
            merge_sort(H, F, SF),
            merge_sort(L - H, B, SB),
            merge_sort.merge(SF, SB, S)
        ; throw(split_error) )
    ; S = U ).
 
:- pred split(int::in, list(T)::in, list(T)::out, list(T)::out) is semidet.
split(N, L, S, E) :-
    ( N = 0 -> S = [], E = L
    ; N > 0, L = [H | L1], S = [H | S1],
      split(N - 1, L1, S1, E) ).
 
:- pred merge(list(T)::in, list(T)::in, list(T)::out) is det.
merge([], [], []).
merge([X|Xs], [], [X|Xs]).
merge([], [Y|Ys], [Y|Ys]).
merge([X|Xs], [Y|Ys], M) :-
    ( compare(>, X, Y) ->
        merge_sort.merge([X|Xs], Ys, M0),
        M = [Y|M0]
    ; merge_sort.merge(Xs, [Y|Ys], M0),
        M = [X|M0] ).

Modula-2[edit]

Iterative[edit]

Divides the input into blocks of 2 entries, and sorts each block by swapping if necessary. Then merges blocks of 2 into blocks of 4, blocks of 4 into blocks of 8, and so on.

DEFINITION MODULE MSIterat;

PROCEDURE IterativeMergeSort( VAR a : ARRAY OF INTEGER);

END MSIterat.
IMPLEMENTATION MODULE MSIterat;

IMPORT Storage;

PROCEDURE IterativeMergeSort( VAR a : ARRAY OF INTEGER);
VAR
  n, bufLen, len, endBuf : CARDINAL;
  k, nL, nR, b, h, i, j, startR, endR: CARDINAL;
  temp : INTEGER; (* array element *)
  pbuf : POINTER TO ARRAY CARDINAL OF INTEGER;
BEGIN
  n := HIGH(a) + 1; (* length of array *)
  IF (n < 2) THEN RETURN; END;
  (* Sort blocks of length 2 by swapping elements if necessary.
     Start at high end of array; ignore a[0] if n is odd.*)
  k := n;
  REPEAT
    DEC(k, 2);
    IF (a[k] > a[k + 1]) THEN
      temp := a[k]; a[k] := a[k + 1]; a[k + 1] := temp;
    END;
  UNTIL (k < 2);
  IF (n = 2) THEN RETURN; END;

  (* Set up a buffer for temporary storage when merging. *)
  (* TopSpeed Modula-2 doesn't seem to have dynamic arrays,
     so we use a workaround *)
  bufLen := n DIV 2;
  Storage.ALLOCATE( pbuf, bufLen*SIZE(INTEGER));

  nR := 2; (* length of right-hand block when merging *)
  REPEAT
    len := 2*nR; (* maximum length of a merged block in this iteration *)
    k := n; (* start at the high end of the array *)
    WHILE (k > nR) DO
      IF (k >= len) THEN
        nL := nR; DEC(k, len);
      ELSE
        nL := k - nR; k := 0; END;

      (* Merging 2 adjacent blocks, already sorted.
         k = start index of left block;
         nL, nR = lengths of left and right blocks *)
      startR := k + nL;  endR := startR + nR;

      (* Skip elements in left block that are already in correct place *)
      temp := a[startR]; (* first (smallest) element in right block *)
      j := k;
      WHILE (j < startR) AND (a[j] <= temp) DO INC(j); END;

      endBuf := startR - j; (* length of buffer actually used *)
      IF (endBuf > 0) THEN (* if endBuf = 0 then already sorted *)
        (* Copy from left block to buffer, omitting elements
           that are already in correct place *)
        h := j;
        FOR b := 0 TO endBuf - 1 DO
          pbuf^[b] := a[h]; INC(h);
        END;
        (* Fill in values from right block or buffer *)
        b := 0;
        i := startR;
     (* j = startR - endBuf from above *)
        WHILE (b < endBuf) AND (i < endR) DO
          IF (pbuf^[b] <= a[i]) THEN
            a[j] := pbuf^[b]; INC(b)
          ELSE
            a[j] := a[i]; INC(i); END;
          INC(j);
        END;
        (* If now b = endBuf then the merge is complete.
           Else just copy the remaining elements in the buffer. *)
        WHILE (b < endBuf) DO
          a[j] := pbuf^[b]; INC(j); INC(b);
        END;
      END;
    END;
    nR := len;
  UNTIL (nR >= n);
  Storage.DEALLOCATE( pbuf, bufLen*SIZE(INTEGER));
END IterativeMergeSort;

END MSIterat.
MODULE MSItDemo;
(* Demo of iterative merge sort *)

IMPORT IO, Lib;
FROM MSIterat IMPORT IterativeMergeSort;

(* Procedure to display the values in the demo array *)
PROCEDURE Display( VAR a : ARRAY OF INTEGER);
VAR
  j, nrInLine : CARDINAL;
BEGIN
  nrInLine := 0;
  FOR j := 0 TO HIGH(a) DO
    IO.WrCard( a[j], 5); INC( nrInLine);
    IF (nrInLine = 10) THEN IO.WrLn; nrInLine := 0; END;
  END;
  IF (nrInLine > 0) THEN IO.WrLn; END;
END Display;

(* Main routine *)
CONST
  ArrayLength = 50;
VAR
  arr : ARRAY [0..ArrayLength - 1] OF INTEGER;
  m : CARDINAL;
BEGIN
  Lib.RANDOMIZE;
  FOR m := 0 TO ArrayLength - 1 DO arr[m] := Lib.RANDOM( 1000); END;
  IO.WrStr( 'Before:'); IO.WrLn; Display( arr);
  IterativeMergeSort( arr);
  IO.WrStr( 'After:'); IO.WrLn; Display( arr);
END MSItDemo.
Output:
Before:
  236  542  526  549  869  632  446  518  909  270
  826  562  469  258  681  604  921  772  548  328
  147  679   71  239  772  106  477  556  451   64
  941  207   87  486  280  206  380  689  964  376
  298  635  552  887  387   70  287   77  610  605
After:
   64   70   71   77   87  106  147  206  207  236
  239  258  270  280  287  298  328  376  380  387
  446  451  469  477  486  518  526  542  548  549
  552  556  562  604  605  610  632  635  679  681
  689  772  772  826  869  887  909  921  941  964

Recursive on linked list[edit]

According to Wikipedia, "merge sort is often the best choice for sorting a linked list". The code below shows a general procedure for merge-sorting a linked list. As in the improved Delphi version, only the pointers are moved. To carry out the Rosetta Code task, the demo program sorts an array of records on an integer-valued field.

The method for splitting a linked list is taken from "Merge sort algorithm for a singly linked list" on Techie Delight. Two pointers step through the list, one at twice the speed of the other. When the fast pointer reaches the end, the slow pointer marks the halfway point.

DEFINITION MODULE MergSort;

TYPE MSCompare = PROCEDURE( ADDRESS, ADDRESS) : INTEGER;
TYPE MSGetNext = PROCEDURE( ADDRESS) : ADDRESS;
TYPE MSSetNext = PROCEDURE( ADDRESS, ADDRESS);

PROCEDURE DoMergeSort( VAR start : ADDRESS;
                       Compare : MSCompare;
                       GetNext : MSGetNext;
                       SetNext : MSSetNext);
(*
  Procedures to be supplied by the caller:
  Compare(a1, a2) returns -1 if a1^ is to be placed before a2^;
    +1 if after; 0 if no priority.
  GetNext(a) returns address of next item after a^.
  SetNext(a, n) sets address of next item after a^ to n.
  If a^ is last item, then address of next item is NIL.
  It can be assumed that a, a1, a2 are not NIL.
*)
END MergSort.
IMPLEMENTATION MODULE MergSort;

PROCEDURE DoMergeSort( VAR start : ADDRESS;
                       Compare : MSCompare;
                       GetNext : MSGetNext;
                       SetNext : MSSetNext);
VAR
  p1, p2, q : ADDRESS;
BEGIN
  (* If list has < 2 items, do nothing *)
  IF (start = NIL) THEN RETURN; END;
  p1 := GetNext( start); IF (p1 = NIL) THEN RETURN; END;

  (* If list has only 2 items, we'll not use recursion *)
  p2 := GetNext( p1);
  IF (p2 = NIL) THEN
    IF (Compare( start, p1) > 0) THEN
      q := start; SetNext( p1, q); SetNext( q, NIL);
      start := p1;
    END;
    RETURN;
  END;

  (* List has > 2 items: split list in half *)
  p1 := start;
  REPEAT
    p1 := GetNext( p1);
    p2 := GetNext( p2);
    IF (p2 <> NIL) THEN p2 := GetNext( p2); END;
  UNTIL (p2 = NIL);
  (* Now p1 points to last item in first half of list *)
  p2 := GetNext( p1); SetNext( p1, NIL);
  p1 := start;

  (* Recursive calls to sort each half; p1 and p2 will be updated *)
  DoMergeSort( p1, Compare, GetNext, SetNext);
  DoMergeSort( p2, Compare, GetNext, SetNext);

  (* Merge the sorted halves *)
  IF Compare( p1, p2) < 0 THEN
    start := p1; p1 := GetNext( p1);
  ELSE
    start := p2; p2 := GetNext( p2);
  END;
  q := start;
  WHILE (p1 <> NIL) AND (p2 <> NIL) DO
    IF Compare( p1, p2) < 0 THEN
      SetNext( q, p1); q := p1; p1 := GetNext( p1);
    ELSE
      SetNext( q, p2); q := p2; p2 := GetNext( p2);
    END;
  END;
  IF (p1 = NIL) THEN SetNext( q, p2) ELSE SetNext( q, p1) END;
END DoMergeSort;
END MergSort.
MODULE MergDemo;

IMPORT IO, Lib, MergSort;

TYPE PTestRec = POINTER TO TestRec;
TYPE TestRec = RECORD
  Value : INTEGER;
  Next : PTestRec;
END;

PROCEDURE Compare( a1, a2 : ADDRESS) : INTEGER;
VAR
  p1, p2 : PTestRec;
BEGIN
  p1 := a1; p2 := a2;
  IF (p1^.Value < p2^.Value) THEN RETURN -1
  ELSIF (p1^.Value > p2^.Value) THEN RETURN 1
  ELSE RETURN 0; END;
END Compare;

PROCEDURE GetNext( a : ADDRESS) : ADDRESS;
VAR
  p : PTestRec;
BEGIN
  p := a; RETURN p^.Next;
END GetNext;

PROCEDURE SetNext( a, n : ADDRESS);
VAR
  p : PTestRec;
BEGIN
  p := a; p^.Next := n;
END SetNext;

(* Display the values in the linked list *)
PROCEDURE Display( p : PTestRec);
VAR
  nrInLine : CARDINAL;
BEGIN
  nrInLine := 0;
  WHILE (p <> NIL) DO
    IO.WrCard( p^.Value, 5);
    p := p^.Next;
    INC( nrInLine);
    IF (nrInLine = 10) THEN IO.WrLn; nrInLine := 0; END;
  END;
  IF (nrInLine > 0) THEN IO.WrLn; END;
END Display;

(* Main routine *)
CONST ArraySize = 50;
VAR
  arr : ARRAY [0..ArraySize - 1] OF TestRec;
  j : CARDINAL;
  start, p : PTestRec;
BEGIN
  (* Fill values with random integers *)
  FOR j := 0 TO ArraySize - 1 DO
    arr[j].Value := Lib.RANDOM( 1000);
  END;
  (* Set up the links *)
  IF (ArraySize > 1) THEN (* FOR loop 0 TO -1 crashes program *)
    FOR j := 0 TO ArraySize - 2 DO
      arr[j].Next := ADR( arr[j + 1]);
    END;
  END;
  arr[ArraySize - 1].Next := NIL;
  (* Demonstrate merge sort on the linked list *)
  start := ADR( arr[0]);
  IO.WrStr( 'Before:'); IO.WrLn;
  Display( start);
  MergSort.DoMergeSort( start, Compare, GetNext, SetNext);
  IO.WrStr( 'After:'); IO.WrLn;
  Display( start);
END MergDemo.
Output:
Before:
  683   68  458  645  223  801  485  101  255  590
  381  149   29  298  226  937  866  130  297  153
  551  159  760  403  380  770  296  701  399  775
  236  758  249  314  230  106  626  804  956  149
  706  625  651  727  323   38   66  534   85  663
After:
   29   38   66   68   85  101  106  130  149  149
  153  159  223  226  230  236  249  255  296  297
  298  314  323  380  381  399  403  458  485  534
  551  590  625  626  645  651  663  683  701  706
  727  758  760  770  775  801  804  866  937  956

Nemerle[edit]

This is a translation of a Standard ML example from Wikipedia.

using System;
using System.Console;
using Nemerle.Collections;

module Mergesort
{
    MergeSort[TEnu, TItem] (sort_me : TEnu) : list[TItem]
      where TEnu  : Seq[TItem]
      where TItem : IComparable
    {
        def split(xs) {
            def loop (zs, xs, ys) {
                |(x::y::zs, xs, ys) => loop(zs, x::xs, y::ys)
                |(x::[], xs, ys) => (x::xs, ys)
                |([], xs, ys) => (xs, ys)
            }
            
            loop(xs, [], [])
        }
        
        def merge(xs, ys) {
            def loop(res, xs, ys) {
                |(res, [], []) => res.Reverse()
                |(res, x::xs, []) => loop(x::res, xs, [])
                |(res, [], y::ys) => loop(y::res, [], ys)
                |(res, x::xs, y::ys) => if (x.CompareTo(y) < 0) loop(x::res, xs, y::ys)
                                        else loop(y::res, x::xs, ys)
            }
            loop ([], xs, ys)
        }
        
        def ms(xs) {
            |[] => []
            |[x] => [x]
            |_ => { def (left, right) = split(xs); merge(ms(left), ms(right)) }
        }
        
        ms(sort_me.NToList())
    }
    
    Main() : void
    {
        def test1 = MergeSort([1, 5, 9, 2, 7, 8, 4, 6, 3]);
        def test2 = MergeSort(array['a', 't', 'w', 'f', 'c', 'y', 'l']);
        WriteLine(test1);
        WriteLine(test2);
    }
}
Output:
[1, 2, 3, 4, 5, 6, 7, 8, 9]
[a, c, f, l, t, w, y]

NetRexx[edit]

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

import java.util.List

placesList = [String -
    "UK  London",     "US  New York",   "US  Boston",     "US  Washington" -
  , "UK  Washington", "US  Birmingham", "UK  Birmingham", "UK  Boston"     -
]

lists = [ -
    placesList -
  , mergeSort(String[] Arrays.copyOf(placesList, placesList.length)) -
]

loop ln = 0 to lists.length - 1
  cl = lists[ln]
  loop ct = 0 to cl.length - 1
    say cl[ct]
    end ct
    say
  end ln

return

method mergeSort(m = String[]) public constant binary returns String[]

  rl = String[m.length]
  al = List mergeSort(Arrays.asList(m))
  al.toArray(rl)

  return rl

method mergeSort(m = List) public constant binary returns ArrayList

  result = ArrayList(m.size)
  left   = ArrayList()
  right  = ArrayList()
  if m.size > 1 then do
    middle = m.size % 2
    loop x_ = 0 to middle - 1
      left.add(m.get(x_))
      end x_
    loop x_ = middle to m.size - 1
      right.add(m.get(x_))
      end x_
    left  = mergeSort(left)
    right = mergeSort(right)
    if (Comparable left.get(left.size - 1)).compareTo(Comparable right.get(0)) <= 0 then do
      left.addAll(right)
      result.addAll(m)
      end
    else do
      result = merge(left, right)
      end
    end
  else do
    result.addAll(m)
    end

  return result

method merge(left = List, right = List) public constant binary returns ArrayList

  result = ArrayList()
  loop label mx while left.size > 0 & right.size > 0
    if (Comparable left.get(0)).compareTo(Comparable right.get(0)) <= 0 then do
      result.add(left.get(0))
      left.remove(0)
      end
    else do
      result.add(right.get(0))
      right.remove(0)
      end
    end mx
    if left.size > 0 then do
      result.addAll(left)
      end
    if right.size > 0 then do
      result.addAll(right)
      end

  return result
Output:
UK  London
US  New York
US  Boston
US  Washington
UK  Washington
US  Birmingham
UK  Birmingham
UK  Boston

UK  Birmingham
UK  Boston
UK  London
UK  Washington
US  Birmingham
US  Boston
US  New York
US  Washington

Nim[edit]

proc merge[T](a, b: var openarray[T]; left, middle, right: int) =
  let
    leftLen = middle - left
    rightLen = right - middle
  var
    l = 0
    r = leftLen
 
  for i in left ..< middle:
    b[l] = a[i]
    inc l
  for i in middle ..< right:
    b[r] = a[i]
    inc r
 
  l = 0
  r = leftLen
  var i = left
 
  while l < leftLen and r < leftLen + rightLen:
    if b[l] < b[r]:
      a[i] = b[l]
      inc l
    else:
      a[i] = b[r]
      inc r
    inc i
 
  while l < leftLen:
    a[i] = b[l]
    inc l
    inc i
  while r < leftLen + rightLen:
    a[i] = b[r]
    inc r
    inc i
 
proc mergeSort[T](a, b: var openarray[T]; left, right: int) =
  if right - left <= 1: return
 
  let middle = (left + right) div 2
  mergeSort(a, b, left, middle)
  mergeSort(a, b, middle, right)
  merge(a, b, left, middle, right)
 
proc mergeSort[T](a: var openarray[T]) =
  var b = newSeq[T](a.len)
  mergeSort(a, b, 0, a.len)
 
var a = @[4, 65, 2, -31, 0, 99, 2, 83, 782]
mergeSort a
echo a
Output:
@[-31, 0, 2, 2, 4, 65, 83, 99, 782]

OCaml[edit]

let rec split_at n xs =
  match n, xs with
      0, xs ->
        [], xs
    | _, [] ->
        failwith "index too large"
    | n, x::xs when n > 0 ->
        let xs', xs'' = split_at (pred n) xs in
          x::xs', xs''
    | _, _ ->
        invalid_arg "negative argument"

let rec merge_sort cmp = function
    [] -> []
  | [x] -> [x]
  | xs ->
      let xs, ys = split_at (List.length xs / 2) xs in
        List.merge cmp (merge_sort cmp xs) (merge_sort cmp ys)

let _ =
  merge_sort compare [8;6;4;2;1;3;5;7;9]

Oz[edit]

declare
  fun {MergeSort Xs}
     case Xs
     of nil then nil
     [] [X] then [X]
     else
        Middle = {Length Xs} div 2
        Left Right
        {List.takeDrop Xs Middle ?Left ?Right}
     in
        {List.merge {MergeSort Left} {MergeSort Right} Value.'<'}
     end
  end
in
  {Show {MergeSort [3 1 4 1 5 9 2 6 5]}}

PARI/GP[edit]

Note also that the built-in vecsort and listsort use a merge sort internally.

mergeSort(v)={
  if(#v<2, return(v));
  my(m=#v\2,left=vector(m,i,v[i]),right=vector(#v-m,i,v[m+i]));
  left=mergeSort(left);
  right=mergeSort(right);
  merge(left, right)
};
merge(u,v)={
	my(ret=vector(#u+#v),i=1,j=1);
	for(k=1,#ret,
		if(i<=#u & (j>#v | u[i]<v[j]),
			ret[k]=u[i];
			i++
		,
			ret[k]=v[j];
			j++
		)
	);
	ret
};

Pascal[edit]

Works with: FPC
program MergeSortDemo;

{$mode objfpc}{$h+}

procedure MergeSort(var A: array of Integer);
var
  Buf: array of Integer;
  procedure Merge(L, M, R: Integer);
  var
    I, J, K: Integer;
  begin
    I := L;
    J := Succ(M);
    for K := 0 to R - L do
      if (J > R) or (I <= M) and (A[I] <= A[J]) then begin
        Buf[K] := A[I];
        Inc(I);
      end else begin
        Buf[K] := A[J];
        Inc(J);
      end;
    Move(Buf[0], A[L], Succ(R - L) * SizeOf(Integer));
  end;
  procedure MSort(L, R: Integer);
  var
    M: Integer;
  begin
    if R > L then begin
      {$push}{$q-}{$r-}M := (L + R) shr 1;{$pop}
      MSort(L, M);
      MSort(M + 1, R);
      if A[M] > A[M + 1] then
        Merge(L, M, R);
    end;
  end;
begin
  if Length(A) > 1 then begin
    SetLength(Buf, Length(A));
    MSort(0, High(A));
  end;
end;

procedure PrintArray(const Name: string; const A: array of Integer);
var
  I: Integer;
begin
  Write(Name, ': [');
  for I := 0 to High(A) - 1 do
    Write(A[I], ', ');
  WriteLn(A[High(A)], ']');
end;

var
  a1: array[-7..5] of Integer = (27, -47, 14, 39, 47, -2, -8, 20, 18, 22, -49, -40, -8);
  a2: array of Integer = (9, -25, -16, 24, 39, 42, 20, 20, 39, 10, -47, 28);
begin
  MergeSort(a1);
  PrintArray('a1', a1);
  MergeSort(a2);
  PrintArray('a2', a2);
end.
Output:
a1: [-49, -47, -40, -8, -8, -2, 14, 18, 20, 22, 27, 39, 47]
a2: [-47, -25, -16, 9, 10, 20, 20, 24, 28, 39, 39, 42] 

improvement[edit]

uses "only" one halfsized temporary array for merging, which are set to the right size in before. small sized fields are sorted via insertion sort. Only an array of Pointers is sorted, so no complex data transfers are needed.Sort for X,Y or whatever is easy to implement.

Works with ( Turbo -) Delphi too.

{$IFDEF FPC}
  {$MODE DELPHI}
  {$OPTIMIZATION ON,Regvar,ASMCSE,CSE,PEEPHOLE}
{$ELSE}
  {$APPTYPE CONSOLE}
{$ENDIF}
uses
  sysutils; //for timing
type
  tDataElem  =  record
                  myText : AnsiString;
                  myX,
                  myY : double;
                  myTag,
                  myOrgIdx : LongInt;
                end;
                
  tpDataElem = ^tDataElem;
  tData = array of tDataElem;
 
  tSortData = array of tpDataElem;
  tCompFunc = function(A,B:tpDataElem):integer;
var
  Data    : tData;
  Sortdata,
  tmpData : tSortData;
 
procedure InitData(var D:tData;cnt: LongWord);
var
  i,k: LongInt;
begin
  Setlength(D,cnt);
  Setlength(SortData,cnt);
  Setlength(tmpData,cnt shr 1 +1 );
  k := 10*cnt;
  For i := cnt-1 downto 0 do
  Begin
    Sortdata[i] := @D[i];
    with D[i] do
    Begin
      myText := Format('_%.9d',[random(cnt)+1]);
      myX := Random*k;
      myY := Random*k;
      myTag := Random(k);
      myOrgIdx := i;
    end;
  end;
end;
 
procedure FreeData(var D:tData);
begin
  Setlength(tmpData,0);
  Setlength(SortData,0);
  Setlength(D,0);
end;

function CompLowercase(A,B:tpDataElem):integer;
var
  lcA,lcB: String;
Begin
  lcA := lowercase(A^.myText);
  lcB := lowercase(B^.myText);  
  result := ORD(lcA > lcB)-ORD(lcA < lcB);  
end;  

function myCompText(A,B:tpDataElem):integer;
{sort an array (or list) of strings in order of descending length, 
  and in ascending lexicographic order for strings of equal length.}
var
  lA,lB:integer;
  
Begin
  lA := Length(A^.myText);
  lB := Length(B^.myText);
  result := ORD(lA<lB)-ORD(lA>lB);  
  IF result = 0 then
    result := CompLowercase(A,B);
end;
 
function myCompX(A,B:tpDataElem):integer;
//same as sign without jumps in assembler code
begin
  result := ORD(A^.myX > B^.myX)-ORD(A^.myX < B^.myX);
end;
 
function myCompY(A,B:tpDataElem):integer;
Begin
  result := ORD(A^.myY > B^.myY)-ORD(A^.myY < B^.myY);
end;
 
function myCompTag(A,B:tpDataElem):integer;
Begin
  result := ORD(A^.myTag > B^.myTag)-ORD(A^.myTag < B^.myTag);
end;
 
procedure InsertionSort(left,right:integer;var a: tSortData;CompFunc: tCompFunc);
var
   Pivot : tpDataElem;
   i,j  : LongInt;
begin
 for i:=left+1 to right do
 begin
   j :=i;
   Pivot := A[j];
   while (j>left) AND (CompFunc(A[j-1],Pivot)>0) do
   begin
     A[j] := A[j-1];
     dec(j);
   end;
   A[j] :=PiVot;// s.o.
 end;
end;
 
 
procedure mergesort(left,right:integer;var a: tSortData;CompFunc: tCompFunc);
var
  i,j,k,mid :integer;
begin
{// without insertion sort
  If right>left then
}
//{ test insertion sort
  If right-left<=14 then
     InsertionSort(left,right,a,CompFunc)
  else
//}
  begin
    //recursion
    mid := (right+left) div 2;
    mergesort(left, mid,a,CompFunc);
    mergesort(mid+1, right,a,CompFunc);
    //already sorted ?
    IF CompFunc(A[Mid],A[Mid+1])<0 then
      exit;
 
    //##########  Merge  ##########
    //copy lower half to temporary array
    move(A[left],tmpData[0],(mid-left+1)*SizeOf(Pointer));
    i := 0;
    j := mid+1;
    k := left;
    // re-integrate
    while (k<j) AND (j<=right) do
      begin
      IF CompFunc(tmpData[i],A[j])<=0 then
        begin
        A[k] := tmpData[i];
        inc(i);
        end
      else
        begin
        A[k]:= A[j];
        inc(j);
        end;
      inc(k);
      end;
    //the rest of tmpdata a move should do too, in next life
    while (k<j) do
      begin
      A[k] := tmpData[i];
      inc(i);
      inc(k);
      end;
  end;
end;
 
var
  T1,T0: TDateTime;
  i : integer;
Begin
  randomize;
  InitData(Data,1*1000*1000);
 
  T0 := Time;
  mergesort(Low(SortData),High(SortData),SortData,@myCompText);
  T1 := Time;
  Writeln('myText ',FormatDateTime('NN:SS.ZZZ',T1-T0));
//  For i := 0 to High(Data) do  Write(SortData[i].myText);  writeln;  
  T0 := Time;
  mergesort(Low(SortData),High(SortData),SortData,@myCompX);
  T1 := Time;
  Writeln('myX    ',FormatDateTime('NN:SS.ZZZ',T1-T0));
 //check
  For i := 1 to High(Data) do
    IF myCompX(SortData[i-1],SortData[i]) = 1 then
      Write(i:8);
 
  T0 := Time;
  mergesort(Low(SortData),High(SortData),SortData,@myCompY);
  T1 := Time;
  Writeln('myY    ',FormatDateTime('NN:SS.ZZZ',T1-T0));
 
  T0 := Time;
  mergesort(Low(SortData),High(SortData),SortData,@myCompTag);
  T1 := Time;
  Writeln('myTag  ',FormatDateTime('NN:SS.ZZZ',T1-T0));
 
  FreeData (Data);
end.
output
Free pascal 2.6.4 32bit / Win7 / i 4330 3.5 Ghz
myText 00:03.158 / nearly worst case , all strings same sized and starting with '_000..'
myX    00:00.360
myY    00:00.363
myTag  00:00.283

Perl[edit]

sub merge_sort {
    my @x = @_;
    return @x if @x < 2;
    my $m = int @x / 2;
    my @a = merge_sort(@x[0 .. $m - 1]);
    my @b = merge_sort(@x[$m .. $#x]);
    for (@x) {
        $_ = !@a            ? shift @b
           : !@b            ? shift @a
           : $a[0] <= $b[0] ? shift @a
           :                  shift @b;
    }
    @x;
}

my @a = (4, 65, 2, -31, 0, 99, 83, 782, 1);
@a = merge_sort @a;
print "@a\n";

Also note, the built-in function sort uses mergesort.

Phix[edit]

with javascript_semantics

function merge(sequence left, sequence right)
sequence result = {}
    while length(left)>0 and length(right)>0 do
        if left[1]<=right[1] then
            result = append(result, left[1])
            left = left[2..$]
        else
            result = append(result, right[1])
            right = right[2..$]
        end if
    end while
    return result & left & right
end function
 
function mergesort(sequence m)
    if length(m)<=1 then return m end if
    integer middle = floor(length(m)/2)
    sequence left = mergesort(m[1..middle]),
            right = mergesort(m[middle+1..$])
    if left[$]<=right[1] then
        return left & right
    elsif right[$]<=left[1] then
        return right & left
    end if
    return merge(left, right)
end function
 
constant s = shuffle(tagset(10))
? s
? mergesort(deep_copy(s))
Output:
{8,1,2,5,10,3,9,6,7,4}
{1,2,3,4,5,6,7,8,9,10}

PHP[edit]

function mergesort($arr){
	if(count($arr) == 1 ) return $arr;
	$mid = count($arr) / 2;
    $left = array_slice($arr, 0, $mid);
    $right = array_slice($arr, $mid);
	$left = mergesort($left);
	$right = mergesort($right);
	return merge($left, $right);
}

function merge($left, $right){
	$res = array();
	while (count($left) > 0 && count($right) > 0){
		if($left[0] > $right[0]){
			$res[] = $right[0];
			$right = array_slice($right , 1);
		}else{
			$res[] = $left[0];
			$left = array_slice($left, 1);
		}
	}
	while (count($left) > 0){
		$res[] = $left[0];
		$left = array_slice($left, 1);
	}
	while (count($right) > 0){
		$res[] = $right[0];
		$right = array_slice($right, 1);
	}
	return $res;
}

$arr = array( 1, 5, 2, 7, 3, 9, 4, 6, 8);
$arr = mergesort($arr);
echo implode(',',$arr);
Output:
1,2,3,4,5,6,7,8,9

Picat[edit]

Translation of: Prolog
% True if S is a sorted copy of L, using merge sort
msort([],[]).
msort([X],[X]).
msort(U,S) :-
  split(U, L, R),
  msort(L, SL),
  msort(R, SR),
  merge(SL, SR, S).
 
% split(LIST,L,R)
% Alternate elements of LIST in L and R
split([],[],[]).
split([X],[X],[]).
split([L,R|T],[L|LT],[R|RT]) :-
  split( T, LT, RT ).
 
% merge( LS, RS, M )
% Assuming LS and RS are sorted, True if M is the sorted merge of the two
merge([],RS,RS).
merge(LS,[],LS).
merge([L|LS],[R|RS],[L|T]) :-
    L @=< R, 
    merge(LS,[R|RS],T).
merge([L|LS],[R|RS],[R|T]) :-
    L @> R,
    merge([L|LS],RS,T).


PicoLisp[edit]

PicoLisp's built-in sort routine uses merge sort. This is a high level implementation.

(de alt (List)
   (if List (cons (car List) (alt (cddr List))) ()) )

(de merge (L1 L2)
   (cond
      ((not L2) L1)
      ((< (car L1) (car L2))
         (cons (car L1) (merge L2 (cdr L1))))
      (T (cons (car L2) (merge L1 (cdr L2)))) ) )

(de mergesort (List)
   (if (cdr List)
      (merge (mergesort (alt List)) (mergesort (alt (cdr List))))
      List) )

(mergesort (8 1 5 3 9 0 2 7 6 4))

PL/I[edit]

MERGE: PROCEDURE (A,LA,B,LB,C);

/* Merge A(1:LA) with B(1:LB), putting the result in C 
   B and C may share the same memory, but not with A.
*/
   DECLARE (A(*),B(*),C(*)) BYADDR POINTER;
   DECLARE (LA,LB) BYVALUE NONASGN FIXED BIN(31);
   DECLARE (I,J,K) FIXED BIN(31);
   DECLARE (SX) CHAR(58) VAR BASED (PX);
   DECLARE (SY) CHAR(58) VAR BASED (PY);
   DECLARE (PX,PY) POINTER;

   I=1; J=1; K=1;
   DO WHILE ((I <= LA) & (J <= LB));
      PX=A(I); PY=B(J);
      IF(SX <= SY) THEN
         DO; C(K)=A(I); K=K+1; I=I+1; END;
      ELSE
         DO; C(K)=B(J); K=K+1; J=J+1; END;
   END;
   DO WHILE (I <= LA);
      C(K)=A(I); I=I+1; K=K+1;
   END;
   RETURN;
END MERGE;

MERGESORT: PROCEDURE (AP,N) RECURSIVE ;

/* Sort the array AP containing N pointers to strings */

     DECLARE (AP(*))              BYADDR POINTER;
     DECLARE (N)                  BYVALUE NONASGN FIXED BINARY(31);
     DECLARE (M,I)                FIXED BINARY;
     DECLARE AMP1(1)              POINTER BASED(PAM);
     DECLARE (pX,pY,PAM) POINTER;
     DECLARE SX CHAR(58) VAR BASED(pX);
     DECLARE SY CHAR(58) VAR BASED(pY);

   IF (N=1) THEN RETURN;
   M = trunc((N+1)/2);
   IF (M>1) THEN CALL MERGESORT(AP,M);
   PAM=ADDR(AP(M+1));
   IF (N-M > 1) THEN CALL MERGESORT(AMP1,N-M);
   pX=AP(M); pY=AP(M+1);
   IF SX <= SY then return;     /* Skip Merge */
   DO I=1 to M; TP(I)=AP(I); END;
   CALL MERGE(TP,M,AMP1,N-M,AP);
   RETURN;
END MERGESORT;

PowerShell[edit]

function MergeSort([object[]] $SortInput)
{
	# The base case exits for minimal lists that are sorted by definition
	if ($SortInput.Length -le 1) {return $SortInput}
	
	# Divide and conquer
	[int] $midPoint = $SortInput.Length/2
	# The @() operators ensure a single result remains typed as an array
	[object[]] $left = @(MergeSort @($SortInput[0..($midPoint-1)]))
	[object[]] $right = @(MergeSort @($SortInput[$midPoint..($SortInput.Length-1)]))

	# Merge
	[object[]] $result = @()
	while (($left.Length -gt 0) -and ($right.Length -gt 0))
	{
		if ($left[0] -lt $right[0])
		{
			$result += $left[0]
			# Use an if/else rather than accessing the array range as $array[1..0]
			if ($left.Length -gt 1){$left = $left[1..$($left.Length-1)]}
			else {$left = @()}
		}
		else
		{
			$result += $right[0]
			# Without the if/else, $array[1..0] would return the whole array when $array.Length == 1
			if ($right.Length -gt 1){$right = $right[1..$($right.Length-1)]}
			else {$right = @()}
		}
	}
	
	# If we get here, either $left or $right is an empty array (or both are empty!).  Since the
	# rest of the unmerged array is already sorted, we can simply string together what we have.
	# This line outputs the concatenated result.  An explicit 'return' statement is not needed.
	$result + $left + $right
}

Prolog[edit]

% msort( L, S )
% True if S is a sorted copy of L, using merge sort
msort( [], [] ).
msort( [X], [X] ).
msort( U, S ) :- split(U, L, R), msort(L, SL), msort(R, SR), merge(SL, SR, S).

% split( LIST, L, R )
% Alternate elements of LIST in L and R
split( [], [], [] ).
split( [X], [X], [] ).
split( [L,R|T], [L|LT], [R|RT] ) :- split( T, LT, RT ).

% merge( LS, RS, M )
% Assuming LS and RS are sorted, True if M is the sorted merge of the two
merge( [], RS, RS ).
merge( LS, [], LS ).
merge( [L|LS], [R|RS], [L|T] ) :- L =< R, merge(    LS, [R|RS], T).
merge( [L|LS], [R|RS], [R|T] ) :- L > R,  merge( [L|LS],   RS,  T).

PureBasic[edit]

A non-optimized version with lists.

Procedure display(List m())
  ForEach m()
    Print(LSet(Str(m()), 3," "))
  Next
  PrintN("")
EndProcedure

;overwrites list m() with the merger of lists ma() and mb()
Procedure merge(List m(), List ma(), List mb())
  FirstElement(m())
  Protected ma_elementExists = FirstElement(ma())
  Protected mb_elementExists = FirstElement(mb()) 
  Repeat
    If ma() <= mb()
      m() = ma(): NextElement(m())
      ma_elementExists = NextElement(ma())
    Else
      m() = mb(): NextElement(m())
      mb_elementExists = NextElement(mb())
    EndIf
  Until Not (ma_elementExists And mb_elementExists)

  If ma_elementExists
    Repeat
      m() = ma(): NextElement(m())
    Until Not NextElement(ma())
  ElseIf mb_elementExists
    Repeat
      m() = mb(): NextElement(m())
    Until Not NextElement(mb())
  EndIf
EndProcedure

Procedure mergesort(List m())
  Protected NewList ma()
  Protected NewList mb()
  
  If ListSize(m()) > 1
    Protected current, middle = (ListSize(m()) / 2 ) - 1
    
    FirstElement(m())
    While current <= middle
      AddElement(ma())
      ma() = m()
      NextElement(m()): current + 1
    Wend
    
    PreviousElement(m())
    While NextElement(m())
      AddElement(mb())
      mb() = m()
    Wend
    
    mergesort(ma())
    mergesort(mb())
    LastElement(ma()): FirstElement(mb())
    If ma() <= mb() 
      FirstElement(m())
      FirstElement(ma())
      Repeat
        m() = ma(): NextElement(m())
      Until Not NextElement(ma())
      Repeat
        m() = mb(): NextElement(m())
      Until Not NextElement(mb())
    Else 
      merge(m(), ma(), mb())
    EndIf 
  EndIf 
EndProcedure
  
If OpenConsole()
  Define i
  NewList x()
  
  For i = 1 To 21: AddElement(x()): x() = Random(60): Next
  display(x())
  mergesort(x())
  display(x())
  
  Print(#CRLF$ + #CRLF$ + "Press ENTER to exit")
  Input()
  CloseConsole()
EndIf
Sample output:
22 51 31 59 58 45 11 2  16 56 38 42 2  10 23 41 42 25 45 28 42
2  2  10 11 16 22 23 25 28 31 38 41 42 42 42 45 45 51 56 58 59

Python[edit]

Works with: Python version 2.6+
from heapq import merge

def merge_sort(m):
    if len(m) <= 1:
        return m

    middle = len(m) // 2
    left = m[:middle]
    right = m[middle:]

    left = merge_sort(left)
    right = merge_sort(right)
    return list(merge(left, right))

Pre-2.6, merge() could be implemented like this:

def merge(left, right):
    result = []
    left_idx, right_idx = 0, 0
    while left_idx < len(left) and right_idx < len(right):
        # change the direction of this comparison to change the direction of the sort
        if left[left_idx] <= right[right_idx]:
            result.append(left[left_idx])
            left_idx += 1
        else:
            result.append(right[right_idx])
            right_idx += 1

    if left_idx < len(left):
        result.extend(left[left_idx:])
    if right_idx < len(right):
        result.extend(right[right_idx:])
    return result

using only recursions

def merge(x, y):
    if x==[]: return y
    if y==[]: return x
    return [x[0]] + merge(x[1:], y) if x[0]<y[0] else [y[0]] + merge(x, y[1:])

def sort(a, n):
    m = n//2
    return a if n<=1 else merge(sort(a[:m], m), sort(a[m:], n-m))

a = list(map(int, input().split()))
print(sort(a, len(a)))

Quackery[edit]

[ [] temp put
  [ dup  [] != while
    over [] != while
    over 0 peek
    over 0 peek
    > not if dip
      [ 1 split
        temp take
        rot join
        temp put ]
      again ]
    join
    temp take swap join ] is merge     ( [ [ --> [ )

[ dup size 2 < if done
  dup size 2 / split
  swap recurse
  swap recurse
  merge ]                 is mergesort (   [ --> [ )

R[edit]

mergesort <- function(m)
{
   merge_ <- function(left, right)
   {
      result <- c()
      while(length(left) > 0 && length(right) > 0)
      {
         if(left[1] <= right[1])
         {
            result <- c(result, left[1])
            left <- left[-1]
         } else
         {
            result <- c(result, right[1])
            right <- right[-1]
         }         
      }
      if(length(left) > 0) result <- c(result, left)
      if(length(right) > 0) result <- c(result, right)
      result
   }
   
   len <- length(m)
   if(len <= 1) m else
   {
      middle <- length(m) / 2
      left <- m[1:floor(middle)]
      right <- m[floor(middle+1):len]
      left <- mergesort(left)
      right <- mergesort(right)
      if(left[length(left)] <= right[1])
      {
         c(left, right)
      } else
      {
         merge_(left, right)
      } 
   }
}
mergesort(c(4, 65, 2, -31, 0, 99, 83, 782, 1)) # -31   0   1   2   4  65  83  99 782

Racket[edit]

#lang racket

(define (merge xs ys)
  (cond [(empty? xs) ys]
        [(empty? ys) xs]
        [(match* (xs ys)
           [((list* a as) (list* b bs))
            (cond [(<= a b) (cons a (merge as ys))]
                  [         (cons b (merge xs bs))])])]))

(define (merge-sort xs)
  (match xs
    [(or (list) (list _)) xs]
    [_ (define-values (ys zs) (split-at xs (quotient (length xs) 2)))
       (merge (merge-sort ys) (merge-sort zs))]))

This variation is bottom up:

#lang racket

(define (merge-sort xs)
  (merge* (map list xs)))

(define (merge* xss)
  (match xss
    [(list)    '()]
    [(list xs) xss]
    [(list xs ys zss ...) 
     (merge* (cons (merge xs ys) (merge* zss)))]))

(define (merge xs ys)
  (cond [(empty? xs) ys]
        [(empty? ys) xs]
        [(match* (xs ys)
           [((list* a as) (list* b bs))
            (cond [(<= a b) (cons a (merge as ys))]
                  [         (cons b (merge xs bs))])])]))

Raku[edit]

(formerly Perl 6)

Works with: Rakudo Star version 2015.10
sub merge_sort ( @a ) {
    return @a if @a <= 1;

    my $m = @a.elems div 2;
    my @l = flat merge_sort @a[  0 ..^ $m ];
    my @r = flat merge_sort @a[ $m ..^ @a ];

    return flat @l, @r if @l[*-1] !after @r[0];
    return flat gather {
        take @l[0] before @r[0] ?? @l.shift !! @r.shift
            while @l and @r;
        take @l, @r;
    }
}
my @data = 6, 7, 2, 1, 8, 9, 5, 3, 4;
say 'input  = ' ~ @data;
say 'output = ' ~ @data.&merge_sort;
Output:
input  = 6 7 2 1 8 9 5 3 4
output = 1 2 3 4 5 6 7 8 9

REBOL[edit]

msort: function [a compare] [msort-do merge] [
    if (length? a) < 2 [return a]
    ; define a recursive Msort-do function
    msort-do: function [a b l] [mid] [
        either l < 4 [
            if l = 3 [msort-do next b next a 2]
            merge a b 1 next b l - 1
        ] [
            mid: make integer! l / 2
            msort-do b a mid
            msort-do skip b mid skip a mid l - mid
            merge a b mid skip b mid l - mid
        ]
    ]
    ; function Merge is the key part of the algorithm
    merge: func [a b lb c lc] [
        until [
            either (compare first b first c) [
                change/only a first b
                b: next b
                a: next a
                zero? lb: lb - 1
            ] [
                change/only a first c
                c: next c
                a: next a
                zero? lc: lc - 1
            ]
        ]
        loop lb [
            change/only a first b
            b: next b
            a: next a
        ]
        loop lc [
            change/only a first c
            c: next c
            a: next a
        ]
    ]
    msort-do a copy a length? a
    a
]

REXX[edit]

Note:   the array elements can be anything:   integers, floating point (exponentiated), character strings ···

/*REXX pgm sorts a stemmed array (numbers and/or chars) using the  merge─sort algorithm.*/
call init                                        /*sinfully initialize the   @   array. */
call show      'before sort'                     /*show the   "before"  array elements. */
                            say copies('▒', 75)  /*display a separator line to the term.*/
call merge          #                            /*invoke the  merge sort  for the array*/
call show      ' after sort'                     /*show the    "after"  array elements. */
exit 0                                           /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
init: @.=;    @.1= '---The seven deadly sins---'  ;    @.4= "avarice"  ;   @.7= 'gluttony'
              @.2= '==========================='  ;    @.5= "wrath"    ;   @.8= 'sloth'
              @.3= 'pride'                        ;    @.6= "envy"     ;   @.9= 'lust'
      do #=1  until @.#==''; end;   #= #-1;   return      /*#:  # of entries in @ array.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
show: do j=1  for #; say right('element',20) right(j,length(#)) arg(1)":" @.j; end; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
merge: procedure expose @. !.;   parse arg n, L;   if L==''  then do;  !.=;  L= 1;  end
          if n==1  then return;     h= L + 1
          if n==2  then do; if @.L>@.h  then do; _=@.h; @.h=@.L; @.L=_; end; return;  end
          m= n % 2                                     /* [↑]  handle case of two items.*/
          call merge  n-m, L+m                         /*divide items  to the left   ···*/
          call merger m,   L,   1                      /*   "     "     "  "  right  ···*/
          i= 1;                     j= L + m
                     do k=L  while k<j                 /*whilst items on right exist ···*/
                     if j==L+n  |  !.i<=@.j  then do;     @.k= !.i;     i= i + 1;      end
                                             else do;     @.k= @.j;     j= j + 1;      end
                     end   /*k*/
          return
/*──────────────────────────────────────────────────────────────────────────────────────*/
merger: procedure expose @. !.;  parse arg n,L,T
           if n==1  then do;  !.T= @.L;                                       return;  end
           if n==2  then do;  h= L + 1;   q= T + 1;  !.q= @.L;    !.T= @.h;   return;  end
           m= n % 2                                    /* [↑]  handle case of two items.*/
           call merge  m,   L                          /*divide items  to the left   ···*/
           call merger n-m, L+m, m+T                   /*   "     "     "  "  right  ···*/
           i= L;                     j= m + T
                     do k=T  while k<j                 /*whilst items on left exist  ···*/
                     if j==T+n  |  @.i<=!.j  then do;     !.k= @.i;     i= i + 1;      end
                                             else do;     !.k= !.j;     j= j + 1;      end
                     end   /*k*/
           return
output   when using the default input:

(Shown at three-quarter size.)

             element 1 before sort: ---The seven deadly sins---
             element 2 before sort: ===========================
             element 3 before sort: pride
             element 4 before sort: avarice
             element 5 before sort: wrath
             element 6 before sort: envy
             element 7 before sort: gluttony
             element 8 before sort: sloth
             element 9 before sort: lust
▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
             element 1  after sort: ---The seven deadly sins---
             element 2  after sort: ===========================
             element 3  after sort: avarice
             element 4  after sort: envy
             element 5  after sort: gluttony
             element 6  after sort: lust
             element 7  after sort: pride
             element 8  after sort: sloth
             element 9  after sort: wrath

Ruby[edit]

def merge_sort(m)
  return m if m.length <= 1
  
  middle = m.length / 2
  left = merge_sort(m[0...middle])
  right = merge_sort(m[middle..-1])
  merge(left, right)
end

def merge(left, right)
  result = []
  until left.empty? || right.empty?
    result << (left.first<=right.first ? left.shift : right.shift)
  end
  result + left + right
end

ary = [7,6,5,9,8,4,3,1,2,0]
p merge_sort(ary)                  # => [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

Here's a version that monkey patches the Array class, with an example that demonstrates it's a stable sort

class Array
  def mergesort(&comparitor)
    return self if length <= 1
    comparitor ||= proc{|a, b| a <=> b}
    middle = length / 2
    left  = self[0...middle].mergesort(&comparitor)
    right = self[middle..-1].mergesort(&comparitor)
    merge(left, right, comparitor) 
  end
  
  private
  def merge(left, right, comparitor)
    result = []
    until left.empty? || right.empty?
      # change the direction of this comparison to change the direction of the sort
      if comparitor[left.first, right.first] <= 0
        result << left.shift
      else
        result << right.shift
      end
    end
    result + left + right
  end
end

ary = [7,6,5,9,8,4,3,1,2,0]
p ary.mergesort                    # => [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
p ary.mergesort {|a, b| b <=> a}   # => [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]

ary = [["UK", "London"], ["US", "New York"], ["US", "Birmingham"], ["UK", "Birmingham"]]
p ary.mergesort
# => [["UK", "Birmingham"], ["UK", "London"], ["US", "Birmingham"], ["US", "New York"]]
p ary.mergesort {|a, b| a[1] <=> b[1]}
# => [["US", "Birmingham"], ["UK", "Birmingham"], ["UK", "London"], ["US", "New York"]]

Rust[edit]

Works with: rustc version 1.9.0
fn merge<T: Copy + PartialOrd>(x1: &[T], x2: &[T], y: &mut [T]) {
	assert_eq!(x1.len() + x2.len(), y.len());
	let mut i = 0;
	let mut j = 0;
	let mut k = 0;
	while i < x1.len() && j < x2.len() {
		if x1[i] < x2[j] {
			y[k] = x1[i];
			k += 1;
			i += 1;
		} else {
			y[k] = x2[j];
			k += 1;
			j += 1;
		}
	}
	if i < x1.len() {
		y[k..].copy_from_slice(&x1[i..]);
	}
	if j < x2.len() {
		y[k..].copy_from_slice(&x2[j..]);
	}
}

The sort algorithm :

fn merge_sort_rec<T: Copy + Ord>(x: &mut [T]) {
	let n = x.len();
	let m = n / 2;
	
	if n <= 1 {
		return;
	}
	
	merge_sort_rec(&mut x[0..m]);
	merge_sort_rec(&mut x[m..n]);
		
	let mut y: Vec<T> = x.to_vec();
	
	merge(&x[0..m], &x[m..n], &mut y[..]);
	
	x.copy_from_slice(&y);
}

Version without recursion call (faster) :

fn merge_sort<T: Copy + PartialOrd>(x: &mut [T]) {
	let n = x.len();
	let mut y = x.to_vec();
	let mut len = 1;
	while len < n {
		let mut i = 0;
		while i < n {
			if i + len >= n {
				y[i..].copy_from_slice(&x[i..]);
			} else if i + 2 * len > n {
				merge(&x[i..i+len], &x[i+len..], &mut y[i..]);				
			} else {
				merge(&x[i..i+len], &x[i+len..i+2*len], &mut y[i..i+2*len]);
			}
			i += 2 * len;
		}
		len *= 2;
		if len >= n {
			x.copy_from_slice(&y);
			return;
		}
		i = 0;
		while i < n {
			if i + len >= n {
				x[i..].copy_from_slice(&y[i..]);
			} else if i + 2 * len > n {
				merge(&y[i..i+len], &y[i+len..], &mut x[i..]);				
			} else {
				merge(&y[i..i+len], &y[i+len..i+2*len], &mut x[i..i+2*len]);
			}
			i += 2 * len;
		}
		len *= 2;
	}
}

Scala[edit]

The use of LazyList as the merge result avoids stack overflows without resorting to tail recursion, which would typically require reversing the result, as well as being a bit more convoluted.

import scala.language.implicitConversions

object MergeSort extends App {

  def mergeSort(input: List[Int]): List[Int] = {
    def merge(left: List[Int], right: List[Int]): LazyList[Int] = (left, right) match {
      case (x :: xs, y :: ys) if x <= y => x #:: merge(xs, right)
      case (x :: xs, y :: ys) => y #:: merge(left, ys)
      case _ => if (left.isEmpty) right.to(LazyList) else left.to(LazyList)
    }

    def sort(input: List[Int], length: Int): List[Int] = input match {
      case Nil | List(_) => input
      case _ =>
        val middle = length / 2
        val (left, right) = input splitAt middle
        merge(sort(left, middle), sort(right, middle + length % 2)).toList
    }

    sort(input, input.length)
  }

}

Scheme[edit]

(define (merge-sort l gt?)
  (define (merge left right)
    (cond
     ((null? left)
      right)
     ((null? right)
      left)
     ((gt? (car left) (car right))
      (cons (car right)
            (merge left (cdr right))))
     (else
      (cons (car left)
            (merge (cdr left) right)))))
  (define (take l n)
    (if (zero? n)
      (list)
      (cons (car l)
            (take (cdr l) (- n 1)))))
  (let ((half (quotient (length l) 2)))
    (if (zero? half)
      l
      (merge (merge-sort (take      l half) gt?)
             (merge-sort (list-tail l half) gt?)))))
(merge-sort '(1 3 5 7 9 8 6 4 2) >)

Seed7[edit]

const proc: mergeSort2 (inout array elemType: arr, in integer: lo, in integer: hi, inout array elemType: scratch) is func
  local
    var integer: mid is 0;
    var integer: k is 0;
    var integer: t_lo is 0;
    var integer: t_hi is 0;
  begin
    if lo < hi then
      mid := (lo + hi) div 2;
      mergeSort2(arr, lo, mid, scratch);
      mergeSort2(arr, succ(mid), hi, scratch);
      t_lo := lo;
      t_hi := succ(mid);
      for k range lo to hi do
        if t_lo <= mid and (t_hi > hi or arr[t_lo] <= arr[t_hi]) then
          scratch[k] := arr[t_lo];
          incr(t_lo);
        else
          scratch[k] := arr[t_hi];
          incr(t_hi);
        end if;
      end for;
      for k range lo to hi do
        arr[k] := scratch[k];
      end for;
    end if;
  end func;

const proc: mergeSort2 (inout array elemType: arr) is func
  local
    var array elemType: scratch is 0 times elemType.value;
  begin
    scratch := length(arr) times elemType.value;
    mergeSort2(arr, 1, length(arr), scratch);
  end func;

Original source: [2]

Sidef[edit]

func merge(left, right) {
    var result = []
    while (left && right) {
        result << [right,left].min_by{.first}.shift
    }
    result + left + right
}
 
func mergesort(array) {
    var len = array.len
    len < 2 && return array
 
    var (left, right) = array.part(len//2)
 
    left  = __FUNC__(left)
    right = __FUNC__(right)
 
    merge(left, right)
}
 
# Numeric sort
var nums = rand(1..100, 10)
say mergesort(nums)
 
# String sort
var strings = rand('a'..'z', 10)
say mergesort(strings)

Standard ML[edit]

fun merge cmp ([], ys) = ys
  | merge cmp (xs, []) = xs
  | merge cmp (xs as x::xs', ys as y::ys') =
      case cmp (x, y) of GREATER => y :: merge cmp (xs, ys')
                       | _       => x :: merge cmp (xs', ys)
;
fun merge_sort cmp [] = []
  | merge_sort cmp [x] = [x]
  | merge_sort cmp xs = let
      val ys = List.take (xs, length xs div 2)
      val zs = List.drop (xs, length xs div 2)
    in
      merge cmp (merge_sort cmp ys, merge_sort cmp zs)
    end
;
merge_sort Int.compare [8,6,4,2,1,3,5,7,9]

Swift[edit]

// Merge Sort in Swift 4.2
// Source: https://github.com/raywenderlich/swift-algorithm-club/tree/master/Merge%20Sort
// NOTE: by use of generics you can make it sort arrays of any type that conforms to
//       Comparable protocol, however this is not always optimal

import Foundation

func mergeSort(_ array: [Int]) -> [Int] {
  guard array.count > 1 else { return array }

  let middleIndex = array.count / 2

  let leftPart = mergeSort(Array(array[0..<middleIndex]))
  let rightPart = mergeSort(Array(array[middleIndex..<array.count]))

  func merge(left: [Int], right: [Int]) -> [Int] {
    var leftIndex = 0
    var rightIndex = 0
  
    var merged = [Int]()
    merged.reserveCapacity(left.count + right.count)
  
    while leftIndex < left.count && rightIndex < right.count {
      if left[leftIndex] < right[rightIndex] {
        merged.append(left[leftIndex])
        leftIndex += 1
      } else if left[leftIndex] > right[rightIndex] {
        merged.append(right[rightIndex])
        rightIndex += 1
      } else {
        merged.append(left[leftIndex])
        leftIndex += 1
        merged.append(right[rightIndex])
        rightIndex += 1
      }
    }
  
    while leftIndex < left.count {
      merged.append(left[leftIndex])
      leftIndex += 1
    }
  
    while rightIndex < right.count {
      merged.append(right[rightIndex])
      rightIndex += 1
    }
  
    return merged
  }

  return merge(left: leftPart, right: rightPart)
}

Tailspin[edit]

The standard recursive merge sort

templates mergesort
  templates merge
    @: $(2);
    [ $(1)... -> \(
      when <?($@merge<[](0)>)
      | ..$@merge(1)> do
        $ !
      otherwise
        ^@merge(1) !
        $ -> #
     \),
     $@...] !
  end merge
  $ -> #

  when <[](0..1)> do $!
  otherwise
    def half: $::length ~/ 2;
    [$(1..$half) -> mergesort, $($half+1..last) -> mergesort] -> merge !
end mergesort

[4,5,3,8,1,2,6,7,9,8,5] -> mergesort -> !OUT::write
Output:
[1, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9]

A little different spin where the array is first split into a list of single-element lists and then merged.

templates mergesort
  templates merge
    @: $(2);
    $(1)... -> \(
      when <?($@merge<[](0)>)
      | ..$@merge(1)> do
        $ !
      otherwise
        ^@merge(1) !
        $ -> #
     \) !
     $@... !
  end merge

  templates mergePairs
    when <[](1)> do
      $(1) !
    when <[](2..)> do
      [$(1..2) -> merge] !
      $(3..last) -> #
  end mergePairs

  templates mergeAll
    when <[](0)> do
      $ !
    when <[](1)> do
      $(1) !
    otherwise
      [ $ -> mergePairs ] -> #
  end mergeAll

  $ -> [ $... -> [ $ ] ] -> mergeAll !
end mergesort

[4,5,3,8,1,2,6,7,9,8,5] -> mergesort -> !OUT::write
Output:
[1, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9]

Tcl[edit]

package require Tcl 8.5

proc mergesort m {
    set len [llength $m]
    if {$len <= 1} {
        return $m
    }
    set middle [expr {$len / 2}]
    set left [lrange $m 0 [expr {$middle - 1}]]
    set right [lrange $m $middle end]
    return [merge [mergesort $left] [mergesort $right]]
}

proc merge {left right} {
    set result [list]
    while {[set lleft [llength $left]] > 0 && [set lright [llength $right]] > 0} {
        if {[lindex $left 0] <= [lindex $right 0]} {
            set left [lassign $left value]
        } else {
            set right [lassign $right value]
        }
        lappend result $value
    }
    if {$lleft > 0} {
        lappend result {*}$left
    }
    if {$lright > 0} {
        set result [concat $result $right] ;# another way append elements
    }
    return $result
}

puts [mergesort {8 6 4 2 1 3 5 7 9}] ;# => 1 2 3 4 5 6 7 8 9

Also note that Tcl's built-in lsort command uses the mergesort algorithm.

Unison[edit]

mergeSortBy : (i ->{𝕖} i ->{𝕖} Boolean) ->{𝕖} [i] ->{𝕖} [i]
mergeSortBy cmp =
  merge l1 l2 =
    match (l1, l2) with
      (xs, [])           -> xs
      ([], ys)           -> ys
      (x +: xs, y +: ys) -> if cmp x y then x +: merge xs l2 else y +: merge l1 ys
      ([], [])           -> []
  cases
    []  -> []
    [x] -> [x]
    lst ->
      match halve lst with
        (left, right) -> merge (mergeSortBy cmp left) (mergeSortBy cmp right)

UnixPipes[edit]

Works with: Zsh
split() {
   (while read a b ; do
       echo $a > $1 ; echo $b > $2
   done)
}

mergesort() {
 xargs -n 2 | (read a b; test -n "$b" && (
     lc="1.$1" ; gc="2.$1"
     (echo $a $b;cat)|split >(mergesort $lc >$lc) >( mergesort $gc >$gc)
     sort -m $lc $gc
     rm -f $lc $gc;
 ) || echo $a)
}

cat to.sort | mergesort

Ursala[edit]

#import std

mergesort "p" = @iNCS :-0 ~&B^?a\~&YaO "p"?abh/~&alh2faltPrXPRC ~&arh2falrtPXPRC

#show+

example = mergesort(lleq) <'zoh','zpb','hhh','egi','bff','cii','yid'>
Output:
bff
cii
egi
hhh
yid
zoh
zpb

The mergesort function could also have been defined using the built in sorting operator, -<, because the same algorithm is used.

mergesort "p" = "p"-<

V[edit]

merge uses the helper mergei to merge two lists. The mergei takes a stack of the form [mergedlist] [list1] [list2] it then extracts one element from list2, splits the list1 with it, joins the older merged list, first part of list1 and the element that was used for splitting (taken from list2) into the new merged list. the new list1 is the second part of the split on older list1. new list2 is the list remaining after the element e2 was extracted from it.

[merge
   [mergei
       uncons [swap [>] split] dip
       [[*m] e2 [*a1] b1 a2 : [*m *a1 e2] b1 a2] view].
    
   [a b : [] a b] view
   [size zero?] [pop concat]
       [mergei]
   tailrec].

[msort
  [splitat [arr a : [arr a take arr a drop]] view i].
  [splitarr dup size 2 / >int splitat].

  [small?] []
    [splitarr]
    [merge]
  binrec].
[8 7 6 5 4 2 1 3 9] msort puts

V (Vlang)[edit]

fn main() {
    mut a := [170, 45, 75, -90, -802, 24, 2, 66]
    println("before: $a")
    a = merge_sort(a)
    println("after: $a")
}
 
fn merge_sort(m []int) []int {
    if m.len <= 1{
        return m
    } else {
        mid := m.len / 2
        mut left := merge_sort(m[..mid])
        mut right := merge_sort(m[mid..])
        if m[mid-1] <= m[mid] {
            left << right
            return left
        }
        return merge(mut left, mut right)
    }
}

fn merge(mut left []int,mut right []int) []int {
    mut result := []int{}
    for left.len > 0 && right.len > 0 {
        if left[0] <= right[0]{
            result << left[0]
            left = left[1..]
        } else {
            result << right[0]
            right = right[1..]
        }
    }
    if left.len > 0  {
        result << left
    }
    if right.len > 0 {
        result << right
    }
    return result
}

Wren[edit]

var merge = Fn.new { |left, right|
    var result = []
    while (left.count > 0 && right.count > 0) {
        if (left[0] <= right[0]) {
            result.add(left[0])
            left = left[1..-1]
        } else {
            result.add(right[0])
            right = right[1..-1]
        }
    }
    if (left.count > 0) result.addAll(left)
    if (right.count > 0) result.addAll(right)
    return result
}

var mergeSort // recursive
mergeSort = Fn.new { |m|
    var len = m.count
    if (len <= 1) return m
    var middle = (len/2).floor
    var left = m[0...middle]
    var right = m[middle..-1]
    left = mergeSort.call(left)
    right = mergeSort.call(right)
    if (left[-1] <= right[0]) {
        left.addAll(right)
        return left
    }
    return merge.call(left, right)
}

var as = [ [4, 65, 2, -31, 0, 99, 2, 83, 782, 1], [7, 5, 2, 6, 1, 4, 2, 6, 3] ]
for (a in as) {
    System.print("Before: %(a)")
    a = mergeSort.call(a)
    System.print("After : %(a)")
    System.print()
}
Output:
Before: [4, 65, 2, -31, 0, 99, 2, 83, 782, 1]
After : [-31, 0, 1, 2, 2, 4, 65, 83, 99, 782]

Before: [7, 5, 2, 6, 1, 4, 2, 6, 3]
After : [1, 2, 2, 3, 4, 5, 6, 6, 7]


Alternatively we can just call a library method.

Library: Wren-sort
import "/sort" for Sort

var as = [ [4, 65, 2, -31, 0, 99, 2, 83, 782, 1], [7, 5, 2, 6, 1, 4, 2, 6, 3] ]
for (a in as) {
    System.print("Before: %(a)")
    a = Sort.merge(a)
    System.print("After : %(a)")
    System.print()
}
Output:
As above.

XPL0[edit]

This is based on an example in "Fundamentals of Computer Algorithms" by Horowitz & Sahni.

code Reserve=3, ChOut=8, IntOut=11;

proc MergeSort(A, Low, High);   \Sort array A from Low to High
int  A, Low, High;
int  B, Mid, H, I, J, K;
[if Low >= High then return;
Mid:= (Low+High) >> 1;          \split array in half (roughly)
MergeSort(A, Low, Mid);         \sort left half
MergeSort(A, Mid+1, High);      \sort right half
\Merge the two halves in to sorted order
B:= Reserve((High-Low+1)*4);    \reserve space for working array (4 bytes/int)
H:= Low;  I:= Low;  J:= Mid+1;
while H<=Mid & J<=High do       \merge while both halves have items
    if A(H) <= A(J) then [B(I):= A(H);  I:= I+1;  H:= H+1]
                    else [B(I):= A(J);  I:= I+1;  J:= J+1];
if H > Mid then                 \copy any remaining elements
     for K:= J to High do [B(I):= A(K);  I:= I+1]
else for K:= H to Mid  do [B(I):= A(K);  I:= I+1];
for K:= Low to High do A(K):= B(K);
];

int  A, I;
[A:= [3, 1, 4, 1, -5, 9, 2, 6, 5, 4];
MergeSort(A, 0, 10-1);
for I:= 0 to 10-1 do [IntOut(0, A(I));  ChOut(0, ^ )];
]
Output:
-5 1 1 2 3 4 4 5 6 9 


Yabasic[edit]

Translation of: FreeBASIC
dim b(9)

sub copyArray(a(), inicio, final, b())
    dim b(final - 1)
    for k = inicio to final - 1
        b(k) = a(k)
    next
end sub

// La mitad izquierda es  a(inicio to mitad-1).
// La mitad derecha es    a(mitad  to final-1).
// El resultado es        b(inicio to final-1).
sub topDownMerge(a(), inicio, mitad, final, b())
    i = inicio
    j = mitad
    
    // Si bien hay elementos en los recorridos izquierdo o derecho ...
    for k = inicio to final - 1 
        // Si existe un inicio de recorrido izquierdo y es <= inicio de recorrido derecho existente.
        if (i < mitad) and (j >= final or a(i) <= a(j)) then
            b(k) = a(i)
            i = i + 1
        else
            b(k) = a(j)
            j = j + 1    
        end if
    next 
end sub

// Ordenar la matriz a() usando la matriz b() como fuente.
// inicio es inclusivo; final es exclusivo (a(final) no está en el conjunto).
sub topDownSplitMerge(b(), inicio, final, a())
    if (final - inicio) < 2 then return : fi // Si la diferencia = 1, considérelo ordenado
    // dividir la ejecución de más de 1 elemento en mitades
    mitad = int((final + inicio) / 2)  // mitad = punto medio
    // recursively sort both runs from array a() into b()
    topDownSplitMerge(a(), inicio,  mitad, b())  // ordenar la parte izquierda
    topDownSplitMerge(a(), mitad, final, b())    // ordenar la parte derecha
    // fusionar las ejecuciones resultantes de la matriz b() en a()
    topDownMerge(b(), inicio, mitad, final, a())
end sub

// El array a() tiene los elementos para ordenar; array b() es una matriz de trabajo (inicialmente vacía).
sub topDownMergeSort(a(), b(), n)
    copyArray(a(), 0, n, b())          // duplicar la matriz a() en b()
    topDownSplitMerge(b(), 0, n, a())  // ordenar los datos de b() en a()
end sub

sub printArray(a())
    for i = 1 to arraysize(a(),1)
        print a(i) using "####";
    next
    print
end sub


//--------------------------  
label a1
data 4, 65, 2, -31, 0, 99, 2, 83, 782, 1
label a2
data 7, 5, 2, 6, 1, 4, 2, 6, 3

dim a(9)
restore a1
for i = 0 to 9
    read p 
    a(i) = p
next i
 
dim a2(8)
restore a2
for i = 0 to 8 
    read p 
    a2(i) = p  
next i

print "unsort ";
printArray(a())
topDownMergeSort (a(), b(), 10)
print "  sort ";
printArray(a())
print
print "unsort ";
printArray(a2())
topDownMergeSort (a2(), b(), 9)
print "  sort ";
printArray(a2())
end


ZED[edit]

Source -> http://ideone.com/uZEPL4 Compiled -> http://ideone.com/SJ5EGu

This is a bottom up version of merge sort:

(append) list1 list2
comment:
#true
(003) "append" list1 list2

(car) pair
comment:
#true
(002) "car" pair

(cdr) pair
comment:
#true
(002) "cdr" pair

(cons) one two
comment:
#true
(003) "cons" one two

(map) function list
comment:
#true
(003) "map" function list

(merge) comparator list1 list2
comment:
#true
(merge1) comparator list1 list2 nil

(merge1) comparator list1 list2 collect
comment:
(null?) list2
(append) (reverse) collect list1

(merge1) comparator list1 list2 collect
comment:
(null?) list1
(append) (reverse) collect list2

(merge1) comparator list1 list2 collect
comment:
(003) comparator (car) list2 (car) list1
(merge1) comparator list1 (cdr) list2 (cons) (car) list2 collect

(merge1) comparator list1 list2 collect
comment:
#true
(merge1) comparator (cdr) list1 list2 (cons) (car) list1 collect

(null?) value
comment:
#true
(002) "null?" value

(reverse) list
comment:
#true
(002) "reverse" list

(sort) comparator jumble
comment:
#true
(car) (sort11) comparator (sort1) jumble

(sort1) jumble
comment:
#true
(map) "list" jumble

(sort11) comparator jumble
comment:
(null?) jumble
nil

(sort11) comparator jumble
comment:
(null?) (cdr) jumble
jumble

(sort11) comparator jumble
comment:
#true
(sort11) comparator
         (cons) (merge) comparator (car) jumble (002) "cadr" jumble
                (sort11) comparator (002) "cddr" jumble

zkl[edit]

Pretty wasteful memory wise, probably not suitable for large sorts.

Translation of: Clojure
fcn _merge(left,right){
   if (not left)  return(right);
   if (not right) return(left);
   l:=left[0]; r:=right[0];
   if (l<=r) return(L(l).extend(self.fcn(left[1,*],right)));
   else      return(L(r).extend(self.fcn(left,right[1,*])));
}

fcn merge_sort(L){
   if (L.len()<2) return(L);
   n:=L.len()/2;
   return(_merge(self.fcn(L[0,n]), self.fcn(L[n,*])));
}
merge_sort(T(1,3,5,7,9,8,6,4,2)).println();
merge_sort("big fjords vex quick waltz nymph").concat().println();
Output:
L(1,2,3,4,5,6,7,8,9)
     abcdefghiijklmnopqrstuvwxyz

Or, for lists only:

fcn mergeSort(L){
   if (L.len()<2) return(L.copy());
   n:=L.len()/2;
   self.fcn(L[0,n]).merge(self.fcn(L[n,*]));
}
mergeSort(T(1,3,5,7,9,8,6,4,2)).println();
mergeSort("big fjords vex quick waltz nymph".split("")).concat().println();
Output:
L(1,2,3,4,5,6,7,8,9)
     abcdefghiijklmnopqrstuvwxyz