# Sorting algorithms/Merge sort

Sorting algorithms/Merge sort
You are encouraged to solve this task according to the task description, using any language you may know.

Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.

For other sorting algorithms, see Category:Sorting Algorithms, or:
O(n logn) Sorts
Heapsort | Mergesort | Quicksort
O(n log2n) Sorts
Shell Sort
O(n2) Sorts
Bubble sort | Cocktail sort | Comb sort | Gnome sort | Insertion sort | Selection sort | Strand sort
Other Sorts
Bead sort | Bogosort | Counting sort | Pancake sort | Permutation sort | Radix sort | Sleep sort | Stooge sort

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.

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
```

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.

## 360 Assembly

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                  19/06/2016MAIN   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 mainNN     EQU     ((B-A)/L'A)         number of itemsA      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 storageTEMP   DS      F                   for swapJSTART DS      F                   jstart JMIDDL DS      F                   jmiddlJEND   DS      F                   jendPG     DC      CL80' '             bufferXDEC   DS      CL12                for editSTACK  DSECT                       dynamic areaSAVEXB DS      18F                 " savearea of mergsort (72 bytes)       YREGSRI     EQU     6                   iRJ     EQU     7                   jRK     EQU     8                   kRSTART EQU     6                   istartREND   EQU     7                   iRMIDDL EQU     8                   iRPGI   EQU     3                   pgiRBS    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
```

## ACL2

`(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)))))`

## ActionScript

`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;}`

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

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
```

## Astro

`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`

## AutoHotkey_L

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

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

`DEFPROC_MergeSort(Start%,End%)REM *****************************************************************REM This procedure Merge Sorts the chunk of data% bounded byREM 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   ENDPROCENDIF 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%=0J%=Middle%+1K%=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  ENDIFUNTIL I%=fh_size% OR J%>End% WHILE I% < fh_size%  data%(K%)=fh%(I%)  I%+=1  K%+=1ENDWHILE 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`

## C

`#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
```

## C++

`#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>());}`

## C#

Works with: C# version 3.0+
`namespace Sort {  using System;   public class MergeSort<T> where T : IComparable {    #region Constants    private const Int32 mergesDefault = 6;    private const Int32 insertionLimitDefault = 12;    #endregion     #region Properties    protected Int32[] 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();         if (Positions == null || Positions.Length != merges)          Positions = new Int32[merges];      }    }     public Int32 InsertionLimit { get; set; }    #endregion     #region Constructors    public MergeSort(Int32 merges, Int32 insertionLimit) {      Merges = merges;      InsertionLimit = insertionLimit;    }     public MergeSort()      : this(mergesDefault, insertionLimitDefault) {    }    #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;      else if (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) {      var entry = default(T);      var found = (Int32?)null;      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 index = first + 1; index <= last; index++)        insert(entries, first, index);    }     private static void insert(T[] entries, Int32 first, Int32 index) {      var entry = entries[index];      while (index > first && entries[index - 1].CompareTo(entry) > 0)        entries[index] = entries[--index];      entries[index] = 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`

## Clojure

` (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

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

`# 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

`(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

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 + rtend 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

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 =:= ysintMerge (x:xs) []     zs =  zs =:= x:xsintMerge (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) xssecondhalf xs = drop (length xs `div` 2) xs   goal1 xs = sort intMerge [3,1,2] xsgoal2 xs = sort intMerge [3,1,2,5,4,8] xsgoal3 xs = sort intMerge [3,1,2,5,4,8,6,7,2,9,1,4,3] xs`

## D

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

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

`merge(left, right, items) {  var a = 0;  var t;   while (left.length != 0 && right.length != 0) {    if (right[0] < left[0]) {     t = right[0];     right.removeRange(0,1);    } else {      t = left[0];      left.removeRange(0,1);    }    items[a++] = t;  }   while(left.length != 0) {    t = left[0];    left.removeRange(0,1);    items[a++] = t;  }   while(right.length != 0) {    t = right[0];    right.removeRange(0,1);    items[a++] = t;  }} mSort(items, tmp, l) {  if (l == 1) {    return;  }   var m = (l/2).floor().toInt();  var tmp_l = tmp.getRange(0, m);  var tmp_r = tmp.getRange(m, tmp.length-m);   mSort(tmp_l, items.getRange(0,m), m);  mSort(tmp_r, items.getRange(m, items.length-m), l-m);  merge(tmp_l, tmp_r, items);} merge_sort(items) {  mSort(items,items.getRange(0, items.length),items.length);} void main() {  var arr=[1,5,2,7,3,9,4,6,8];  print("Before sort");  arr.forEach((var i)=>print("\$i"));  merge_sort(arr);  print("After sort");  arr.forEach((var i)=>print("\$i"));}`

## E

`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)))}`

## Eiffel

` 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

`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))  endend`

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

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.

`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

` 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-1END 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  PRINTEND PROGRAM `

## Euphoria

`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 & rightend 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 ifend 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#

`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 tylet rec mergesort list =     match list with        | [] -> []        | [x] -> [x]        | _ -> let (l1,l2) = split list               in merge (mergesort l1) (mergesort l2)`

## Factor

`: mergestep ( accum seq1 seq2 -- accum seq1 seq2 )2dup [ first ] [email protected] <[ [ [ first ] [ rest-slice ] bi [ suffix ] dip ] dip ][ [ first ] [ rest-slice ] bi [ swap [ suffix ] dip ] dip ]if ; : merge ( seq1 seq2 -- merged )[ { } ] 2dip[ 2dup [ length 0 > ] [email protected] and ][ mergestep ] whileappend append ; : mergesort ( seq -- sorted )dup length 1 >[ dup length 2 / floor [ head ] [ tail ] 2bi [ mergesort ] [email protected] merge ][ ] if ;`
`( scratchpad ) { 4 2 6 5 7 1 3 } mergesort .{ 1 2 3 4 5 6 7 }`

## Forth

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

Works with: Fortran version 90 and later
`subroutine Merge(A,NA,B,NB,C,NC)    integer, intent(in) :: NA,NB,NC         ! Normal usage: NA+NB = NC   integer, intent(in out) :: A(NA)        ! B overlays C(NA+1:NC)   integer, intent(in)     :: B(NB)   integer, intent(in out) :: C(NC)    integer :: I,J,K    I = 1; J = 1; K = 1;   do while(I <= NA .and. J <= NB)      if (A(I) <= B(J)) then         C(K) = A(I)         I = I+1      else         C(K) = B(J)         J = J+1      endif      K = K + 1   enddo   do while (I <= NA)      C(K) = A(I)      I = I + 1      K = K + 1   enddo   return end subroutine merge recursive subroutine MergeSort(A,N,T)    integer, intent(in) :: N   integer, dimension(N), intent(in out) :: A   integer, dimension((N+1)/2), intent (out) :: T    integer :: NA,NB,V    if (N < 2) return   if (N == 2) then      if (A(1) > A(2)) then         V = A(1)         A(1) = A(2)         A(2) = V      endif      return   endif         NA=(N+1)/2   NB=N-NA    call MergeSort(A,NA,T)   call MergeSort(A(NA+1),NB,T)    if (A(NA) > A(NA+1)) then      T(1:NA)=A(1:NA)      call Merge(T,NA,A(NA+1),NB,A,N)   endif   return end subroutine MergeSort program TestMergeSort    integer, parameter :: N = 8   integer, dimension(N) :: A = (/ 1, 5, 2, 7, 3, 9, 4, 6 /)   integer, dimension ((N+1)/2) :: T   call MergeSort(A,N,T)   write(*,'(A,/,10I3)')'Sorted array :',A end program TestMergeSort`

## FreeBASIC

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)  NextEnd 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  PrintEnd Sub Dim a(0 To 9) As Integer = {4, 65, 2, -31, 0, 99, 2, 83, 782, 1} Dim b() As IntegerPrint "Unsorted : ";printArray(a())topDownMergeSort a(), b(), 10Print "Sorted   : ";printArray(a())PrintDim a2(0 To 8) As Integer = {7, 5, 2, 6, 1, 4, 2, 6, 3}Erase bPrint "Unsorted : ";printArray(a2())topDownMergeSort a2(), b(), 9Print "Sorted   : ";printArray(a2())PrintPrint "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

`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

`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

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

It is possible to write a version based on tail recursion, similar to that written in Haskel, 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() `

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                   = ysmerge xs         []                   = xsmerge 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 sortedsmergePairs sorteds = sorteds mergeSortBottomUp list = mergeAll (map (\x -> [x]) list) mergeAll [sorted] = sortedmergeAll 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 comparesortBy 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.

## Io

`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)`

## Icon and Unicon

`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 listlocal 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)```

## J

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.

Solution

`merge     =: ,`(({[email protected]] , (\$: }.))~` ({[email protected]] , (\$: }.)) @.(>&{.))@.(*@*&#)split     =: </.~ 0 1\$~#mergeSort =: merge & \$: &>/ @ split ` ] @. (1>:#)`

This version is usable for relative small arrays due to stack limitations for the recursive verb 'merge'. For larger arrays replace 'merge' with the following explicit non-recursive version:

`merge=: 4 : 0 if. 0= x *@*&# y do. x,y return. end. la=.x ra=.y z=.i.0 while. la *@*&# ra do.  if. la  >&{. ra do.     z=.z,{.ra    ra=.}.ra  else.    z=.z,{.la    la=.}.la   end. end. z,la,ra  )`

But don't forget to use J's primitives /: or \: if you really need a sort-function.

## Java

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

`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`

## jq

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

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 rstend 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

`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]```

## Liberty BASIC

`    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 itemCountend '------------------------------------------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, theEndend 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)    nextend sub '===========================================sub printArray itemCount    for i = 1 to itemCount        print using("###", A(i));    next i    printend sub`

## Logo

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 :halfend`

## Logtalk

`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

`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 resend 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

`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

` 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

`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

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

`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 %ifend %mergeSort`

Sample Usage:

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

## Maxima

`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

`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

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] ). `

## Nim

`proc merge[T](a, b: var openarray[T], left, middle, right) =  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) =  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 aecho a`
Output:
`@[-31, 0, 2, 2, 4, 65, 83, 99, 782]`

## OCaml

`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

`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  endin  {Show {MergeSort [3 1 4 1 5 9 2 6 5]}}`

## Nemerle

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

`/* 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
```

## PARI/GP

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

`program MergeSortDemo; type  TIntArray = array of integer; function merge(left, right: TIntArray): TIntArray;  var    i, j: integer;  begin    j := 0;    setlength(merge, length(left) + length(right));    while (length(left) > 0) and (length(right) > 0) do    begin      if left[0] <= right[0] then      begin	merge[j] := left[0];	inc(j);	for i := low(left) to high(left) - 1 do	  left[i] := left[i+1];	setlength(left, length(left) - 1);      end      else      begin	merge[j] := right[0];	inc(j);	for i := low(right) to high(right) - 1 do	  right[i] := right[i+1];	setlength(right, length(right) - 1);      end;    end;    if length(left) > 0 then      for i := low(left) to high(left) do	  merge[j + i] := left[i];    j := j + length(left);    if length(right) > 0 then      for i := low(right) to high(right) do	  merge[j + i] := right[i];  end; function mergeSort(m: TIntArray): TIntArray;  var    left, right: TIntArray;    i, middle: integer;  begin    setlength(mergeSort, length(m));    if length(m) = 1 then      mergeSort[0] := m[0]    else if length(m) > 1 then    begin      middle := length(m) div 2;      setlength(left, middle);      setlength(right, length(m)-middle);      for i := low(left) to high(left) do        left[i] := m[i];      for i := low(right) to high(right) do        right[i] := m[middle+i];      left  := mergeSort(left);      right := mergeSort(right);      mergeSort := merge(left, right);    end;  end; var  data: TIntArray;  i: integer; begin  setlength(data, 8);  Randomize;  writeln('The data before sorting:');  for i := low(data) to high(data) do  begin    data[i] := Random(high(data));    write(data[i]:4);  end;  writeln;  data := mergeSort(data);  writeln('The data after sorting:');  for i := low(data) to high(data) do  begin    write(data[i]:4);  end;  writeln;end.`
Output:
```./MergeSort
The data before sorting:
6   1   2   1   5   2   1   5
The data after sorting:
1   1   1   2   2   5   5   6
```

### improvement

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 timingtype  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 codebegin  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

`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.

## 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```

## Phix

Copy of Euphoria

`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 & rightend function function mergesort(sequence m)sequence left, rightinteger middle    if length(m)<=1 then        return m    end if    middle = floor(length(m)/2)    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(s) `
Output:
```{8,1,2,5,10,3,9,6,7,4}
{1,2,3,4,5,6,7,8,9,10}
```

## PHP

`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`

## PicoLisp

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

`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

` 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

`% msort( L, S )% True if S is a sorted copy of L, using merge sortmsort( [], [] ).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 Rsplit( [], [], [] ).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 twomerge( [], 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

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())  EndIfEndProcedure 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

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`

## R

`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

` #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))])])])) `

## REBOL

```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

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

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

`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 + rightend 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  endend 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

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

The use of Stream 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.

Works with: Scala version 2.8
`def mergeSort(input: List[Int]) = {  def merge(left: List[Int], right: List[Int]): Stream[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.toStream else left.toStream  }  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)}`
Works with: Scala version 2.7

Replace the first two lines of `merge` by the following:

`    case (x :: xs, y :: ys) if x < y => Stream.cons(x, merge(xs, right))    case (x :: xs, y :: ys) => Stream.cons(y, merge(left, ys))`

I suppose I should have written this version to begin with, but I think the 2.8 version is more clear.

## Scheme

`(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

`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

`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 sortvar nums = rand(1..100, 10)say mergesort(nums) # String sortvar strings = rand('a'..'z', 10)say mergesort(strings)`

## Standard ML

`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

`// 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)}`

## Tcl

`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.

## UnixPipes

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

`#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

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
```

## XPL0

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 Highint  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 halfMergeSort(A, Mid+1, High);      \sort right half\Merge the two halves in to sorted orderB:= 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
```

## ZED

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

This is a bottom up version of merge sort:

`(append) list1 list2comment:#true(003) "append" list1 list2 (car) paircomment:#true(002) "car" pair (cdr) paircomment:#true(002) "cdr" pair (cons) one twocomment:#true(003) "cons" one two (map) function listcomment:#true(003) "map" function list (merge) comparator list1 list2comment:#true(merge1) comparator list1 list2 nil (merge1) comparator list1 list2 collectcomment:(null?) list2(append) (reverse) collect list1 (merge1) comparator list1 list2 collectcomment:(null?) list1(append) (reverse) collect list2 (merge1) comparator list1 list2 collectcomment:(003) comparator (car) list2 (car) list1(merge1) comparator list1 (cdr) list2 (cons) (car) list2 collect (merge1) comparator list1 list2 collectcomment:#true(merge1) comparator (cdr) list1 list2 (cons) (car) list1 collect (null?) valuecomment:#true(002) "null?" value (reverse) listcomment:#true(002) "reverse" list (sort) comparator jumblecomment:#true(car) (sort11) comparator (sort1) jumble (sort1) jumblecomment:#true(map) "list" jumble (sort11) comparator jumblecomment:(null?) jumblenil (sort11) comparator jumblecomment:(null?) (cdr) jumblejumble (sort11) comparator jumblecomment:#true(sort11) comparator         (cons) (merge) comparator (car) jumble (002) "cadr" jumble                (sort11) comparator (002) "cddr" jumble`

## zkl

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
```