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Sorting algorithms/Merge sort

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

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

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

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

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

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


Task

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


The merge sort algorithm comes in two parts:

   a sort function     and 
   a merge function 

The functions in pseudocode look like this:

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

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


See also


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

360 Assembly[edit]

Translation of: BBC BASIC

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

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

AArch64 Assembly[edit]

Works with: as version Raspberry Pi 3B version Buster 64 bits
 
/* ARM assembly AARCH64 Raspberry PI 3B */
/* program mergeSort64.s */
 
/*******************************************/
/* Constantes file */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeConstantesARM64.inc"
 
/*********************************/
/* Initialized data */
/*********************************/
.data
szMessSortOk: .asciz "Table sorted.\n"
szMessSortNok: .asciz "Table not sorted !!!!!.\n"
sMessResult: .asciz "Value  : @ \n"
szCarriageReturn: .asciz "\n"
 
.align 4
TableNumber: .quad 1,3,11,6,2,5,9,10,8,4,7
#TableNumber: .quad 10,9,8,7,6,-5,4,3,2,1
.equ NBELEMENTS, (. - TableNumber) / 8
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
sZoneConv: .skip 24
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: // entry of program
ldr x0,qAdrTableNumber // address number table
mov x1,0 // first element
mov x2,NBELEMENTS // number of élements
bl mergeSort
ldr x0,qAdrTableNumber // address number table
bl displayTable
 
ldr x0,qAdrTableNumber // address number table
mov x1,NBELEMENTS // number of élements
bl isSorted // control sort
cmp x0,1 // sorted ?
beq 1f
ldr x0,qAdrszMessSortNok // no !! error sort
bl affichageMess
b 100f
1: // yes
ldr x0,qAdrszMessSortOk
bl affichageMess
100: // standard end of the program
mov x0,0 // return code
mov x8,EXIT // request to exit program
svc 0 // perform the system call
 
qAdrsZoneConv: .quad sZoneConv
qAdrszCarriageReturn: .quad szCarriageReturn
qAdrsMessResult: .quad sMessResult
qAdrTableNumber: .quad TableNumber
qAdrszMessSortOk: .quad szMessSortOk
qAdrszMessSortNok: .quad szMessSortNok
/******************************************************************/
/* control sorted table */
/******************************************************************/
/* x0 contains the address of table */
/* x1 contains the number of elements > 0 */
/* x0 return 0 if not sorted 1 if sorted */
isSorted:
stp x2,lr,[sp,-16]! // save registers
stp x3,x4,[sp,-16]! // save registers
mov x2,0
ldr x4,[x0,x2,lsl 3]
1:
add x2,x2,1
cmp x2,x1
bge 99f
ldr x3,[x0,x2, lsl 3]
cmp x3,x4
blt 98f
mov x4,x3
b 1b
98:
mov x0,0 // not sorted
b 100f
99:
mov x0,1 // sorted
100:
ldp x3,x4,[sp],16 // restaur 2 registers
ldp x2,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* merge */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains first start index
/* r2 contains second start index */
/* r3 contains the last index */
merge:
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
stp x4,x5,[sp,-16]! // save registers
stp x6,x7,[sp,-16]! // save registers
str x8,[sp,-16]!
mov x5,x2 // init index x2->x5
1: // begin loop first section
ldr x6,[x0,x1,lsl 3] // load value first section index r1
ldr x7,[x0,x5,lsl 3] // load value second section index r5
cmp x6,x7
ble 4f // <= -> location first section OK
str x7,[x0,x1,lsl 3] // store value second section in first section
add x8,x5,1
cmp x8,x3 // end second section ?
ble 2f
str x6,[x0,x5,lsl 3]
b 4f // loop
2: // loop insert element part 1 into part 2
sub x4,x8,1
ldr x7,[x0,x8,lsl 3] // load value 2
cmp x6,x7 // value <
bge 3f
str x6,[x0,x4,lsl 3] // store value
b 4f // loop
3:
str x7,[x0,x4,lsl 3] // store value 2
add x8,x8,1
cmp x8,x3 // end second section ?
ble 2b // no loop
sub x8,x8,1
str x6,[x0,x8,lsl 3] // store value 1
4:
add x1,x1,1
cmp x1,x2 // end first section ?
blt 1b
 
100:
ldr x8,[sp],16 // restaur 1 register
ldp x6,x7,[sp],16 // restaur 2 registers
ldp x4,x5,[sp],16 // restaur 2 registers
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* merge sort */
/******************************************************************/
/* x0 contains the address of table */
/* x1 contains the index of first element */
/* x2 contains the number of element */
mergeSort:
stp x3,lr,[sp,-16]! // save registers
stp x4,x5,[sp,-16]! // save registers
stp x6,x7,[sp,-16]! // save registers
cmp x2,2 // end ?
blt 100f
lsr x4,x2,1 // number of element of each subset
add x5,x4,1
tst x2,#1 // odd ?
csel x4,x5,x4,ne
mov x5,x1 // save first element
mov x6,x2 // save number of element
mov x7,x4 // save number of element of each subset
mov x2,x4
bl mergeSort
mov x1,x7 // restaur number of element of each subset
mov x2,x6 // restaur number of element
sub x2,x2,x1
mov x3,x5 // restaur first element
add x1,x1,x3 // + 1
bl mergeSort // sort first subset
mov x1,x5 // restaur first element
mov x2,x7 // restaur number of element of each subset
add x2,x2,x1
mov x3,x6 // restaur number of element
add x3,x3,x1
sub x3,x3,1 // last index
bl merge
100:
ldp x6,x7,[sp],16 // restaur 2 registers
ldp x4,x5,[sp],16 // restaur 2 registers
ldp x3,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
 
/******************************************************************/
/* Display table elements */
/******************************************************************/
/* x0 contains the address of table */
displayTable:
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
mov x2,x0 // table address
mov x3,0
1: // loop display table
ldr x0,[x2,x3,lsl 3]
ldr x1,qAdrsZoneConv
bl conversion10S // décimal conversion
ldr x0,qAdrsMessResult
ldr x1,qAdrsZoneConv
bl strInsertAtCharInc // insert result at // character
bl affichageMess // display message
add x3,x3,1
cmp x3,NBELEMENTS - 1
ble 1b
ldr x0,qAdrszCarriageReturn
bl affichageMess
mov x0,x2
100:
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/********************************************************/
/* File Include fonctions */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"
 

ACL2[edit]

(defun split (xys)
(if (endp (rest xys))
(mv xys nil)
(mv-let (xs ys)
(split (rest (rest xys)))
(mv (cons (first xys) xs)
(cons (second xys) ys)))))
 
(defun mrg (xs ys)
(declare (xargs :measure (+ (len xs) (len ys))))
(cond ((endp xs) ys)
((endp ys) xs)
((< (first xs) (first ys))
(cons (first xs) (mrg (rest xs) ys)))
(t (cons (first ys) (mrg xs (rest ys))))))
 
(defthm split-shortens
(implies (consp (rest xs))
(mv-let (ys zs)
(split xs)
(and (< (len ys) (len xs))
(< (len zs) (len xs))))))
 
(defun msort (xs)
(declare (xargs
:measure (len xs)
:hints (("Goal"
:use ((:instance split-shortens))))))
(if (endp (rest xs))
xs
(mv-let (ys zs)
(split xs)
(mrg (msort ys)
(msort zs)))))

ActionScript[edit]

function mergesort(a:Array)
{
//Arrays of length 1 and 0 are always sorted
if(a.length <= 1) return a;
else
{
var middle:uint = a.length/2;
//split the array into two
var left:Array = new Array(middle);
var right:Array = new Array(a.length-middle);
var j:uint = 0, k:uint = 0;
//fill the left array
for(var i:uint = 0; i < middle; i++)
left[j++]=a[i];
//fill the right array
for(i = middle; i< a.length; i++)
right[k++]=a[i];
//sort the arrays
left = mergesort(left);
right = mergesort(right);
//If the last element of the left array is less than or equal to the first
//element of the right array, they are in order and don't need to be merged
if(left[left.length-1] <= right[0])
return left.concat(right);
a = merge(left, right);
return a;
}
}
 
function merge(left:Array, right:Array)
{
var result:Array = new Array(left.length + right.length);
var j:uint = 0, k:uint = 0, m:uint = 0;
//merge the arrays in order
while(j < left.length && k < right.length)
{
if(left[j] <= right[k])
result[m++] = left[j++];
else
result[m++] = right[k++];
}
//If one of the arrays has remaining entries that haven't been merged, they
//will be greater than the rest of the numbers merged so far, so put them on the
//end of the array.
for(; j < left.length; j++)
result[m++] = left[j];
for(; k < right.length; k++)
result[m++] = right[k];
return result;
}

Ada[edit]

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

generic
type Element_Type is private;
type Index_Type is (<>);
type Collection_Type is array(Index_Type range <>) of Element_Type;
with function "<"(Left, Right : Element_Type) return Boolean is <>;
 
package Mergesort is
function Sort(Item : Collection_Type) return Collection_Type;
end MergeSort;
package body Mergesort is
 
-----------
-- Merge --
-----------
 
function Merge(Left, Right : Collection_Type) return Collection_Type is
Result : Collection_Type(Left'First..Right'Last);
Left_Index : Index_Type := Left'First;
Right_Index : Index_Type := Right'First;
Result_Index : Index_Type := Result'First;
begin
while Left_Index <= Left'Last and Right_Index <= Right'Last loop
if Left(Left_Index) <= Right(Right_Index) then
Result(Result_Index) := Left(Left_Index);
Left_Index := Index_Type'Succ(Left_Index); -- increment Left_Index
else
Result(Result_Index) := Right(Right_Index);
Right_Index := Index_Type'Succ(Right_Index); -- increment Right_Index
end if;
Result_Index := Index_Type'Succ(Result_Index); -- increment Result_Index
end loop;
if Left_Index <= Left'Last then
Result(Result_Index..Result'Last) := Left(Left_Index..Left'Last);
end if;
if Right_Index <= Right'Last then
Result(Result_Index..Result'Last) := Right(Right_Index..Right'Last);
end if;
return Result;
end Merge;
 
----------
-- Sort --
----------
 
function Sort (Item : Collection_Type) return Collection_Type is
Result : Collection_Type(Item'range);
Middle : Index_Type;
begin
if Item'Length <= 1 then
return Item;
else
Middle := Index_Type'Val((Item'Length / 2) + Index_Type'Pos(Item'First));
declare
Left : Collection_Type(Item'First..Index_Type'Pred(Middle));
Right : Collection_Type(Middle..Item'Last);
begin
for I in Left'range loop
Left(I) := Item(I);
end loop;
for I in Right'range loop
Right(I) := Item(I);
end loop;
Left := Sort(Left);
Right := Sort(Right);
Result := Merge(Left, Right);
end;
return Result;
end if;
end Sort;
 
end Mergesort;

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

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

ALGOL 68[edit]

Translation of: python

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

MODE DATA = CHAR;
 
PROC merge sort = ([]DATA m)[]DATA: (
IF LWB m >= UPB m THEN
m
ELSE
INT middle = ( UPB m + LWB m ) OVER 2;
[]DATA left = merge sort(m[:middle]);
[]DATA right = merge sort(m[middle+1:]);
flex merge(left, right)[AT LWB m]
FI
);
 
# FLEX version: A demonstration of FLEX for manipulating arrays #
PROC flex merge = ([]DATA in left, in right)[]DATA:(
[UPB in left + UPB in right]DATA result;
FLEX[0]DATA left := in left;
FLEX[0]DATA right := in right;
 
FOR index TO UPB result DO
# change the direction of this comparison to change the direction of the sort #
IF LWB right > UPB right THEN
result[index:] := left;
stop iteration
ELIF LWB left > UPB left THEN
result[index:] := right;
stop iteration
ELIF left[1] <= right[1] THEN
result[index] := left[1];
left := left[2:]
ELSE
result[index] := right[1];
right := right[2:]
FI
OD;
stop iteration:
result
);
 
[32]CHAR char array data := "big fjords vex quick waltz nymph";
print((merge sort(char array data), new line));
Output:
     abcdefghiijklmnopqrstuvwxyz

Optimised version:

  1. avoids FLEX array copies and manipulations
  2. avoids type DATA memory copies, useful in cases where DATA is a large STRUCT
PROC opt merge sort = ([]REF DATA m)[]REF DATA: (
IF LWB m >= UPB m THEN
m
ELSE
INT middle = ( UPB m + LWB m ) OVER 2;
[]REF DATA left = opt merge sort(m[:middle]);
[]REF DATA right = opt merge sort(m[middle+1:]);
opt merge(left, right)[AT LWB m]
FI
);
 
PROC opt merge = ([]REF DATA left, right)[]REF DATA:(
[UPB left - LWB left + 1 + UPB right - LWB right + 1]REF DATA result;
INT index left:=LWB left, index right:=LWB right;
 
FOR index TO UPB result DO
# change the direction of this comparison to change the direction of the sort #
IF index right > UPB right THEN
result[index:] := left[index left:];
stop iteration
ELIF index left > UPB left THEN
result[index:] := right[index right:];
stop iteration
ELIF left[index left] <= right[index right] THEN
result[index] := left[index left]; index left +:= 1
ELSE
result[index] := right[index right]; index right +:= 1
FI
OD;
stop iteration:
result
);
 
# create an array of pointers to the data being sorted #
[UPB char array data]REF DATA data; FOR i TO UPB char array data DO data[i] := char array data[i] OD;
 
[]REF CHAR result = opt merge sort(data);
FOR i TO UPB result DO print((result[i])) OD; print(new line)
Output:
     abcdefghiijklmnopqrstuvwxyz

AppleScript[edit]

This is an iterative implementation in which the entire sort range is swept multiple times with the partition size doubling on each pass. Only one additional list is required throughout the entire sort and the two lists swap source and destination roles at the end of each pass. The process is "in place" in that it's the original list object passed to the handler which ends up sorted.

(*
In-place, iterative binary merge sort
Merge sort algorithm: John von Neumann, 1945.
 
Terminology used here:
list: a list (array) object.
range: the range specified to be sorted in the list.
partition: one of two subranges being merged.
block: the subrange covering the two partitions being merged.
*)

on mergeSort(theList, l, r) -- Sort items l thru r of theList.
-- Script object to hold the main (original) list and the sort range indices.
script main
property l : missing value
property r : missing value
property lst : theList
end script
-- Script object to hold the auxiliary list and its start and end indices.
script aux
property l : missing value
property r : missing value
property lst : missing value
end script
 
set listLength to (count theList)
if (listLength < 2) then return
-- Convert negative and/or transposed range indices.
if (l < 0) then set l to listLength + l + 1
if (r < 0) then set r to listLength + r + 1
if (l > r) then set {l, r} to {r, l}
 
-- Do the sort.
-- As a minor optimisation, this first pass over the sort range simply arranges pairs of adjacent items in the main list.
-- Better still would be a series of short insertion sorts to create larger initial partitions.
repeat with j from (l + 1) to r by 2
set i to j - 1
set leftValue to item i of main's lst
set rightValue to item j of main's lst
if (rightValue < leftValue) then
set item i of main's lst to rightValue
set item j of main's lst to leftValue
end if
end repeat
 
set rangeLength to r - l + 1
if (rangeLength < 3) then return -- The sort's complete if there are less than three items in the sort range.
 
-- Set the script objects' range index properties.
set main's l to l
set main's r to r
set aux's l to 1
set aux's r to rangeLength
-- Set an auxiliary list containing just the items in the sort range (as ordered so far).
set aux's lst to items l thru r of main's lst
 
-- Work out how many more passes are needed.
set passesRequired to 0
set blockLength to 2
repeat while (blockLength < rangeLength)
set passesRequired to passesRequired + 1
set blockLength to blockLength + blockLength
end repeat
-- Set the initial source and destination objects so that the final pass will merge back to the original list.
set {srce, dest} to item (passesRequired mod 2 + 1) of {{main, aux}, {aux, main}}
 
-- Do the remaining passes.
set blockLength to 2
repeat passesRequired times
-- Set the partition and block lengths for this pass and initialise the destination traversal index.
set partitionLength to blockLength
set blockLength to partitionLength + partitionLength
set k to (dest's l) - 1
 
-- Merge each two-partition block in the source range into the equivalent block in the destination list.
-- The last block in the range will usually be truncated at the range boundary.
repeat with leftStart from srce's l to srce's r by blockLength
set kEnd to k + blockLength -- Destination block end index.
if (kEnd comes after dest's r) then set kEnd to dest's r
set i to leftStart -- Left partition traversal index.
set leftEnd to leftStart + partitionLength - 1 -- Left partition end index.
 
-- If enough source items remain for more than one partition, set up the right partition and merge.
if (leftEnd comes before srce's r) then
set j to leftEnd + 1 -- Right partition traversal index.
set rightEnd to leftEnd + partitionLength -- Right partition end index.
if (rightEnd comes after srce's r) then set rightEnd to srce's r
 
-- The merge process:
set leftValue to item i of srce's lst
set rightValue to item j of srce's lst
repeat with k from (k + 1) to kEnd
if (rightValue < leftValue) then
set item k of dest's lst to rightValue
if (j = rightEnd) then exit repeat
set j to j + 1
set rightValue to item j of srce's lst
else
set item k of dest's lst to leftValue
if (i = leftEnd) then
set i to j -- For the copy-over repeat below.
exit repeat
end if
set i to i + 1
set leftValue to item i of srce's lst
end if
end repeat
end if
 
-- Copy remaining items straight over.
repeat with k from (k + 1) to kEnd
set item k of dest's lst to item i of srce's lst
set i to i + 1
end repeat
end repeat
 
-- Swap the source and destination roles for the next pass.
tell srce
set srce to dest
set dest to it
end tell
end repeat
 
return -- nothing
end mergeSort
 
-- Test:
set aList to {}
repeat with i from 1 to 25
set end of aList to (random number 100)
end repeat
 
-- Sort items 1 thru -1 of a copy.
set sortedCopy to aList's items
mergeSort(sortedCopy, 1, -1)
 
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to ", "
set output to "Original: {" & aList & "}
Sorted: {"
& sortedCopy & "}"
set AppleScript's text item delimiters to astid
 
return output
Output:
"Original: {25, 2, 8, 81, 94, 91, 63, 27, 79, 47, 29, 98, 46, 20, 74, 1, 52, 14, 68, 27, 76, 8, 91, 47, 69}
Sorted: {1, 2, 8, 8, 14, 20, 25, 27, 27, 29, 46, 47, 47, 52, 63, 68, 69, 74, 76, 79, 81, 91, 91, 94, 98}"

ARM Assembly[edit]

Works with: as version Raspberry Pi
 
/* ARM assembly Raspberry PI */
/* program mergeSort.s */
 
/* REMARK 1 : this program use routines in a include file
see task Include a file language arm assembly
for the routine affichageMess conversion10
see at end of this program the instruction include */
/* for constantes see task include a file in arm assembly */
/************************************/
/* Constantes */
/************************************/
.include "../constantes.inc"
 
/*********************************/
/* Initialized data */
/*********************************/
.data
szMessSortOk: .asciz "Table sorted.\n"
szMessSortNok: .asciz "Table not sorted !!!!!.\n"
sMessResult: .asciz "Value  : @ \n"
szCarriageReturn: .asciz "\n"
 
.align 4
#TableNumber: .int 1,11,3,6,2,5,9,10,8,4,7
TableNumber: .int 10,9,8,7,6,5,4,3,2,1
.equ NBELEMENTS, (. - TableNumber) / 4
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
sZoneConv: .skip 24
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: @ entry of program
 
ldr r0,iAdrTableNumber @ address number table
mov r1,#0 @ first element
mov r2,#NBELEMENTS @ number of élements
bl mergeSort
ldr r0,iAdrTableNumber @ address number table
bl displayTable
 
ldr r0,iAdrTableNumber @ address number table
mov r1,#NBELEMENTS @ number of élements
bl isSorted @ control sort
cmp r0,#1 @ sorted ?
beq 1f
ldr r0,iAdrszMessSortNok @ no !! error sort
bl affichageMess
b 100f
1: @ yes
ldr r0,iAdrszMessSortOk
bl affichageMess
100: @ standard end of the program
mov r0, #0 @ return code
mov r7, #EXIT @ request to exit program
svc #0 @ perform the system call
 
iAdrszCarriageReturn: .int szCarriageReturn
iAdrsMessResult: .int sMessResult
iAdrTableNumber: .int TableNumber
iAdrszMessSortOk: .int szMessSortOk
iAdrszMessSortNok: .int szMessSortNok
/******************************************************************/
/* control sorted table */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the number of elements > 0 */
/* r0 return 0 if not sorted 1 if sorted */
isSorted:
push {r2-r4,lr} @ save registers
mov r2,#0
ldr r4,[r0,r2,lsl #2]
1:
add r2,#1
cmp r2,r1
movge r0,#1
bge 100f
ldr r3,[r0,r2, lsl #2]
cmp r3,r4
movlt r0,#0
blt 100f
mov r4,r3
b 1b
100:
pop {r2-r4,lr}
bx lr @ return
 
/******************************************************************/
/* merge */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains first start index
/* r2 contains second start index */
/* r3 contains the last index */
merge:
push {r1-r8,lr} @ save registers
mov r5,r2 @ init index r2->r5
1: @ begin loop first section
ldr r6,[r0,r1,lsl #2] @ load value first section index r1
ldr r7,[r0,r5,lsl #2] @ load value second section index r5
cmp r6,r7
ble 3f @ <= -> location first section OK
str r7,[r0,r1,lsl #2] @ store value second section in first section
add r8,r5,#1
cmp r8,r3 @ end second section ?
strgt r6,[r0,r5,lsl #2]
bgt 3f @ loop
2: @ loop insert element part 1 into part 2
sub r4,r8,#1
ldr r7,[r0,r8,lsl #2] @ load value 2
cmp r6,r7 @ value <
strlt r6,[r0,r4,lsl #2] @ store value
blt 3f
str r7,[r0,r4,lsl #2] @ store value 2
add r8,#1
cmp r8,r3 @ end second section ?
ble 2b @ no loop
sub r8,#1
str r6,[r0,r8,lsl #2] @ store value 1
3:
add r1,#1
cmp r1,r2 @ end first section ?
blt 1b
 
100:
pop {r1-r8,lr}
bx lr @ return
/******************************************************************/
/* merge sort */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the index of first element */
/* r2 contains the number of element */
mergeSort:
push {r3-r7,lr} @ save registers
cmp r2,#2
blt 100f
lsr r4,r2,#1 @ number of element of each subset
tst r2,#1
addne r4,#1
mov r5,r1 @ save first element
mov r6,r2 @ save number of element
mov r7,r4 @ save number of element of each subset
mov r2,r4
bl mergeSort
mov r1,r7 @ restaur number of element of each subset
mov r2,r6 @ restaur number of element
sub r2,r1
mov r3,r5 @ restaur first element
add r1,r3 @ + 1
bl mergeSort @ sort first subset
mov r1,r5 @ restaur first element
mov r2,r7 @ restaur number of element of each subset
add r2,r1
mov r3,r6 @ restaur number of element
add r3,r1
sub r3,#1 @ last index
bl merge
100:
pop {r3-r7,lr}
bx lr @ return
 
/******************************************************************/
/* Display table elements */
/******************************************************************/
/* r0 contains the address of table */
displayTable:
push {r0-r3,lr} @ save registers
mov r2,r0 @ table address
mov r3,#0
1: @ loop display table
ldr r0,[r2,r3,lsl #2]
ldr r1,iAdrsZoneConv @
bl conversion10S @ décimal conversion
ldr r0,iAdrsMessResult
ldr r1,iAdrsZoneConv @ insert conversion
bl strInsertAtCharInc
bl affichageMess @ display message
add r3,#1
cmp r3,#NBELEMENTS - 1
ble 1b
ldr r0,iAdrszCarriageReturn
bl affichageMess
mov r0,r2
100:
pop {r0-r3,lr}
bx lr
iAdrsZoneConv: .int sZoneConv
/***************************************************/
/* ROUTINES INCLUDE */
/***************************************************/
.include "../affichage.inc"
 

Astro[edit]

fun mergesort(m):
if m.lenght <= 1: return m
let middle = floor m.lenght / 2
let left = merge(m[:middle])
let right = merge(m[middle-1:]);
 
fun merge(left, right):
let result = []
while not (left.isempty or right.isempty):
if left[1] <= right[1]:
result.push! left.shift!()
else:
result.push! right.shift!()
result.push! left.push! right
 
let arr = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0]
print mergesort arr

AutoHotkey_L[edit]

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

#NoEnv
 
Test := []
Loop 100 {
Random n, 0, 999
Test.Insert(n)
}
Result := MergeSort(Test)
Loop % Result.MaxIndex() {
MsgBox, 1, , % Result[A_Index]
IfMsgBox Cancel
Break
}
Return
 
 
/*
Function MergeSort
Sorts an array by first recursively splitting it down to its
individual elements and then merging those elements in their
correct order.
 
Parameters
Array The array to be sorted
 
Returns
The sorted array
*/

MergeSort(Array)
{
; Return single element arrays
If (! Array.HasKey(2))
Return Array
 
; Split array into Left and Right halfs
Left := [], Right := [], Middle := Array.MaxIndex() // 2
Loop % Middle
Right.Insert(Array.Remove(Middle-- + 1)), Left.Insert(Array.Remove(1))
If (Array.MaxIndex())
Right.Insert(Array.Remove(1))
 
Left := MergeSort(Left), Right := MergeSort(Right)
 
; If all the Right values are greater than all the
; Left values, just append Right at the end of Left.
If (Left[Left.MaxIndex()] <= Right[1]) {
Loop % Right.MaxIndex()
Left.Insert(Right.Remove(1))
Return Left
}
; Loop until one of the arrays is empty
While(Left.MaxIndex() and Right.MaxIndex())
Left[1] <= Right[1] ? Array.Insert(Left.Remove(1))
 : Array.Insert(Right.Remove(1))
 
Loop % Left.MaxIndex()
Array.Insert(Left.Remove(1))
 
Loop % Right.MaxIndex()
Array.Insert(Right.Remove(1))
 
Return Array
}

AutoHotkey[edit]

Contributed by Laszlo on the ahk forum

MsgBox % MSort("")
MsgBox % MSort("xxx")
MsgBox % MSort("3,2,1")
MsgBox % MSort("dog,000000,cat,pile,abcde,1,zz,xx,z")
 
MSort(x) { ; Merge-sort of a comma separated list
If (2 > L:=Len(x))
Return x ; empty or single item lists are sorted
StringGetPos p, x, `,, % "L" L//2 ; Find middle comma
Return Merge(MSort(SubStr(x,1,p)), MSort(SubStr(x,p+2))) ; Split, Sort, Merge
}
 
Len(list) {
StringReplace t, list,`,,,UseErrorLevel ; #commas -> ErrorLevel
Return list="" ? 0 : ErrorLevel+1
}
 
Item(list,ByRef p) { ; item at position p, p <- next position
Return (p := InStr(list,",",0,i:=p+1)) ? SubStr(list,i,p-i) : SubStr(list,i)
}
 
Merge(list0,list1) { ; Merge 2 sorted lists
IfEqual list0,, Return list1
IfEqual list1,, Return list0
i0 := Item(list0,p0:=0)
i1 := Item(list1,p1:=0)
Loop {
i := i0>i1
list .= "," i%i% ; output smaller
If (p%i%)
i%i% := Item(list%i%,p%i%) ; get next item from processed list
Else {
i ^= 1 ; list is exhausted: attach rest of other
Return SubStr(list "," i%i% (p%i% ? "," SubStr(list%i%,p%i%+1) : ""), 2)
}
}
}

BBC BASIC[edit]

DEFPROC_MergeSort(Start%,End%)
REM *****************************************************************
REM This procedure Merge Sorts the chunk of data% bounded by
REM Start% & End%.
REM *****************************************************************
 
LOCAL Middle%
IF End%=Start% ENDPROC
 
IF End%-Start%=1 THEN
IF data%(End%)<data%(Start%) THEN
SWAP data%(Start%),data%(End%)
ENDIF
ENDPROC
ENDIF
 
Middle%=Start%+(End%-Start%)/2
 
PROC_MergeSort(Start%,Middle%)
PROC_MergeSort(Middle%+1,End%)
PROC_Merge(Start%,Middle%,End%)
 
ENDPROC
:
DEF PROC_Merge(Start%,Middle%,End%)
 
LOCAL fh_size%
fh_size% = Middle%-Start%+1
 
FOR I%=0 TO fh_size%-1
fh%(I%)=data%(Start%+I%)
NEXT I%
 
I%=0
J%=Middle%+1
K%=Start%
 
REPEAT
IF fh%(I%) <= data%(J%) THEN
data%(K%)=fh%(I%)
I%+=1
K%+=1
ELSE
data%(K%)=data%(J%)
J%+=1
K%+=1
ENDIF
UNTIL I%=fh_size% OR J%>End%
 
WHILE I% < fh_size%
data%(K%)=fh%(I%)
I%+=1
K%+=1
ENDWHILE
 
ENDPROC

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

REM Example of merge sort usage.
Size%=1000
 
S1%=Size%/2
 
DIM data%(Size%)
DIM fh%(S1%)
 
FOR I%=1 TO Size%
data%(I%)=RND(100000)
NEXT
 
PROC_MergeSort(1,Size%)
 
END

C[edit]

#include <stdio.h>
#include <stdlib.h>
 
void merge (int *a, int n, int m) {
int i, j, k;
int *x = malloc(n * sizeof (int));
for (i = 0, j = m, k = 0; k < n; k++) {
x[k] = j == n ? a[i++]
: i == m ? a[j++]
: a[j] < a[i] ? a[j++]
: a[i++];
}
for (i = 0; i < n; i++) {
a[i] = x[i];
}
free(x);
}
 
void merge_sort (int *a, int n) {
if (n < 2)
return;
int m = n / 2;
merge_sort(a, m);
merge_sort(a + m, n - m);
merge(a, n, m);
}
 
int main () {
int a[] = {4, 65, 2, -31, 0, 99, 2, 83, 782, 1};
int n = sizeof a / sizeof a[0];
int i;
for (i = 0; i < n; i++)
printf("%d%s", a[i], i == n - 1 ? "\n" : " ");
merge_sort(a, n);
for (i = 0; i < n; i++)
printf("%d%s", a[i], i == n - 1 ? "\n" : " ");
return 0;
}
Output:
4 65 2 -31 0 99 2 83 782 1
-31 0 1 2 2 4 65 83 99 782

C#[edit]

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

C++[edit]

#include <iterator>
#include <algorithm> // for std::inplace_merge
#include <functional> // for std::less
 
template<typename RandomAccessIterator, typename Order>
void mergesort(RandomAccessIterator first, RandomAccessIterator last, Order order)
{
if (last - first > 1)
{
RandomAccessIterator middle = first + (last - first) / 2;
mergesort(first, middle, order);
mergesort(middle, last, order);
std::inplace_merge(first, middle, last, order);
}
}
 
template<typename RandomAccessIterator>
void mergesort(RandomAccessIterator first, RandomAccessIterator last)
{
mergesort(first, last, std::less<typename std::iterator_traits<RandomAccessIterator>::value_type>());
}

Clojure[edit]

Translation of: Haskell
 
(defn merge [left right]
(cond (nil? left) right
(nil? right) left
:else (let [[l & *left] left
[r & *right] right]
(if (<= l r) (cons l (merge *left right))
(cons r (merge left *right))))))
 
(defn merge-sort [list]
(if (< (count list) 2)
list
(let [[left right] (split-at (/ (count list) 2) list)]
(merge (merge-sort left) (merge-sort right)))))
 

COBOL[edit]

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

       IDENTIFICATION DIVISION.
PROGRAM-ID. MERGESORT.
AUTHOR. DAVE STRATFORD.
DATE-WRITTEN. APRIL 2010.
INSTALLATION. HEXAGON SYSTEMS LIMITED.
******************************************************************
* MERGE SORT *
* The Merge sort uses a completely different paradigm, one of *
* divide and conquer, to many of the other sorts. The data set *
* is split into smaller sub sets upon which are sorted and then *
* merged together to form the final sorted data set. *
* This version uses the recursive method. Split the data set in *
* half and perform a merge sort on each half. This in turn splits*
* each half again and again until each set is just one or 2 items*
* long. A set of one item is already sorted so is ignored, a set *
* of two is compared and swapped as necessary. The smaller data *
* sets are then repeatedly merged together to eventually form the*
* full, sorted, set. *
* Since cobol cannot do recursion this module only simulates it *
* so is not as fast as a normal recursive version would be. *
* Scales very well to larger data sets, its relative complexity *
* means it is not suited to sorting smaller data sets: use an *
* Insertion sort instead as the Merge sort is a stable sort. *
******************************************************************
 
ENVIRONMENT DIVISION.
CONFIGURATION SECTION.
SOURCE-COMPUTER. ICL VME.
OBJECT-COMPUTER. ICL VME.
 
INPUT-OUTPUT SECTION.
FILE-CONTROL.
SELECT FA-INPUT-FILE ASSIGN FL01.
SELECT FB-OUTPUT-FILE ASSIGN FL02.
 
DATA DIVISION.
FILE SECTION.
FD FA-INPUT-FILE.
01 FA-INPUT-REC.
03 FA-DATA PIC 9(6).
 
FD FB-OUTPUT-FILE.
01 FB-OUTPUT-REC PIC 9(6).
 
WORKING-STORAGE SECTION.
01 WA-IDENTITY.
03 WA-PROGNAME PIC X(10) VALUE "MERGESORT".
03 WA-VERSION PIC X(6) VALUE "000001".
 
01 WB-TABLE.
03 WB-ENTRY PIC 9(8) COMP SYNC OCCURS 100000
INDEXED BY WB-IX-1
WB-IX-2.
 
01 WC-VARS.
03 WC-SIZE PIC S9(8) COMP SYNC.
03 WC-TEMP PIC S9(8) COMP SYNC.
03 WC-START PIC S9(8) COMP SYNC.
03 WC-MIDDLE PIC S9(8) COMP SYNC.
03 WC-END PIC S9(8) COMP SYNC.
 
01 WD-FIRST-HALF.
03 WD-FH-MAX PIC S9(8) COMP SYNC.
03 WD-ENTRY PIC 9(8) COMP SYNC OCCURS 50000
INDEXED BY WD-IX.
 
01 WF-CONDITION-FLAGS.
03 WF-EOF-FLAG PIC X.
88 END-OF-FILE VALUE "Y".
03 WF-EMPTY-FILE-FLAG PIC X.
88 EMPTY-FILE VALUE "Y".
 
01 WS-STACK.
* This stack is big enough to sort a list of 1million items.
03 WS-STACK-ENTRY OCCURS 20 INDEXED BY WS-STACK-TOP.
05 WS-START PIC S9(8) COMP SYNC.
05 WS-MIDDLE PIC S9(8) COMP SYNC.
05 WS-END PIC S9(8) COMP SYNC.
05 WS-FS-FLAG PIC X.
88 FIRST-HALF VALUE "F".
88 SECOND-HALF VALUE "S".
88 WS-ALL VALUE "A".
05 WS-IO-FLAG PIC X.
88 WS-IN VALUE "I".
88 WS-OUT VALUE "O".
 
PROCEDURE DIVISION.
A-MAIN SECTION.
A-000.
PERFORM B-INITIALISE.
 
IF NOT EMPTY-FILE
PERFORM C-PROCESS.
 
PERFORM D-FINISH.
 
A-999.
STOP RUN.
 
B-INITIALISE SECTION.
B-000.
DISPLAY "*** " WA-PROGNAME " VERSION "
WA-VERSION " STARTING ***".
 
MOVE ALL "N" TO WF-CONDITION-FLAGS.
OPEN INPUT FA-INPUT-FILE.
SET WB-IX-1 TO 0.
 
READ FA-INPUT-FILE AT END MOVE "Y" TO WF-EOF-FLAG
WF-EMPTY-FILE-FLAG.
 
PERFORM BA-READ-INPUT UNTIL END-OF-FILE.
 
CLOSE FA-INPUT-FILE.
 
SET WC-SIZE TO WB-IX-1.
 
B-999.
EXIT.
 
BA-READ-INPUT SECTION.
BA-000.
SET WB-IX-1 UP BY 1.
MOVE FA-DATA TO WB-ENTRY(WB-IX-1).
 
READ FA-INPUT-FILE AT END MOVE "Y" TO WF-EOF-FLAG.
 
BA-999.
EXIT.
 
C-PROCESS SECTION.
C-000.
DISPLAY "SORT STARTING".
 
MOVE 1 TO WS-START(1).
MOVE WC-SIZE TO WS-END(1).
MOVE "F" TO WS-FS-FLAG(1).
MOVE "I" TO WS-IO-FLAG(1).
SET WS-STACK-TOP TO 2.
 
PERFORM E-MERGE-SORT UNTIL WS-OUT(1).
 
DISPLAY "SORT FINISHED".
 
C-999.
EXIT.
 
D-FINISH SECTION.
D-000.
OPEN OUTPUT FB-OUTPUT-FILE.
SET WB-IX-1 TO 1.
 
PERFORM DA-WRITE-OUTPUT UNTIL WB-IX-1 > WC-SIZE.
 
CLOSE FB-OUTPUT-FILE.
 
DISPLAY "*** " WA-PROGNAME " FINISHED ***".
 
D-999.
EXIT.
 
DA-WRITE-OUTPUT SECTION.
DA-000.
WRITE FB-OUTPUT-REC FROM WB-ENTRY(WB-IX-1).
SET WB-IX-1 UP BY 1.
 
DA-999.
EXIT.
 
******************************************************************
E-MERGE-SORT SECTION.
*===================== *
* This section controls the simulated recursion. *
******************************************************************
E-000.
IF WS-OUT(WS-STACK-TOP - 1)
GO TO E-010.
 
MOVE WS-START(WS-STACK-TOP - 1) TO WC-START.
MOVE WS-END(WS-STACK-TOP - 1) TO WC-END.
 
* First check size of part we are dealing with.
IF WC-END - WC-START = 0
* Only 1 number in range, so simply set for output, and move on
MOVE "O" TO WS-IO-FLAG(WS-STACK-TOP - 1)
GO TO E-010.
 
IF WC-END - WC-START = 1
* 2 numbers, so compare and swap as necessary. Set for output
MOVE "O" TO WS-IO-FLAG(WS-STACK-TOP - 1)
IF WB-ENTRY(WC-START) > WB-ENTRY(WC-END)
MOVE WB-ENTRY(WC-START) TO WC-TEMP
MOVE WB-ENTRY(WC-END) TO WB-ENTRY(WC-START)
MOVE WC-TEMP TO WB-ENTRY(WC-END)
GO TO E-010
ELSE
GO TO E-010.
 
* More than 2, so split and carry on down
COMPUTE WC-MIDDLE = ( WC-START + WC-END ) / 2.
 
MOVE WC-START TO WS-START(WS-STACK-TOP).
MOVE WC-MIDDLE TO WS-END(WS-STACK-TOP).
MOVE "F" TO WS-FS-FLAG(WS-STACK-TOP).
MOVE "I" TO WS-IO-FLAG(WS-STACK-TOP).
SET WS-STACK-TOP UP BY 1.
 
GO TO E-999.
 
E-010.
SET WS-STACK-TOP DOWN BY 1.
 
IF SECOND-HALF(WS-STACK-TOP)
GO TO E-020.
 
MOVE WS-START(WS-STACK-TOP - 1) TO WC-START.
MOVE WS-END(WS-STACK-TOP - 1) TO WC-END.
COMPUTE WC-MIDDLE = ( WC-START + WC-END ) / 2 + 1.
 
MOVE WC-MIDDLE TO WS-START(WS-STACK-TOP).
MOVE WC-END TO WS-END(WS-STACK-TOP).
MOVE "S" TO WS-FS-FLAG(WS-STACK-TOP).
MOVE "I" TO WS-IO-FLAG(WS-STACK-TOP).
SET WS-STACK-TOP UP BY 1.
 
GO TO E-999.
 
E-020.
MOVE WS-START(WS-STACK-TOP - 1) TO WC-START.
MOVE WS-END(WS-STACK-TOP - 1) TO WC-END.
COMPUTE WC-MIDDLE = ( WC-START + WC-END ) / 2.
PERFORM H-PROCESS-MERGE.
MOVE "O" TO WS-IO-FLAG(WS-STACK-TOP - 1).
 
E-999.
EXIT.
 
******************************************************************
H-PROCESS-MERGE SECTION.
*======================== *
* This section identifies which data is to be merged, and then *
* merges the two data streams into a single larger data stream. *
******************************************************************
H-000.
INITIALISE WD-FIRST-HALF.
COMPUTE WD-FH-MAX = WC-MIDDLE - WC-START + 1.
SET WD-IX TO 1.
 
PERFORM HA-COPY-OUT VARYING WB-IX-1 FROM WC-START BY 1
UNTIL WB-IX-1 > WC-MIDDLE.
 
SET WB-IX-1 TO WC-START.
SET WB-IX-2 TO WC-MIDDLE.
SET WB-IX-2 UP BY 1.
SET WD-IX TO 1.
 
PERFORM HB-MERGE UNTIL WD-IX > WD-FH-MAX OR WB-IX-2 > WC-END.
 
PERFORM HC-COPY-BACK UNTIL WD-IX > WD-FH-MAX.
 
H-999.
EXIT.
 
HA-COPY-OUT SECTION.
HA-000.
MOVE WB-ENTRY(WB-IX-1) TO WD-ENTRY(WD-IX).
SET WD-IX UP BY 1.
 
HA-999.
EXIT.
 
HB-MERGE SECTION.
HB-000.
IF WB-ENTRY(WB-IX-2) < WD-ENTRY(WD-IX)
MOVE WB-ENTRY(WB-IX-2) TO WB-ENTRY(WB-IX-1)
SET WB-IX-2 UP BY 1
ELSE
MOVE WD-ENTRY(WD-IX) TO WB-ENTRY(WB-IX-1)
SET WD-IX UP BY 1.
 
SET WB-IX-1 UP BY 1.
 
HB-999.
EXIT.
 
HC-COPY-BACK SECTION.
HC-000.
MOVE WD-ENTRY(WD-IX) TO WB-ENTRY(WB-IX-1).
SET WD-IX UP BY 1.
SET WB-IX-1 UP BY 1.
 
HC-999.
EXIT.

CoffeeScript[edit]

# This is a simple version of mergesort that returns brand-new arrays.
# A more sophisticated version would do more in-place optimizations.
merge_sort = (arr) ->
if arr.length <= 1
return (elem for elem in arr)
m = Math.floor(arr.length / 2)
arr1 = merge_sort(arr.slice 0, m)
arr2 = merge_sort(arr.slice m)
result = []
p1 = p2 = 0
while true
if p1 >= arr1.length
if p2 >= arr2.length
return result
result.push arr2[p2]
p2 += 1
else if p2 >= arr2.length or arr1[p1] < arr2[p2]
result.push arr1[p1]
p1 += 1
else
result.push arr2[p2]
p2 += 1
 
do ->
console.log merge_sort [2,4,6,8,1,3,5,7,9,10,11,0,13,12]
Output:
> coffee mergesort.coffee 
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]

Common Lisp[edit]

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

merge is a standard Common Lisp function.

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

Crystal[edit]

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

Curry[edit]

Copied from Curry: Example Programs

-- merge sort: sorting two lists by merging the sorted first
-- and second half of the list
 
sort :: ([a] -> [a] -> [a] -> Success) -> [a] -> [a] -> Success
 
sort merge xs ys =
if length xs < 2 then ys =:= xs
else sort merge (firsthalf xs) us
& sort merge (secondhalf xs) vs
& merge us vs ys
where us,vs free
 
 
intMerge :: [Int] -> [Int] -> [Int] -> Success
 
intMerge [] ys zs = zs =:= ys
intMerge (x:xs) [] zs = zs =:= x:xs
intMerge (x:xs) (y:ys) zs =
if (x > y) then intMerge (x:xs) ys us & zs =:= y:us
else intMerge xs (y:ys) vs & zs =:= x:vs
where us,vs free
 
firsthalf xs = take (length xs `div` 2) xs
secondhalf xs = drop (length xs `div` 2) xs
 
 
 
goal1 xs = sort intMerge [3,1,2] xs
goal2 xs = sort intMerge [3,1,2,5,4,8] xs
goal3 xs = sort intMerge [3,1,2,5,4,8,6,7,2,9,1,4,3] xs

D[edit]

Arrays only, not in-place.

import std.stdio, std.algorithm, std.array, std.range;
 
T[] mergeSorted(T)(in T[] D) /*pure nothrow @safe*/ {
if (D.length < 2)
return D.dup;
return [D[0 .. $ / 2].mergeSorted, D[$ / 2 .. $].mergeSorted]
.nWayUnion.array;
}
 
void main() {
[3, 4, 2, 5, 1, 6].mergeSorted.writeln;
}

Alternative Version[edit]

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

import std.stdio, std.algorithm, core.stdc.stdlib, std.exception,
std.range;
 
void mergeSort(T)(T[] data) if (hasSwappableElements!(typeof(data))) {
immutable L = data.length;
if (L < 2) return;
T* ptr = cast(T*)alloca(L * T.sizeof);
enforce(ptr != null);
ptr[0 .. L] = data[];
mergeSort(ptr[0 .. L/2]);
mergeSort(ptr[L/2 .. L]);
[ptr[0 .. L/2], ptr[L/2 .. L]].nWayUnion().copy(data);
}
 
void main() {
auto a = [3, 4, 2, 5, 1, 6];
a.mergeSort();
writeln(a);
}

Dart[edit]

void main() {
MergeSortInDart sampleSort = MergeSortInDart();
 
List<int> theResultingList = sampleSort.sortTheList([54, 89, 125, 47899, 32, 61, 42, 895647, 215, 345, 6, 21, 2, 78]);
 
print('Here\'s the sorted list: ${theResultingList}');
}
 
/////////////////////////////////////
 
class MergeSortInDart {
 
List<int> sortedList;
 
// In Dart we often put helper functions at the bottom.
// You could put them anywhere, we just like it this way
// for organizational purposes. It's nice to be able to
// read them in the order they're called.
 
// Start here
List<int> sortTheList(List<int> sortThis){
// My parameters are listed vertically for readability. Dart
// doesn't care how you list them, vertically or horizontally.
sortedList = mSort(
sortThis,
sortThis.sublist(0, sortThis.length),
sortThis.length,
);
return sortThis;
}
 
mSort(
List<int> sortThisList,
List<int> tempList,
int thisListLength) {
 
if (thisListLength == 1) {
return;
}
 
// In Dart using ~/ is more efficient than using .floor()
int middle = (thisListLength ~/ 2);
 
// If you use something in a try/on/catch/finally block then
// be sure to declare it outside the block (for scope)
List<int> tempLeftList;
 
// This was used for troubleshooting. It was left here to show
// how a basic block try/on can be better than a debugPrint since
// it won't print unless there's a problem.
try {
tempLeftList = tempList.sublist(0, middle);
} on RangeError {
print(
'tempLeftList length = ${tempList.length}, thisListLength '
'was supposedly $thisListLength and Middle was $middle');
}
 
// If you see "myList.getRange(x,y)" that's a sign the code is
// from Dart 1 and needs to be updated. It's "myList.sublist" in Dart 2
List<int> tempRightList = tempList.sublist(middle);
 
// Left side.
mSort(
tempLeftList,
sortThisList.sublist(0, middle),
middle,
);
 
// Right side.
mSort(
tempRightList,
sortThisList.sublist(middle),
sortThisList.length - middle,
);
 
// Merge it.
dartMerge(
tempLeftList,
tempRightList,
sortThisList,
);
}
 
dartMerge(
List<int> leftSide,
List<int> rightSide,
List<int> sortThisList,
) {
int index = 0;
int elementValue;
 
// This should be human readable.
while (leftSide.isNotEmpty && rightSide.isNotEmpty) {
if (rightSide[0] < leftSide[0]) {
elementValue = rightSide[0];
rightSide.removeRange(0, 1);
} else {
elementValue = leftSide[0];
leftSide.removeRange(0, 1);
}
sortThisList[index++] = elementValue;
}
 
while (leftSide.isNotEmpty) {
elementValue = leftSide[0];
leftSide.removeRange(0, 1);
sortThisList[index++] = elementValue;
}
 
while (rightSide.isNotEmpty) {
elementValue = rightSide[0];
rightSide.removeRange(0, 1);
sortThisList[index++] = elementValue;
}
sortedList = sortThisList;
}
}

E[edit]

def merge(var xs :List, var ys :List) {
var result := []
while (xs =~ [x] + xr && ys =~ [y] + yr) {
if (x <= y) {
result with= x
xs := xr
} else {
result with= y
ys := yr
}
}
return result + xs + ys
}
 
def sort(list :List) {
if (list.size() <= 1) { return list }
def split := list.size() // 2
return merge(sort(list.run(0, split)),
sort(list.run(split)))
}

EasyLang[edit]

subr merge
mid = left + sz
if mid > sz_data
mid = sz_data
.
right = mid + sz
if right > sz_data
right = sz_data
.
l = left
r = mid
for i = left to right - 1
if r = right or l < mid and tmp[l] < tmp[r]
data[i] = tmp[l]
l += 1
else
data[i] = tmp[r]
r += 1
.
.
.
subr sort
sz_data = len data[]
len tmp[] sz_data
sz = 1
while sz < sz_data
swap tmp[] data[]
left = 0
while left < sz_data
call merge
left += sz + sz
.
sz += sz
.
.
data[] = [ 29 4 72 44 55 26 27 77 92 5 ]
call sort
print data[]

Eiffel[edit]

 
class
MERGE_SORT [G -> COMPARABLE]
 
create
sort
 
feature
 
sort (ar: ARRAY [G])
-- Sorted array in ascending order.
require
ar_not_empty: not ar.is_empty
do
create sorted_array.make_empty
mergesort (ar, 1, ar.count)
sorted_array := ar
ensure
sorted_array_not_empty: not sorted_array.is_empty
sorted: is_sorted (sorted_array, 1, sorted_array.count)
end
 
sorted_array: ARRAY [G]
 
feature {NONE}
 
mergesort (ar: ARRAY [G]; l, r: INTEGER)
-- Sorting part of mergesort.
local
m: INTEGER
do
if l < r then
m := (l + r) // 2
mergesort (ar, l, m)
mergesort (ar, m + 1, r)
merge (ar, l, m, r)
end
end
 
merge (ar: ARRAY [G]; l, m, r: INTEGER)
-- Merge part of mergesort.
require
positive_index_l: l >= 1
positive_index_m: m >= 1
positive_index_r: r >= 1
ar_not_empty: not ar.is_empty
local
merged: ARRAY [G]
h, i, j, k: INTEGER
do
i := l
j := m + 1
k := l
create merged.make_filled (ar [1], 1, ar.count)
from
until
i > m or j > r
loop
if ar.item (i) <= ar.item (j) then
merged.force (ar.item (i), k)
i := i + 1
elseif ar.item (i) > ar.item (j) then
merged.force (ar.item (j), k)
j := j + 1
end
k := k + 1
end
if i > m then
from
h := j
until
h > r
loop
merged.force (ar.item (h), k + h - j)
h := h + 1
end
elseif j > m then
from
h := i
until
h > m
loop
merged.force (ar.item (h), k + h - i)
h := h + 1
end
end
from
h := l
until
h > r
loop
ar.item (h) := merged.item (h)
h := h + 1
end
ensure
is_partially_sorted: is_sorted (ar, l, r)
end
 
is_sorted (ar: ARRAY [G]; l, r: INTEGER): BOOLEAN
-- Is 'ar' sorted in ascending order?
require
ar_not_empty: not ar.is_empty
l_in_range: l >= 1
r_in_range: r <= ar.count
local
i: INTEGER
do
Result := True
from
i := l
until
i = r
loop
if ar [i] > ar [i + 1] then
Result := False
end
i := i + 1
end
end
 
end
 

Test:

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

Elixir[edit]

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

Example:

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

Erlang[edit]

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

Single-threaded version:

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

Multi-process version:

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


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

 
merge_sort(List) -> m(List, erlang:system_info(schedulers)).
 
m([L],_) -> [L];
m(L, N) when N > 1 ->
{L1,L2} = lists:split(length(L) div 2, L),
{Parent, Ref} = {self(), make_ref()},
spawn(fun()-> Parent ! {l1, Ref, m(L1, N-2)} end),
spawn(fun()-> Parent ! {l2, Ref, m(L2, N-2)} end),
{L1R, L2R} = receive_results(Ref, undefined, undefined),
lists:merge(L1R, L2R);
m(L, _) -> {L1,L2} = lists:split(length(L) div 2, L), lists:merge(m(L1, 0), m(L2, 0)).
 
receive_results(Ref, L1, L2) ->
receive
{l1, Ref, L1R} when L2 == undefined -> receive_results(Ref, L1R, L2);
{l2, Ref, L2R} when L1 == undefined -> receive_results(Ref, L1, L2R);
{l1, Ref, L1R} -> {L1R, L2};
{l2, Ref, L2R} -> {L1, L2R}
after 5000 -> receive_results(Ref, L1, L2)
end.
 

ERRE[edit]

 
PROGRAM MERGESORT_DEMO
 
! Example of merge sort usage.
 
CONST SIZE%=100,S1%=50
 
DIM DTA%[SIZE%],FH%[S1%],STACK%[20,2]
 
 
PROCEDURE MERGE(START%,MIDDLE%,ENDS%)
 
LOCAL FHSIZE%
 
FHSIZE%=MIDDLE%-START%+1
 
FOR I%=0 TO FHSIZE%-1 DO
FH%[I%]=DTA%[START%+I%]
END FOR
 
I%=0
J%=MIDDLE%+1
K%=START%
 
REPEAT
IF FH%[I%]<=DTA%[J%] THEN
DTA%[K%]=FH%[I%]
I%=I%+1
K%=K%+1
ELSE
DTA%[K%]=DTA%[J%]
J%=J%+1
K%=K%+1
END IF
UNTIL I%=FHSIZE% OR J%>ENDS%
 
WHILE I%<FHSIZE% DO
DTA%[K%]=FH%[I%]
I%=I%+1
K%=K%+1
END WHILE
 
END PROCEDURE
 
PROCEDURE MERGE_SORT(LEV->LEV)
 
! *****************************************************************
! This procedure Merge Sorts the chunk of DTA% bounded by
! Start% & Ends%.
! *****************************************************************
 
LOCAL MIDDLE%
 
IF ENDS%=START% THEN LEV=LEV-1 EXIT PROCEDURE END IF
 
IF ENDS%-START%=1 THEN
IF DTA%[ENDS%]<DTA%[START%] THEN
SWAP(DTA%[START%],DTA%[ENDS%])
END IF
LEV=LEV-1
EXIT PROCEDURE
END IF
 
MIDDLE%=START%+(ENDS%-START%)/2
 
STACK%[LEV,0]=START% STACK%[LEV,1]=ENDS% STACK%[LEV,2]=MIDDLE%
START%=START% ENDS%=MIDDLE%
MERGE_SORT(LEV+1->LEV)
START%=STACK%[LEV,0] ENDS%=STACK%[LEV,1] MIDDLE%=STACK%[LEV,2]
 
STACK%[LEV,0]=START% STACK%[LEV,1]=ENDS% STACK%[LEV,2]=MIDDLE%
START%=MIDDLE%+1 ENDS%=ENDS%
MERGE_SORT(LEV+1->LEV)
START%=STACK%[LEV,0] ENDS%=STACK%[LEV,1] MIDDLE%=STACK%[LEV,2]
 
MERGE(START%,MIDDLE%,ENDS%)
 
LEV=LEV-1
END PROCEDURE
 
BEGIN
FOR I%=1 TO SIZE% DO
DTA%[I%]=RND(1)*10000
END FOR
 
START%=1 ENDS%=SIZE%
MERGE_SORT(0->LEV)
 
FOR I%=1 TO SIZE% DO
WRITE("#####";DTA%[I%];)
END FOR
PRINT
END PROGRAM
 

Euphoria[edit]

function merge(sequence left, sequence right)
sequence result
result = {}
while length(left) > 0 and length(right) > 0 do
if compare(left[1], right[1]) <= 0 then
result = append(result, left[1])
left = left[2..$]
else
result = append(result, right[1])
right = right[2..$]
end if
end while
return result & left & right
end function
 
function mergesort(sequence m)
sequence left, right
integer middle
if length(m) <= 1 then
return m
else
middle = floor(length(m)/2)
left = mergesort(m[1..middle])
right = mergesort(m[middle+1..$])
if compare(left[$], right[1]) <= 0 then
return left & right
elsif compare(right[$], left[1]) <= 0 then
return right & left
else
return merge(left, right)
end if
end if
end function
 
constant s = rand(repeat(1000,10))
? s
? mergesort(s)
Output:
{385,599,284,650,457,804,724,300,434,722}
{284,300,385,434,457,599,650,722,724,804}

F#[edit]

let split list =
let rec aux l acc1 acc2 =
match l with
| [] -> (acc1,acc2)
| [x] -> (x::acc1,acc2)
| x::y::tail ->
aux tail (x::acc1) (y::acc2)
in aux list [] []
 
let rec merge l1 l2 =
match (l1,l2) with
| (x,[]) -> x
| ([],y) -> y
| (x::tx,y::ty) ->
if x <= y then x::merge tx l2
else y::merge l1 ty
let rec mergesort list =
match list with
| [] -> []
| [x] -> [x]
| _ -> let (l1,l2) = split list
in merge (mergesort l1) (mergesort l2)

Factor[edit]

: mergestep ( accum seq1 seq2 -- accum seq1 seq2 )
2dup [ first ] [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 ] while
append 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[edit]

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

: merge-step ( right mid left -- right mid+ left+ )
over @ over @ < if
over @ >r
2dup - over dup cell+ rot move
r> over !
>r cell+ 2dup = if rdrop dup else r> then
then cell+ ;
: merge ( right mid left -- right left )
dup >r begin 2dup > while merge-step repeat 2drop r> ;
 
: mid ( l r -- mid ) over - 2/ cell negate and + ;
 
: mergesort ( right left -- right left )
2dup cell+ <= if exit then
swap 2dup mid recurse rot recurse merge ;
 
: sort ( addr len -- ) cells over + swap mergesort 2drop ;
 
create test 8 , 1 , 5 , 3 , 9 , 0 , 2 , 7 , 6 , 4 ,
 
: .array ( addr len -- ) 0 do dup i cells + @ . loop drop ;
 
test 10 2dup sort .array \ 0 1 2 3 4 5 6 7 8 9

Fortran[edit]

Works with: Fortran version 95 and later and with both free or fixed form syntax.
      program TestMergeSort
implicit none
integer, parameter :: N = 8
integer :: A(N) = (/ 1, 5, 2, 7, 3, 9, 4, 6 /)
integer :: work((size(A) + 1) / 2)
write(*,'(A,/,10I3)')'Unsorted array :',A
call MergeSort(A, work)
write(*,'(A,/,10I3)')'Sorted array :',A
contains
 
subroutine merge(A, B, C)
implicit none
! The targe attribute is necessary, because A .or. B might overlap with C.
integer, target, intent(in) :: A(:), B(:)
integer, target, intent(inout) :: C(:)
integer :: i, j, k
 
if (size(A) + size(B) > size(C)) stop(1)
 
i = 1; j = 1
do k = 1, size(C)
if (i <= size(A) .and. j <= size(B)) then
if (A(i) <= B(j)) then
C(k) = A(i)
i = i + 1
else
C(k) = B(j)
j = j + 1
end if
else if (i <= size(A)) then
C(k) = A(i)
i = i + 1
else if (j <= size(B)) then
C(k) = B(j)
j = j + 1
end if
end do
end subroutine merge
 
subroutine swap(x, y)
implicit none
integer, intent(inout) :: x, y
integer :: tmp
tmp = x; x = y; y = tmp
end subroutine
 
recursive subroutine MergeSort(A, work)
implicit none
integer, intent(inout) :: A(:)
integer, intent(inout) :: work(:)
integer :: half
half = (size(A) + 1) / 2
if (size(A) < 2) then
continue
else if (size(A) == 2) then
if (A(1) > A(2)) then
call swap(A(1), A(2))
end if
else
call MergeSort(A( : half), work)
call MergeSort(A(half + 1 :), work)
if (A(half) > A(half + 1)) then
work(1 : half) = A(1 : half)
call merge(work(1 : half), A(half + 1:), A)
endif
end if
end subroutine MergeSort
end program TestMergeSort
 

FreeBASIC[edit]

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

' FB 1.05.0 Win64
 
Sub copyArray(a() As Integer, iBegin As Integer, iEnd As Integer, b() As Integer)
Redim b(iBegin To iEnd - 1) As Integer
For k As Integer = iBegin To iEnd - 1
b(k) = a(k)
Next
End Sub
 
' Left source half is a(iBegin To iMiddle-1).
' Right source half is a(iMiddle To iEnd-1).
' Result is b(iBegin To iEnd-1).
Sub topDownMerge(a() As Integer, iBegin As Integer, iMiddle As Integer, iEnd As Integer, b() As Integer)
Dim i As Integer = iBegin
Dim j As Integer = iMiddle
 
' While there are elements in the left or right runs...
For k As Integer = iBegin To iEnd - 1
' If left run head exists and is <= existing right run head.
If i < iMiddle AndAlso (j >= iEnd OrElse a(i) <= a(j)) Then
b(k) = a(i)
i += 1
Else
b(k) = a(j)
j += 1
End If
Next
End Sub
 
' Sort the given run of array a() using array b() as a source.
' iBegin is inclusive; iEnd is exclusive (a(iEnd) is not in the set).
Sub topDownSplitMerge(b() As Integer, iBegin As Integer, iEnd As Integer, a() As Integer)
If (iEnd - iBegin) < 2 Then Return '' If run size = 1, consider it sorted
' split the run longer than 1 item into halves
Dim iMiddle As Integer = (iEnd + iBegin) \ 2 '' iMiddle = mid point
' recursively sort both runs from array a() into b()
topDownSplitMerge(a(), iBegin, iMiddle, b()) '' sort the left run
topDownSplitMerge(a(), iMiddle, iEnd, b()) '' sort the right run
' merge the resulting runs from array b() into a()
topDownMerge(b(), iBegin, iMiddle, iEnd, a())
End Sub
 
' Array a() has the items to sort; array b() is a work array (empty initially).
Sub topDownMergeSort(a() As Integer, b() As Integer, n As Integer)
copyArray(a(), 0, n, b()) '' duplicate array a() into b()
topDownSplitMerge(b(), 0, n, a()) '' sort data from b() into a()
End Sub
 
Sub printArray(a() As Integer)
For i As Integer = LBound(a) To UBound(a)
Print Using "####"; a(i);
Next
Print
End Sub
 
Dim a(0 To 9) As Integer = {4, 65, 2, -31, 0, 99, 2, 83, 782, 1}
 
Dim b() As Integer
Print "Unsorted : ";
printArray(a())
topDownMergeSort a(), b(), 10
Print "Sorted  : ";
printArray(a())
Print
Dim a2(0 To 8) As Integer = {7, 5, 2, 6, 1, 4, 2, 6, 3}
Erase b
Print "Unsorted : ";
printArray(a2())
topDownMergeSort a2(), b(), 9
Print "Sorted  : ";
printArray(a2())
Print
Print "Press any key to quit"
Sleep
Output:
Unsorted :    4  65   2 -31   0  99   2  83 782   1
Sorted   :  -31   0   1   2   2   4  65  83  99 782

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

FunL[edit]

def
sort( [] ) = []
sort( [x] ) = [x]
sort( xs ) =
val (l, r) = xs.splitAt( xs.length()\2 )
merge( sort(l), sort(r) )
 
merge( [], xs ) = xs
merge( xs, [] ) = xs
merge( x:xs, y:ys )
| x <= y = x : merge( xs, y:ys )
| otherwise = y : merge( x:xs, ys )
 
println( sort([94, 37, 16, 56, 72, 48, 17, 27, 58, 67]) )
println( sort(['Sofía', 'Alysha', 'Sophia', 'Maya', 'Emma', 'Olivia', 'Emily']) )
Output:
[16, 17, 27, 37, 48, 56, 58, 67, 72, 94]
[Alysha, Emily, Emma, Maya, Olivia, Sofía, Sophia]

Go[edit]

package main
 
import "fmt"
 
var a = []int{170, 45, 75, -90, -802, 24, 2, 66}
var s = make([]int, len(a)/2+1) // scratch space for merge step
 
func main() {
fmt.Println("before:", a)
mergeSort(a)
fmt.Println("after: ", a)
}
 
func mergeSort(a []int) {
if len(a) < 2 {
return
}
mid := len(a) / 2
mergeSort(a[:mid])
mergeSort(a[mid:])
if a[mid-1] <= a[mid] {
return
}
// merge step, with the copy-half optimization
copy(s, a[:mid])
l, r := 0, mid
for i := 0; ; i++ {
if s[l] <= a[r] {
a[i] = s[l]
l++
if l == mid {
break
}
} else {
a[i] = a[r]
r++
if r == len(a) {
copy(a[i+1:], s[l:mid])
break
}
}
}
return
}

Groovy[edit]

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

def merge = { List left, List right ->
List mergeList = []
while (left && right) {
print "."
mergeList << ((left[-1] > right[-1]) ? left.pop() : right.pop())
}
mergeList = mergeList.reverse()
mergeList = left + right + mergeList
}
 
def mergeSort;
mergeSort = { List list ->
 
def n = list.size()
if (n < 2) return list
 
def middle = n.intdiv(2)
def left = [] + list[0..<middle]
def right = [] + list[middle..<n]
left = mergeSort(left)
right = mergeSort(right)
 
if (left[-1] <= right[0]) return left + right
 
merge(left, right)
}

Test:

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

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

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

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

Tail recursion version[edit]

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

split = { list ->
list.collate((list.size()+1)/2 as int)
}
 
merge = { left, right, headBuffer=[] ->
if(left.size() == 0) headBuffer+right
else if(right.size() == 0) headBuffer+left
else if(left.head() <= right.head()) merge.trampoline(left.tail(), right, headBuffer+left.head())
else merge.trampoline(right.tail(), left, headBuffer+right.head())
}.trampoline()
 
mergesort = { List list ->
if(list.size() < 2) list
else merge(split(list).collect {mergesort it})
}
 
assert mergesort((500..1)) == (1..500)
assert mergesort([5,4,6,3,1,2]) == [1,2,3,4,5,6]
assert mergesort([3,3,1,4,6,78,9,1,3,5]) == [1,1,3,3,3,4,5,6,9,78]
 

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

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

Haskell[edit]

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

merge []         ys                   = ys
merge xs [] = xs
merge xs@(x:xt) ys@(y:yt) | x <= y = x : merge xt ys
| otherwise = y : merge xs yt
 
split (x:y:zs) = let (xs,ys) = split zs in (x:xs,y:ys)
split [x] = ([x],[])
split [] = ([],[])
 
mergeSort [] = []
mergeSort [x] = [x]
mergeSort xs = let (as,bs) = split xs
in merge (mergeSort as) (mergeSort bs)

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

mergePairs (sorted1 : sorted2 : sorteds) = merge sorted1 sorted2 : mergePairs sorteds
mergePairs sorteds = sorteds
 
mergeSortBottomUp list = mergeAll (map (\x -> [x]) list)
 
mergeAll [sorted] = sorted
mergeAll sorteds = mergeAll (mergePairs sorteds)

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

sort = sortBy compare
sortBy cmp = mergeAll . sequences
where
sequences (a:b:xs)
| a `cmp` b == GT = descending b [a] xs
| otherwise = ascending b (a:) xs
sequences xs = [xs]
 
descending a as (b:bs)
| a `cmp` b == GT = descending b (a:as) bs
descending a as bs = (a:as): sequences bs
 
ascending a as (b:bs)
| a `cmp` b /= GT = ascending b (\ys -> as (a:ys)) bs
ascending a as bs = as [a]: sequences bs

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

Icon and Unicon[edit]

procedure main()                                                         #: demonstrate various ways to sort a list and string 
demosort(mergesort,[3, 14, 1, 5, 9, 2, 6, 3],"qwerty")
end
 
procedure mergesort(X,op,lower,upper) #: return sorted list ascending(or descending)
local middle
 
if /lower := 1 then { # top level call setup
upper := *X
op := sortop(op,X) # select how and what we sort
}
 
if upper ~= lower then { # sort all sections with 2 or more elements
X := mergesort(X,op,lower,middle := lower + (upper - lower) / 2)
X := mergesort(X,op,middle+1,upper)
 
if op(X[middle+1],X[middle]) then # @middle+1 < @middle merge if halves reversed
X := merge(X,op,lower,middle,upper)
}
return X
end
 
procedure merge(X,op,lower,middle,upper) # merge two list sections within a larger list
local p1,p2,add
 
p1 := lower
p2 := middle + 1
add := if type(X) ~== "string" then put else "||" # extend X, strings require X := add (until ||:= is invocable)
 
while p1 <= middle & p2 <= upper do
if op(X[p1],X[p2]) then { # @p1 < @p2
X := add(X,X[p1]) # extend X temporarily (rather than use a separate temporary list)
p1 +:= 1
}
else {
X := add(X,X[p2]) # extend X temporarily
p2 +:= 1
}
 
while X := add(X,X[middle >= p1]) do p1 +:= 1 # and rest of lower or ...
while X := add(X,X[upper >= p2]) do p2 +:= 1 # ... upper trailers if any
 
if type(X) ~== "string" then # pull section's sorted elements from extension
every X[upper to lower by -1] := pull(X)
else
(X[lower+:(upper-lower+1)] := X[0-:(upper-lower+1)])[0-:(upper-lower+1)] := ""
 
return X
end

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

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

Io[edit]

List do (
merge := method(lst1, lst2,
result := list()
while(lst1 isNotEmpty or lst2 isNotEmpty,
if(lst1 first <= lst2 first) then(
result append(lst1 removeFirst)
) else (
result append(lst2 removeFirst)
)
)
result)
 
mergeSort := method(
if (size > 1) then(
half_size := (size / 2) ceil
return merge(slice(0, half_size) mergeSort,
slice(half_size, size) mergeSort)
) else (return self)
)
 
mergeSortInPlace := method(
copy(mergeSort)
)
)
 
lst := list(9, 5, 3, -1, 15, -2)
lst mergeSort println # ==> list(-2, -1, 3, 5, 9, 15)
lst mergeSortInPlace println # ==> list(-2, -1, 3, 5, 9, 15)

Isabelle[edit]

theory Mergesort
  imports Main
begin
 
fun merge :: "int list ⇒ int list ⇒ int list" where
  "merge [] ys = ys"
| "merge xs [] = xs"
| "merge (x#xs) (y#ys) = (if x ≤ y
                          then x # merge xs (y#ys)
                          else y # merge (x # xs) ys)"
 
text‹example:›
lemma "merge [1,3,6] [1,2,5,8] = [1,1,2,3,5,6,8]" by simp
 
lemma merge_set: "set (merge xs ys) = set xs ∪ set ys"
  by(induction xs ys rule: merge.induct) auto
 
lemma merge_sorted:
  "sorted xs ⟹ sorted ys ⟹ sorted (merge xs ys)"
proof(induction xs ys rule: merge.induct)
  case (1 ys)
  then show "sorted (merge [] ys)" by simp
next
  case (2 x xs)
  then show "sorted (merge (x # xs) [])" by simp
next
  case (3 x xs y ys)
  assume premx: "sorted (x # xs)"
     and premy: "sorted (y # ys)"
     and IHx: "x ≤ y ⟹ sorted xs ⟹ sorted (y # ys) ⟹
                 sorted (merge xs (y # ys))"
     and IHy: "¬ x ≤ y ⟹ sorted (x # xs) ⟹ sorted ys ⟹
                 sorted (merge (x # xs) ys)"
  then show "sorted (merge (x # xs) (y # ys))"
  proof(cases "x ≤ y")
    case True
    with premx IHx premy have IH: "sorted (merge xs (y # ys))" by simp
    from ‹x ≤ y› premx premy merge_set have
      "∀z ∈ set (merge xs (y # ys)). x ≤ z" by fastforce
    with ‹x ≤ y› IH show "sorted (merge (x # xs) (y # ys))" by(simp)
  next
    case False
    with premy IHy premx have IH: "sorted (merge (x # xs) ys)" by simp
    from ‹¬x ≤ y› premx premy merge_set have
      "∀z ∈ set (merge (x # xs) ys). y ≤ z" by fastforce
    with ‹¬x ≤ y› IH show "sorted (merge (x # xs) (y # ys))" by(simp)
  qed
qed
 
fun mergesort :: "int list ⇒ int list" where
  "mergesort [] = []"
| "mergesort [x] = [x]"
| "mergesort xs = merge (mergesort (take (length xs div 2) xs))
                        (mergesort (drop (length xs div 2) xs))"
 
theorem mergesort_set: "set xs = set (mergesort xs)"
proof(induction xs rule: mergesort.induct)
  case 1
  show "set [] = set (mergesort [])" by simp
next
  case (2 x)
  show "set [x] = set (mergesort [x])" by simp
next
  case (3 x1 x2 xs)
  from 3 have IH_simplified_take:
    "set (mergesort (x1 # take (length xs div 2) (x2 # xs))) =
     insert x1 (set (take (length xs div 2) (x2 # xs)))"
  and IH_simplified_drop:
    "set (mergesort (drop (length xs div 2) (x2 # xs))) =
     set (drop (length xs div 2) (x2 # xs))" by simp+
 
  have "(set (take n as) ∪ set (drop n as)) = set as"
    for n and as::"int list"
  proof -
    from set_append[of "take n as" "drop n as"] have
      "(set (take n as) ∪ set (drop n as)) =
       set (take n as @ drop n as)" by simp
    moreover have
      "set (take n as @ drop n as) =
       set as" using append_take_drop_id by simp
    ultimately show ?thesis by simp
  qed
  hence "(set (take (length xs div 2) (x2 # xs)) ∪
        set (drop (length xs div 2) (x2 # xs))) =
        set (x2 # xs)"by(simp)
  with IH_simplified_take IH_simplified_drop show
    "set (x1 # x2 # xs) = set (mergesort (x1 # x2 # xs))"
    by(simp add: merge_set)
qed
 
theorem mergesort_sorted: "sorted (mergesort xs)"
  by(induction xs rule: mergesort.induct) (simp add: merge_sorted)+
 
text‹example:›
lemma "mergesort [42, 5, 1, 3, 67, 3, 9, 0, 33, 32] =
                 [0, 1, 3, 3, 5, 9, 32, 33, 42, 67]" by simp
end
 

J[edit]

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

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[edit]

Works with: Java version 1.5+
import java.util.List;
import java.util.ArrayList;
import java.util.Iterator;
 
public class Merge{
public static <E extends Comparable<? super E>> List<E> mergeSort(List<E> m){
if(m.size() <= 1) return m;
 
int middle = m.size() / 2;
List<E> left = m.subList(0, middle);
List<E> right = m.subList(middle, m.size());
 
right = mergeSort(right);
left = mergeSort(left);
List<E> result = merge(left, right);
 
return result;
}
 
public static <E extends Comparable<? super E>> List<E> merge(List<E> left, List<E> right){
List<E> result = new ArrayList<E>();
Iterator<E> it1 = left.iterator();
Iterator<E> it2 = right.iterator();
 
E x = it1.next();
E y = it2.next();
while (true){
//change the direction of this comparison to change the direction of the sort
if(x.compareTo(y) <= 0){
result.add(x);
if(it1.hasNext()){
x = it1.next();
}else{
result.add(y);
while(it2.hasNext()){
result.add(it2.next());
}
break;
}
}else{
result.add(y);
if(it2.hasNext()){
y = it2.next();
}else{
result.add(x);
while (it1.hasNext()){
result.add(it1.next());
}
break;
}
}
}
return result;
}
}

JavaScript[edit]

function merge(left, right, arr) {
var a = 0;
 
while (left.length && right.length) {
arr[a++] = (right[0] < left[0]) ? right.shift() : left.shift();
}
while (left.length) {
arr[a++] = left.shift();
}
while (right.length) {
arr[a++] = right.shift();
}
}
 
function mergeSort(arr) {
var len = arr.length;
 
if (len === 1) { return; }
 
var mid = Math.floor(len / 2),
left = arr.slice(0, mid),
right = arr.slice(mid);
 
mergeSort(left);
mergeSort(right);
merge(left, right, arr);
}
 
var arr = [1, 5, 2, 7, 3, 9, 4, 6, 8];
mergeSort(arr); // arr will now: 1, 2, 3, 4, 5, 6, 7, 8, 9

jq[edit]

The sort function defined here will sort any JSON array.

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

Example:

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

Julia[edit]

Works with: Julia version 0.6
function mergesort(arr::Vector)
if length(arr) ≤ 1 return arr end
mid = length(arr) ÷ 2
lpart = mergesort(arr[1:mid])
rpart = mergesort(arr[mid+1:end])
rst = similar(arr)
i = ri = li = 1
@inbounds while li ≤ length(lpart) && ri ≤ length(rpart)
if lpart[li] ≤ rpart[ri]
rst[i] = lpart[li]
li += 1
else
rst[i] = rpart[ri]
ri += 1
end
i += 1
end
if li ≤ length(lpart)
copy!(rst, i, lpart, li)
else
copy!(rst, i, rpart, ri)
end
return rst
end
 
v = rand(-10:10, 10)
println("# unordered: $v\n -> ordered: ", mergesort(v))
Output:
# unordered: [8, 6, 7, 1, -1, 0, -4, 7, -7, 0]
 -> ordered: [-7, -4, -1, 0, 0, 1, 6, 7, 7, 8]

Kotlin[edit]

fun mergeSort(list: List<Int>): List<Int> {
if (list.size <= 1) {
return list
}
 
val left = mutableListOf<Int>()
val right = mutableListOf<Int>()
 
val middle = list.size / 2
list.forEachIndexed { index, number ->
if (index < middle) {
left.add(number)
} else {
right.add(number)
}
}
 
fun merge(left: List<Int>, right: List<Int>): List<Int> = mutableListOf<Int>().apply {
var indexLeft = 0
var indexRight = 0
 
while (indexLeft < left.size && indexRight < right.size) {
if (left[indexLeft] <= right[indexRight]) {
add(left[indexLeft])
indexLeft++
} else {
add(right[indexRight])
indexRight++
}
}
 
while (indexLeft < left.size) {
add(left[indexLeft])
indexLeft++
}
 
while (indexRight < right.size) {
add(right[indexRight])
indexRight++
}
}
 
return merge(mergeSort(left), mergeSort(right))
}
 
fun main(args: Array<String>) {
val numbers = listOf(5, 2, 3, 17, 12, 1, 8, 3, 4, 9, 7)
println("Unsorted: $numbers")
println("Sorted: ${mergeSort(numbers)}")
}
Output:
Unsorted: [5, 2, 3, 17, 12, 1, 8, 3, 4, 9, 7]
Sorted:   [1, 2, 3, 3, 4, 5, 7, 8, 9, 12, 17]

Lambdatalk[edit]

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

 
{def alt
{lambda {:list}
{if {A.empty? :list}
then {A.new}
else {A.addfirst! {A.first :list}
{alt {A.rest {A.rest :list}}}} }}}
-> alt
 
{def merge
{lambda {:l1 :l2}
{if {A.empty? :l2}
then :l1
else {if {< {A.first :l1} {A.first :l2}}
then {A.addfirst! {A.first :l1} {merge :l2 {A.rest :l1}}}
else {A.addfirst! {A.first :l2} {merge :l1 {A.rest :l2}}} }}}}
-> merge
 
{def mergesort
{lambda {:list}
{if {A.empty? {A.rest :list}}
then :list
else {merge {mergesort {alt :list}}
{mergesort {alt {A.rest :list}}}} }}}
-> mergesort
 
{mergesort {A.new 8 1 5 3 9 0 2 7 6 4}}
-> [0,1,2,3,4,5,6,7,8,9]
 

Liberty BASIC[edit]

    itemCount = 20
dim A(itemCount)
dim tmp(itemCount) 'merge sort needs additionally same amount of storage
 
for i = 1 to itemCount
A(i) = int(rnd(1) * 100)
next i
 
print "Before Sort"
call printArray itemCount
 
call mergeSort 1,itemCount
 
print "After Sort"
call printArray itemCount
end
 
'------------------------------------------
sub mergeSort start, theEnd
if theEnd-start < 1 then exit sub
if theEnd-start = 1 then
if A(start)>A(theEnd) then
tmp=A(start)
A(start)=A(theEnd)
A(theEnd)=tmp
end if
exit sub
end if
middle = int((start+theEnd)/2)
call mergeSort start, middle
call mergeSort middle+1, theEnd
call merge start, middle, theEnd
end sub
 
sub merge start, middle, theEnd
i = start: j = middle+1: k = start
while i<=middle OR j<=theEnd
select case
case i<=middle AND j<=theEnd
if A(i)<=A(j) then
tmp(k)=A(i)
i=i+1
else
tmp(k)=A(j)
j=j+1
end if
k=k+1
case i<=middle
tmp(k)=A(i)
i=i+1
k=k+1
case else 'j<=theEnd
tmp(k)=A(j)
j=j+1
k=k+1
end select
wend
 
for i = start to theEnd
A(i)=tmp(i)
next
end sub
 
'===========================================
sub printArray itemCount
for i = 1 to itemCount
print using("###", A(i));
next i
print
end sub

[edit]

Works with: UCB Logo
to split :size :front :list
if :size < 1 [output list :front :list]
output split :size-1 (lput first :list :front) (butfirst :list)
end
 
to merge :small :large
if empty? :small [output :large]
ifelse lessequal? first :small first :large ~
[output fput first :small merge butfirst :small :large] ~
[output fput first :large merge butfirst :large :small]
end
 
to mergesort :list
localmake "half split (count :list) / 2 [] :list
if empty? first :half [output :list]
output merge mergesort first :half mergesort last :half
end

Logtalk[edit]

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

Lua[edit]

function getLower(a,b)
local i,j=1,1
return function()
if not b[j] or a[i] and a[i]<b[j] then
i=i+1; return a[i-1]
else
j=j+1; return b[j-1]
end
end
end
 
function merge(a,b)
local res={}
for v in getLower(a,b) do res[#res+1]=v end
return res
end
 
function mergesort(list)
if #list<=1 then return list end
local s=math.floor(#list/2)
return merge(mergesort{unpack(list,1,s)}, mergesort{unpack(list,s+1)})
end

Lucid[edit]

[1]

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

M2000 Interpreter[edit]

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

Maple[edit]

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

Mathematica / Wolfram Language[edit]

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

MATLAB[edit]

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

Sample Usage:

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

Maxima[edit]

merge(a, b) := block(
[c: [ ], i: 1, j: 1, p: length(a), q: length(b)],
while i <= p and j <= q do (
if a[i] < b[j] then (
c: endcons(a[i], c),
i: i + 1
) else (
c: endcons(b[j], c),
j: j + 1
)
),
if i > p then append(c, rest(b, j - 1)) else append(c, rest(a, i - 1))
)$
 
mergesort(u) := block(
[n: length(u), k, a, b],
if n <= 1 then u else (
a: rest(u, k: quotient(n, 2)),
b: rest(u, k - n),
merge(mergesort(a), mergesort(b))
)
)$

MAXScript[edit]

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

Output:

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

Mercury[edit]

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

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

Nemerle[edit]

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

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

NetRexx[edit]

/* NetRexx */
options replace format comments java crossref savelog symbols binary
 
import java.util.List
 
placesList = [String -
"UK London", "US New York", "US Boston", "US Washington" -
, "UK Washington", "US Birmingham", "UK Birmingham", "UK Boston" -
]
 
lists = [ -
placesList -
, mergeSort(String[] Arrays.copyOf(placesList, placesList.length)) -
]
 
loop ln = 0 to lists.length - 1
cl = lists[ln]
loop ct = 0 to cl.length - 1
say cl[ct]
end ct
say
end ln
 
return
 
method mergeSort(m = String[]) public constant binary returns String[]
 
rl = String[m.length]
al = List mergeSort(Arrays.asList(m))
al.toArray(rl)
 
return rl
 
method mergeSort(m = List) public constant binary returns ArrayList
 
result = ArrayList(m.size)
left = ArrayList()
right = ArrayList()
if m.size > 1 then do
middle = m.size % 2
loop x_ = 0 to middle - 1
left.add(m.get(x_))
end x_
loop x_ = middle to m.size - 1
right.add(m.get(x_))
end x_
left = mergeSort(left)
right = mergeSort(right)
if (Comparable left.get(left.size - 1)).compareTo(Comparable right.get(0)) <= 0 then do
left.addAll(right)
result.addAll(m)
end
else do
result = merge(left, right)
end
end
else do
result.addAll(m)
end
 
return result
 
method merge(left = List, right = List) public constant binary returns ArrayList
 
result = ArrayList()
loop label mx while left.size > 0 & right.size > 0
if (Comparable left.get(0)).compareTo(Comparable right.get(0)) <= 0 then do
result.add(left.get(0))
left.remove(0)
end
else do
result.add(right.get(0))
right.remove(0)
end
end mx
if left.size > 0 then do
result.addAll(left)
end
if right.size > 0 then do
result.addAll(right)
end
 
return result
 
Output:
UK  London
US  New York
US  Boston
US  Washington
UK  Washington
US  Birmingham
UK  Birmingham
UK  Boston

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

Nim[edit]

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

OCaml[edit]

let rec split_at n xs =
match n, xs with
0, xs ->
[], xs
| _, [] ->
failwith "index too large"
| n, x::xs when n > 0 ->
let xs', xs'' = split_at (pred n) xs in
x::xs', xs''
| _, _ ->
invalid_arg "negative argument"
 
let rec merge_sort cmp = function
[] -> []
| [x] -> [x]
| xs ->
let xs, ys = split_at (List.length xs / 2) xs in
List.merge cmp (merge_sort cmp xs) (merge_sort cmp ys)
 
let _ =
merge_sort compare [8;6;4;2;1;3;5;7;9]

Oz[edit]

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

PARI/GP[edit]

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

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

Pascal[edit]

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[edit]

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

Works with ( Turbo -) Delphi too.

{$IFDEF FPC}
{$MODE DELPHI}
{$OPTIMIZATION ON,Regvar,ASMCSE,CSE,PEEPHOLE}
{$ELSE}
{$APPTYPE CONSOLE}
{$ENDIF}
uses
sysutils; //for timing
type
tDataElem = record
myText : AnsiString;
myX,
myY : double;
myTag,
myOrgIdx : LongInt;
end;
 
tpDataElem = ^tDataElem;
tData = array of tDataElem;
 
tSortData = array of tpDataElem;
tCompFunc = function(A,B:tpDataElem):integer;
var
Data : tData;
Sortdata,
tmpData : tSortData;
 
procedure InitData(var D:tData;cnt: LongWord);
var
i,k: LongInt;
begin
Setlength(D,cnt);
Setlength(SortData,cnt);
Setlength(tmpData,cnt shr 1 +1 );
k := 10*cnt;
For i := cnt-1 downto 0 do
Begin
Sortdata[i] := @D[i];
with D[i] do
Begin
myText := Format('_%.9d',[random(cnt)+1]);
myX := Random*k;
myY := Random*k;
myTag := Random(k);
myOrgIdx := i;
end;
end;
end;
 
procedure FreeData(var D:tData);
begin
Setlength(tmpData,0);
Setlength(SortData,0);
Setlength(D,0);
end;
 
function CompLowercase(A,B:tpDataElem):integer;
var
lcA,lcB: String;
Begin
lcA := lowercase(A^.myText);
lcB := lowercase(B^.myText);
result := ORD(lcA > lcB)-ORD(lcA < lcB);
end;
 
function myCompText(A,B:tpDataElem):integer;
{sort an array (or list) of strings in order of descending length,
and in ascending lexicographic order for strings of equal length.}

var
lA,lB:integer;
 
Begin
lA := Length(A^.myText);
lB := Length(B^.myText);
result := ORD(lA<lB)-ORD(lA>lB);
IF result = 0 then
result := CompLowercase(A,B);
end;
 
function myCompX(A,B:tpDataElem):integer;
//same as sign without jumps in assembler code
begin
result := ORD(A^.myX > B^.myX)-ORD(A^.myX < B^.myX);
end;
 
function myCompY(A,B:tpDataElem):integer;
Begin
result := ORD(A^.myY > B^.myY)-ORD(A^.myY < B^.myY);
end;
 
function myCompTag(A,B:tpDataElem):integer;
Begin
result := ORD(A^.myTag > B^.myTag)-ORD(A^.myTag < B^.myTag);
end;
 
procedure InsertionSort(left,right:integer;var a: tSortData;CompFunc: tCompFunc);
var
Pivot : tpDataElem;
i,j : LongInt;
begin
for i:=left+1 to right do
begin
j :=i;
Pivot := A[j];
while (j>left) AND (CompFunc(A[j-1],Pivot)>0) do
begin
A[j] := A[j-1];
dec(j);
end;
A[j] :=PiVot;// s.o.
end;
end;
 
 
procedure mergesort(left,right:integer;var a: tSortData;CompFunc: tCompFunc);
var
i,j,k,mid :integer;
begin
{// without insertion sort
If right>left then
}

//{ test insertion sort
If right-left<=14 then
InsertionSort(left,right,a,CompFunc)
else
//}
begin
//recursion
mid := (right+left) div 2;
mergesort(left, mid,a,CompFunc);
mergesort(mid+1, right,a,CompFunc);
//already sorted ?
IF CompFunc(A[Mid],A[Mid+1])<0 then
exit;
 
//########## Merge ##########
//copy lower half to temporary array
move(A[left],tmpData[0],(mid-left+1)*SizeOf(Pointer));
i := 0;
j := mid+1;
k := left;
// re-integrate
while (k<j) AND (j<=right) do
begin
IF CompFunc(tmpData[i],A[j])<=0 then
begin
A[k] := tmpData[i];
inc(i);
end
else
begin
A[k]:= A[j];
inc(j);
end;
inc(k);
end;
//the rest of tmpdata a move should do too, in next life
while (k<j) do
begin
A[k] := tmpData[i];
inc(i);
inc(k);
end;
end;
end;
 
var
T1,T0: TDateTime;
i : integer;
Begin
randomize;
InitData(Data,1*1000*1000);
 
T0 := Time;
mergesort(Low(SortData),High(SortData),SortData,@myCompText);
T1 := Time;
Writeln('myText ',FormatDateTime('NN:SS.ZZZ',T1-T0));
// For i := 0 to High(Data) do Write(SortData[i].myText); writeln;
T0 := Time;
mergesort(Low(SortData),High(SortData),SortData,@myCompX);
T1 := Time;
Writeln('myX ',FormatDateTime('NN:SS.ZZZ',T1-T0));
//check
For i := 1 to High(Data) do
IF myCompX(SortData[i-1],SortData[i]) = 1 then
Write(i:8);
 
T0 := Time;
mergesort(Low(SortData),High(SortData),SortData,@myCompY);
T1 := Time;
Writeln('myY ',FormatDateTime('NN:SS.ZZZ',T1-T0));
 
T0 := Time;
mergesort(Low(SortData),High(SortData),SortData,@myCompTag);
T1 := Time;
Writeln('myTag ',FormatDateTime('NN:SS.ZZZ',T1-T0));
 
FreeData (Data);
end.
 
output
Free pascal 2.6.4 32bit / Win7 / i 4330 3.5 Ghz
myText 00:03.158 / nearly worst case , all strings same sized and starting with '_000..'
myX    00:00.360
myY    00:00.363
myTag  00:00.283

Perl[edit]

sub merge_sort {
my @x = @_;
return @x if @x < 2;
my $m = int @x / 2;
my @a = merge_sort(@x[0 .. $m - 1]);
my @b = merge_sort(@x[$m .. $#x]);
for (@x) {
$_ = !@a ? shift @b
: !@b ? shift @a
: $a[0] <= $b[0] ? shift @a
: shift @b;
}
@x;
}
 
my @a = (4, 65, 2, -31, 0, 99, 83, 782, 1);
@a = merge_sort @a;
print "@a\n";

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

Phix[edit]

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 & right
end function
 
function mergesort(sequence m)
sequence left, right
integer 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[edit]

function mergesort($arr){
if(count($arr) == 1 ) return $arr;
$mid = count($arr) / 2;
$left = array_slice($arr, 0, $mid);
$right = array_slice($arr, $mid);
$left = mergesort($left);
$right = mergesort($right);
return merge($left, $right);
}
 
function merge($left, $right){
$res = array();
while (count($left) > 0 && count($right) > 0){
if($left[0] > $right[0]){
$res[] = $right[0];
$right = array_slice($right , 1);
}else{
$res[] = $left[0];
$left = array_slice($left, 1);
}
}
while (count($left) > 0){
$res[] = $left[0];
$left = array_slice($left, 1);
}
while (count($right) > 0){
$res[] = $right[0];
$right = array_slice($right, 1);
}
return $res;
}
 
$arr = array( 1, 5, 2, 7, 3, 9, 4, 6, 8);
$arr = mergesort($arr);
echo implode(',',$arr);
Output:
1,2,3,4,5,6,7,8,9

PicoLisp[edit]

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

(de alt (List)
(if List (cons (car List) (alt (cddr List))) ()) )
 
(de merge (L1 L2)
(cond
((not L2) L1)
((< (car L1) (car L2))
(cons (car L1) (merge L2 (cdr L1))))
(T (cons (car L2) (merge L1 (cdr L2)))) ) )
 
(de mergesort (List)
(if (cdr List)
(merge (mergesort (alt List)) (mergesort (alt (cdr List))))
List) )
 
(mergesort (8 1 5 3 9 0 2 7 6 4))

PL/I[edit]

MERGE: PROCEDURE (A,LA,B,LB,C);
 
/* Merge A(1:LA) with B(1:LB), putting the result in C
B and C may share the same memory, but not with A.
*/

DECLARE (A(*),B(*),C(*)) BYADDR POINTER;
DECLARE (LA,LB) BYVALUE NONASGN FIXED BIN(31);
DECLARE (I,J,K) FIXED BIN(31);
DECLARE (SX) CHAR(58) VAR BASED (PX);
DECLARE (SY) CHAR(58) VAR BASED (PY);
DECLARE (PX,PY) POINTER;
 
I=1; J=1; K=1;
DO WHILE ((I <= LA) & (J <= LB));
PX=A(I); PY=B(J);
IF(SX <= SY) THEN
DO; C(K)=A(I); K=K+1; I=I+1; END;
ELSE
DO; C(K)=B(J); K=K+1; J=J+1; END;
END;
DO WHILE (I <= LA);
C(K)=A(I); I=I+1; K=K+1;
END;
RETURN;
END MERGE;
 
MERGESORT: PROCEDURE (AP,N) RECURSIVE ;
 
/* Sort the array AP containing N pointers to strings */
 
DECLARE (AP(*)) BYADDR POINTER;
DECLARE (N) BYVALUE NONASGN FIXED BINARY(31);
DECLARE (M,I) FIXED BINARY;
DECLARE AMP1(1) POINTER BASED(PAM);
DECLARE (pX,pY,PAM) POINTER;
DECLARE SX CHAR(58) VAR BASED(pX);
DECLARE SY CHAR(58) VAR BASED(pY);
 
IF (N=1) THEN RETURN;
M = trunc((N+1)/2);
IF (M>1) THEN CALL MERGESORT(AP,M);
PAM=ADDR(AP(M+1));
IF (N-M > 1) THEN CALL MERGESORT(AMP1,N-M);
pX=AP(M); pY=AP(M+1);
IF SX <= SY then return; /* Skip Merge */
DO I=1 to M; TP(I)=AP(I); END;
CALL MERGE(TP,M,AMP1,N-M,AP);
RETURN;
END MERGESORT;

PowerShell[edit]

 
function MergeSort([object[]] $SortInput)
{
# The base case exits for minimal lists that are sorted by definition
if ($SortInput.Length -le 1) {return $SortInput}
 
# Divide and conquer
[int] $midPoint = $SortInput.Length/2
# The @() operators ensure a single result remains typed as an array
[object[]] $left = @(MergeSort @($SortInput[0..($midPoint-1)]))
[object[]] $right = @(MergeSort @($SortInput[$midPoint..($SortInput.Length-1)]))
 
# Merge
[object[]] $result = @()
while (($left.Length -gt 0) -and ($right.Length -gt 0))
{
if ($left[0] -lt $right[0])
{
$result += $left[0]
# Use an if/else rather than accessing the array range as $array[1..0]
if ($left.Length -gt 1){$left = $left[1..$($left.Length-1)]}
else {$left = @()}
}
else
{
$result += $right[0]
# Without the if/else, $array[1..0] would return the whole array when $array.Length == 1
if ($right.Length -gt 1){$right = $right[1..$($right.Length-1)]}
else {$right = @()}
}
}
 
# If we get here, either $left or $right is an empty array (or both are empty!). Since the
# rest of the unmerged array is already sorted, we can simply string together what we have.
# This line outputs the concatenated result. An explicit 'return' statement is not needed.
$result + $left + $right
}
 

Prolog[edit]

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

PureBasic[edit]

A non-optimized version with lists.

Procedure display(List m())
ForEach m()
Print(LSet(Str(m()), 3," "))
Next
PrintN("")
EndProcedure
 
;overwrites list m() with the merger of lists ma() and mb()
Procedure merge(List m(), List ma(), List mb())
FirstElement(m())
Protected ma_elementExists = FirstElement(ma())
Protected mb_elementExists = FirstElement(mb())
Repeat
If ma() <= mb()
m() = ma(): NextElement(m())
ma_elementExists = NextElement(ma())
Else
m() = mb(): NextElement(m())
mb_elementExists = NextElement(mb())
EndIf
Until Not (ma_elementExists And mb_elementExists)
 
If ma_elementExists
Repeat
m() = ma(): NextElement(m())
Until Not NextElement(ma())
ElseIf mb_elementExists
Repeat
m() = mb(): NextElement(m())
Until Not NextElement(mb())
EndIf
EndProcedure
 
Procedure mergesort(List m())
Protected NewList ma()
Protected NewList mb()
 
If ListSize(m()) > 1
Protected current, middle = (ListSize(m()) / 2 ) - 1
 
FirstElement(m())
While current <= middle
AddElement(ma())
ma() = m()
NextElement(m()): current + 1
Wend
 
PreviousElement(m())
While NextElement(m())
AddElement(mb())
mb() = m()
Wend
 
mergesort(ma())
mergesort(mb())
LastElement(ma()): FirstElement(mb())
If ma() <= mb()
FirstElement(m())
FirstElement(ma())
Repeat
m() = ma(): NextElement(m())
Until Not NextElement(ma())
Repeat
m() = mb(): NextElement(m())
Until Not NextElement(mb())
Else
merge(m(), ma(), mb())
EndIf
EndIf
EndProcedure
 
If OpenConsole()
Define i
NewList x()
 
For i = 1 To 21: AddElement(x()): x() = Random(60): Next
display(x())
mergesort(x())
display(x())
 
Print(#CRLF$ + #CRLF$ + "Press ENTER to exit")
Input()
CloseConsole()
EndIf
Sample output:
22 51 31 59 58 45 11 2  16 56 38 42 2  10 23 41 42 25 45 28 42
2  2  10 11 16 22 23 25 28 31 38 41 42 42 42 45 45 51 56 58 59

Python[edit]

Works with: Python version 2.6+
from heapq import merge
 
def merge_sort(m):
if len(m) <= 1:
return m
 
middle = len(m) // 2
left = m[:middle]
right = m[middle:]
 
left = merge_sort(left)
right = merge_sort(right)
return list(merge(left, right))

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

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

R[edit]

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

Racket[edit]

 
#lang racket
 
(define (merge xs ys)
(cond [(empty? xs) ys]
[(empty? ys) xs]
[(match* (xs ys)
[((list* a as) (list* b bs))
(cond [(<= a b) (cons a (merge as ys))]
[ (cons b (merge xs bs))])])]))
 
(define (merge-sort xs)
(match xs
[(or (list) (list _)) xs]
[_ (define-values (ys zs) (split-at xs (quotient (length xs) 2)))
(merge (merge-sort ys) (merge-sort zs))]))
 

This variation is bottom up:

 
#lang racket
 
(define (merge-sort xs)
(merge* (map list xs)))
 
(define (merge* xss)
(match xss
[(list) '()]
[(list xs) xss]
[(list xs ys zss ...)
(merge* (cons (merge xs ys) (merge* zss)))]))
 
(define (merge xs ys)
(cond [(empty? xs) ys]
[(empty? ys) xs]
[(match* (xs ys)
[((list* a as) (list* b bs))
(cond [(<= a b) (cons a (merge as ys))]
[ (cons b (merge xs bs))])])]))
 

Raku[edit]

(formerly Perl 6)

Works with: Rakudo Star version 2015.10
sub merge_sort ( @a ) {
return @a if @a <= 1;
 
my $m = @a.elems div 2;
my @l = flat merge_sort @a[ 0 ..^ $m ];
my @r = flat merge_sort @a[ $m ..^ @a ];
 
return flat @l, @r if @l[*-1] !after @r[0];
return flat gather {
take @l[0] before @r[0] ?? @l.shift !! @r.shift
while @l and @r;
take @l, @r;
}
}
my @data = 6, 7, 2, 1, 8, 9, 5, 3, 4;
say 'input = ' ~ @data;
say 'output = ' ~ @data.&merge_sort;
Output:
input  = 6 7 2 1 8 9 5 3 4
output = 1 2 3 4 5 6 7 8 9

REBOL[edit]

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

REXX[edit]

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

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

(Shown at three-quarter size.)

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

Ruby[edit]

def merge_sort(m)
return m if m.length <= 1
 
middle = m.length / 2
left = merge_sort(m[0...middle])
right = merge_sort(m[middle..-1])
merge(left, right)
end
 
def merge(left, right)
result = []
until left.empty? || right.empty?
result << (left.first<=right.first ? left.shift : right.shift)
end
result + left + right
end
 
ary = [7,6,5,9,8,4,3,1,2,0]
p merge_sort(ary) # => [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

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

class Array
def mergesort(&comparitor)
return self if length <= 1
comparitor ||= proc{|a, b| a <=> b}
middle = length / 2
left = self[0...middle].mergesort(&comparitor)
right = self[middle..-1].mergesort(&comparitor)
merge(left, right, comparitor)
end
 
private
def merge(left, right, comparitor)
result = []
until left.empty? || right.empty?
# change the direction of this comparison to change the direction of the sort
if comparitor[left.first, right.first] <= 0
result << left.shift
else
result << right.shift
end
end
result + left + right
end
end
 
ary = [7,6,5,9,8,4,3,1,2,0]
p ary.mergesort # => [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
p ary.mergesort {|a, b| b <=> a} # => [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
 
ary = [["UK", "London"], ["US", "New York"], ["US", "Birmingham"], ["UK", "Birmingham"]]
p ary.mergesort
# => [["UK", "Birmingham"], ["UK", "London"], ["US", "Birmingham"], ["US", "New York"]]
p ary.mergesort {|a, b| a[1] <=> b[1]}
# => [["US", "Birmingham"], ["UK", "Birmingham"], ["UK", "London"], ["US", "New York"]]

Rust[edit]

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

The sort algorithm :

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

Version without recursion call (faster) :

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

Scala[edit]

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

 
import scala.language.implicitConversions
 
object MergeSort extends App {
 
def mergeSort(input: List[Int]): List[Int] = {
def merge(left: List[Int], right: List[Int]): LazyList[Int] = (left, right) match {
case (x :: xs, y :: ys) if x <= y => x #:: merge(xs, right)
case (x :: xs, y :: ys) => y #:: merge(left, ys)
case _ => if (left.isEmpty) right.to(LazyList) else left.to(LazyList)
}
 
def sort(input: List[Int], length: Int): List[Int] = input match {
case Nil | List(_) => input
case _ =>
val middle = length / 2
val (left, right) = input splitAt middle
merge(sort(left, middle), sort(right, middle + length % 2)).toList
}
 
sort(input, input.length)
}
 
}
 

Scheme[edit]

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

Seed7[edit]

const proc: mergeSort2 (inout array elemType: arr, in integer: lo, in integer: hi, inout array elemType: scratch) is func
local
var integer: mid is 0;
var integer: k is 0;
var integer: t_lo is 0;
var integer: t_hi is 0;
begin
if lo < hi then
mid := (lo + hi) div 2;
mergeSort2(arr, lo, mid, scratch);
mergeSort2(arr, succ(mid), hi, scratch);
t_lo := lo;
t_hi := succ(mid);
for k range lo to hi do
if t_lo <= mid and (t_hi > hi or arr[t_lo] <= arr[t_hi]) then
scratch[k] := arr[t_lo];
incr(t_lo);
else
scratch[k] := arr[t_hi];
incr(t_hi);
end if;
end for;
for k range lo to hi do
arr[k] := scratch[k];
end for;
end if;
end func;
 
const proc: mergeSort2 (inout array elemType: arr) is func
local
var array elemType: scratch is 0 times elemType.value;
begin
scratch := length(arr) times elemType.value;
mergeSort2(arr, 1, length(arr), scratch);
end func;

Original source: [2]

Sidef[edit]

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

Standard ML[edit]

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

Swift[edit]

// Merge Sort in Swift 4.2
// Source: https://github.com/raywenderlich/swift-algorithm-club/tree/master/Merge%20Sort
// NOTE: by use of generics you can make it sort arrays of any type that conforms to
// Comparable protocol, however this is not always optimal
 
import Foundation
 
func mergeSort(_ array: [Int]) -> [Int] {
guard array.count > 1 else { return array }
 
let middleIndex = array.count / 2
 
let leftPart = mergeSort(Array(array[0..<middleIndex]))
let rightPart = mergeSort(Array(array[middleIndex..<array.count]))
 
func merge(left: [Int], right: [Int]) -> [Int] {
var leftIndex = 0
var rightIndex = 0
 
var merged = [Int]()
merged.reserveCapacity(left.count + right.count)
 
while leftIndex < left.count && rightIndex < right.count {
if left[leftIndex] < right[rightIndex] {
merged.append(left[leftIndex])
leftIndex += 1
} else if left[leftIndex] > right[rightIndex] {
merged.append(right[rightIndex])
rightIndex += 1
} else {
merged.append(left[leftIndex])
leftIndex += 1
merged.append(right[rightIndex])
rightIndex += 1
}
}
 
while leftIndex < left.count {
merged.append(left[leftIndex])
leftIndex += 1
}
 
while rightIndex < right.count {
merged.append(right[rightIndex])
rightIndex += 1
}
 
return merged
}
 
return merge(left: leftPart, right: rightPart)
}

Tailspin[edit]

The standard recursive merge sort

 
templates mergesort
templates merge
@: $(2);
[ $(1)... -> \(
when <?([email protected]<[](0)>)
| [email protected](1)> do
$ !
otherwise
^@merge(1) !
$ -> #
\),
[email protected]] !
end merge
$ -> #
 
when <[](0..1)> do $!
otherwise
def half: $::length ~/ 2;
[$(1..$half) -> mergesort, $($half+1..last) -> mergesort] -> merge !
end mergesort
 
[4,5,3,8,1,2,6,7,9,8,5] -> mergesort -> !OUT::write
 
Output:
[1, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9]

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

 
templates mergesort
templates merge
@: $(2);
$(1)... -> \(
when <?([email protected]<[](0)>)
| [email protected](1)> do
$ !
otherwise
^@merge(1) !
$ -> #
\) !
[email protected] !
end merge
 
templates mergePairs
when <[](1)> do
$(1) !
when <[](2..)> do
[$(1..2) -> merge] !
$(3..last) -> #
end mergePairs
 
templates mergeAll
when <[](0)> do
$ !
when <[](1)> do
$(1) !
otherwise
[ $ -> mergePairs ] -> #
end mergeAll
 
$ -> [ $... -> [ $ ] ] -> mergeAll !
end mergesort
 
[4,5,3,8,1,2,6,7,9,8,5] -> mergesort -> !OUT::write
 
Output:
[1, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9]

Tcl[edit]

package require Tcl 8.5
 
proc mergesort m {
set len [llength $m]
if {$len <= 1} {
return $m
}
set middle [expr {$len / 2}]
set left [lrange $m 0 [expr {$middle - 1}]]
set right [lrange $m $middle end]
return [merge [mergesort $left] [mergesort $right]]
}
 
proc merge {left right} {
set result [list]
while {[set lleft [llength $left]] > 0 && [set lright [llength $right]] > 0} {
if {[lindex $left 0] <= [lindex $right 0]} {
set left [lassign $left value]
} else {
set right [lassign $right value]
}
lappend result $value
}
if {$lleft > 0} {
lappend result {*}$left
}
if {$lright > 0} {
set result [concat $result $right] ;# another way append elements
}
return $result
}
 
puts [mergesort {8 6 4 2 1 3 5 7 9}] ;# => 1 2 3 4 5 6 7 8 9

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

Unison[edit]

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

UnixPipes[edit]

Works with: Zsh
split() {
(while read a b ; do
echo $a > $1 ; echo $b > $2
done)
}
 
mergesort() {
xargs -n 2 | (read a b; test -n "$b" && (
lc="1.$1" ; gc="2.$1"
(echo $a $b;cat)|split >(mergesort $lc >$lc) >( mergesort $gc >$gc)
sort -m $lc $gc
rm -f $lc $gc;
) || echo $a)
}
 
cat to.sort | mergesort

Ursala[edit]

#import std
 
mergesort "p" = @iNCS :-0 ~&B^?a\~&YaO "p"?abh/~&alh2faltPrXPRC ~&arh2falrtPXPRC
 
#show+
 
example = mergesort(lleq) <'zoh','zpb','hhh','egi','bff','cii','yid'>
Output:
bff
cii
egi
hhh
yid
zoh
zpb

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

mergesort "p" = "p"-<

V[edit]

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

[merge
[mergei
uncons [swap [>] split] dip
[[*m] e2 [*a1] b1 a2 : [*m *a1 e2] b1 a2] view].
 
[a b : [] a b] view
[size zero?] [pop concat]
[mergei]
tailrec].
 
[msort
[splitat [arr a : [arr a take arr a drop]] view i].
[splitarr dup size 2 / >int splitat].
 
[small?] []
[splitarr]
[merge]
binrec].
[8 7 6 5 4 2 1 3 9] msort puts

Wren[edit]

var merge = Fn.new { |left, right|
var result = []
while (left.count > 0 && right.count > 0) {
if (left[0] <= right[0]) {
result.add(left[0])
left = left[1..-1]
} else {
result.add(right[0])
right = right[1..-1]
}
}
if (left.count > 0) result.addAll(left)
if (right.count > 0) result.addAll(right)
return result
}
 
var mergeSort // recursive
mergeSort = Fn.new { |m|
var len = m.count
if (len <= 1) return m
var middle = (len/2).floor
var left = m[0...middle]
var right = m[middle..-1]
left = mergeSort.call(left)
right = mergeSort.call(right)
if (left[-1] <= right[0]) {
left.addAll(right)
return left
}
return merge.call(left, right)
}
 
var as = [ [4, 65, 2, -31, 0, 99, 2, 83, 782, 1], [7, 5, 2, 6, 1, 4, 2, 6, 3] ]
for (a in as) {
System.print("Before: %(a)")
a = mergeSort.call(a)
System.print("After : %(a)")
System.print()
}
Output:
Before: [4, 65, 2, -31, 0, 99, 2, 83, 782, 1]
After : [-31, 0, 1, 2, 2, 4, 65, 83, 99, 782]

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


Alternatively we can just call a library method.

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

XPL0[edit]

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

code Reserve=3, ChOut=8, IntOut=11;
 
proc MergeSort(A, Low, High); \Sort array A from Low to High
int A, Low, High;
int B, Mid, H, I, J, K;
[if Low >= High then return;
Mid:= (Low+High) >> 1; \split array in half (roughly)
MergeSort(A, Low, Mid); \sort left half
MergeSort(A, Mid+1, High); \sort right half
\Merge the two halves in to sorted order
B:= Reserve((High-Low+1)*4); \reserve space for working array (4 bytes/int)
H:= Low; I:= Low; J:= Mid+1;
while H<=Mid & J<=High do \merge while both halves have items
if A(H) <= A(J) then [B(I):= A(H); I:= I+1; H:= H+1]
else [B(I):= A(J); I:= I+1; J:= J+1];
if H > Mid then \copy any remaining elements
for K:= J to High do [B(I):= A(K); I:= I+1]
else for K:= H to Mid do [B(I):= A(K); I:= I+1];
for K:= Low to High do A(K):= B(K);
];
 
int A, I;
[A:= [3, 1, 4, 1, -5, 9, 2, 6, 5, 4];
MergeSort(A, 0, 10-1);
for I:= 0 to 10-1 do [IntOut(0, A(I)); ChOut(0, ^ )];
]
Output:
-5 1 1 2 3 4 4 5 6 9 

ZED[edit]

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

This is a bottom up version of merge sort:

(append) list1 list2
comment:
#true
(003) "append" list1 list2
 
(car) pair
comment:
#true
(002) "car" pair
 
(cdr) pair
comment:
#true
(002) "cdr" pair
 
(cons) one two
comment:
#true
(003) "cons" one two
 
(map) function list
comment:
#true
(003) "map" function list
 
(merge) comparator list1 list2
comment:
#true
(merge1) comparator list1 list2 nil
 
(merge1) comparator list1 list2 collect
comment:
(null?) list2
(append) (reverse) collect list1
 
(merge1) comparator list1 list2 collect
comment:
(null?) list1
(append) (reverse) collect list2
 
(merge1) comparator list1 list2 collect
comment:
(003) comparator (car) list2 (car) list1
(merge1) comparator list1 (cdr) list2 (cons) (car) list2 collect
 
(merge1) comparator list1 list2 collect
comment:
#true
(merge1) comparator (cdr) list1 list2 (cons) (car) list1 collect
 
(null?) value
comment:
#true
(002) "null?" value
 
(reverse) list
comment:
#true
(002) "reverse" list
 
(sort) comparator jumble
comment:
#true
(car) (sort11) comparator (sort1) jumble
 
(sort1) jumble
comment:
#true
(map) "list" jumble
 
(sort11) comparator jumble
comment:
(null?) jumble
nil
 
(sort11) comparator jumble
comment:
(null?) (cdr) jumble
jumble
 
(sort11) comparator jumble
comment:
#true
(sort11) comparator
(cons) (merge) comparator (car) jumble (002) "cadr" jumble
(sort11) comparator (002) "cddr" jumble

zkl[edit]

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

Translation of: Clojure
fcn _merge(left,right){
if (not left) return(right);
if (not right) return(left);
l:=left[0]; r:=right[0];
if (l<=r) return(L(l).extend(self.fcn(left[1,*],right)));
else return(L(r).extend(self.fcn(left,right[1,*])));
}
 
fcn merge_sort(L){
if (L.len()<2) return(L);
n:=L.len()/2;
return(_merge(self.fcn(L[0,n]), self.fcn(L[n,*])));
}
merge_sort(T(1,3,5,7,9,8,6,4,2)).println();
merge_sort("big fjords vex quick waltz nymph").concat().println();
Output:
L(1,2,3,4,5,6,7,8,9)
     abcdefghiijklmnopqrstuvwxyz

Or, for lists only:

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