Sorting algorithms/Merge sort: Difference between revisions
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N=. #r=. y |
N=. #r=. y |
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while.stride < N do. |
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stride=. 2*mid=. stride |
stride=. 2*mid=. stride |
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r=. ;(-stride) (mid&}. <@merge (mid<.#) {.])\ r |
r=. ;(-stride) (mid&}. <@merge (mid<.#) {.])\ r |
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Revision as of 18:53, 2 June 2022
You are encouraged to solve this task according to the task description, using any language you may know.
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
Heap sort | Merge sort | Patience sort | Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
The merge sort is a recursive sort of order n*log(n).
It is notable for having a worst case and average complexity of O(n*log(n)), and a best case complexity of O(n) (for pre-sorted input).
The basic idea is to split the collection into smaller groups by halving it until the groups only have one element or no elements (which are both entirely sorted groups).
Then merge the groups back together so that their elements are in order.
This is how the algorithm gets its divide and conquer description.
- 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
- the Wikipedia entry: merge sort
Note: better performance can be expected if, rather than recursing until length(m) ≤ 1, an insertion sort is used for length(m) smaller than some threshold larger than 1. However, this complicates the example code, so it is not shown here.
11l
<lang 11l>F merge(left, right)
[Int] result
V left_idx = 0
V right_idx = 0
L left_idx < left.len & right_idx < right.len
I left[left_idx] <= right[right_idx]
result.append(left[left_idx])
left_idx++
E
result.append(right[right_idx])
right_idx++
I left_idx < left.len
result.extend(left[left_idx ..])
I right_idx < right.len
result.extend(right[right_idx ..])
R result
F merge_sort(m)
I m.len <= 1
R m
V middle = m.len I/ 2 V left = m[0.<middle] V right = m[middle..]
left = merge_sort(left) right = merge_sort(right) R Array(merge(left, right))
V arr = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0] print(merge_sort(arr))</lang>
- Output:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
360 Assembly
The program uses ASM structured macros and two ASSIST macros (XDECO, XPRNT) to keep the code as short as possible. <lang 360asm>* 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</lang>
- Output:
-31 0 1 2 2 4 45 58 65 69 74 82 82 83 88 89 99 104 112 782
AArch64 Assembly
<lang AArch64 Assembly> /* 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" </lang>
ACL2
<lang Lisp>(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)))))</lang>
Action!
Action! language does not support recursion. Therefore an iterative approach has been proposed. <lang Action!>DEFINE MAX_COUNT="100"
PROC PrintArray(INT ARRAY a INT size)
INT i
Put('[)
FOR i=0 TO size-1
DO
IF i>0 THEN Put(' ) FI
PrintI(a(i))
OD
Put(']) PutE()
RETURN
PROC Merge(INT ARRAY a INT first,mid,last)
INT ARRAY left(MAX_COUNT),right(MAX_COUNT)
INT leftSize,rightSize,i,j,k
leftSize=mid-first+1
rightSize=last-mid
FOR i=0 TO leftSize-1
DO
left(i)=a(first+i)
OD
FOR i=0 TO rightSize-1
DO
right(i)=a(mid+1+i)
OD
i=0 j=0
k=first
WHILE i<leftSize AND j<rightSize
DO
IF left(i)<=right(j) THEN
a(k)=left(i)
i==+1
ELSE
a(k)=right(j)
j==+1
FI
k==+1
OD
WHILE i<leftSize
DO
a(k)=left(i)
i==+1 k==+1
OD
WHILE j<rightSize
DO
a(k)=right(j)
j==+1 k==+1
OD
RETURN
PROC MergeSort(INT ARRAY a INT size)
INT currSize,first,mid,last
currSize=1
WHILE currSize<size
DO
first=0
WHILE first<size-1
DO
mid=first+currSize-1
IF mid>size-1 THEN
mid=size-1
FI
last=first+2*currSize-1
IF last>size-1 THEN
last=size-1
FI
Merge(a,first,mid,last);
first==+2*currSize OD currSize==*2 OD
RETURN
PROC Test(INT ARRAY a INT size)
PrintE("Array before sort:")
PrintArray(a,size)
MergeSort(a,size)
PrintE("Array after sort:")
PrintArray(a,size)
PutE()
RETURN
PROC Main()
INT ARRAY
a(10)=[1 4 65535 0 3 7 4 8 20 65530],
b(21)=[10 9 8 7 6 5 4 3 2 1 0
65535 65534 65533 65532 65531
65530 65529 65528 65527 65526],
c(8)=[101 102 103 104 105 106 107 108],
d(12)=[1 65535 1 65535 1 65535 1
65535 1 65535 1 65535]
Test(a,10)
Test(b,21)
Test(c,8)
Test(d,12)
RETURN</lang>
- Output:
Screenshot from Atari 8-bit computer
Array before sort: [1 4 -1 0 3 7 4 8 20 -6] Array after sort: [-6 -1 0 1 3 4 4 7 8 20] Array before sort: [10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10] Array after sort: [-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10] Array before sort: [101 102 103 104 105 106 107 108] Array after sort: [101 102 103 104 105 106 107 108] Array before sort: [1 -1 1 -1 1 -1 1 -1 1 -1 1 -1] Array after sort: [-1 -1 -1 -1 -1 -1 1 1 1 1 1 1]
ActionScript
<lang ActionScript>function mergesort(a:Array) { //Arrays of length 1 and 0 are always sorted if(a.length <= 1) return a; else { var middle:uint = a.length/2; //split the array into two var left:Array = new Array(middle); var right:Array = new Array(a.length-middle); var j:uint = 0, k:uint = 0; //fill the left array for(var i:uint = 0; i < middle; i++) left[j++]=a[i]; //fill the right array for(i = middle; i< a.length; i++) right[k++]=a[i]; //sort the arrays left = mergesort(left); right = mergesort(right); //If the last element of the left array is less than or equal to the first //element of the right array, they are in order and don't need to be merged if(left[left.length-1] <= right[0]) return left.concat(right); a = merge(left, right); return a; } }
function merge(left:Array, right:Array) { var result:Array = new Array(left.length + right.length); var j:uint = 0, k:uint = 0, m:uint = 0; //merge the arrays in order while(j < left.length && k < right.length) { if(left[j] <= right[k]) result[m++] = left[j++]; else result[m++] = right[k++]; } //If one of the arrays has remaining entries that haven't been merged, they //will be greater than the rest of the numbers merged so far, so put them on the //end of the array. for(; j < left.length; j++) result[m++] = left[j]; for(; k < right.length; k++) result[m++] = right[k]; return result; }</lang>
Ada
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. <lang ada>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;</lang>
<lang ada>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;</lang> The following code provides an usage example for the generic package defined above. <lang ada>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;</lang>
- Output:
1 5 2 7 3 9 4 6 1 2 3 4 5 6 7 9
ALGOL 68
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. <lang algol68>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));</lang>
- Output:
abcdefghiijklmnopqrstuvwxyz
Optimised version:
- avoids FLEX array copies and manipulations
- avoids type DATA memory copies, useful in cases where DATA is a large STRUCT
<lang algol68>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)</lang>
- Output:
abcdefghiijklmnopqrstuvwxyz
AppleScript
<lang applescript>(*
In-place, iterative binary merge sort
Merge sort algorithm: John von Neumann, 1945.
Convenience terminology used here:
run: one of two adjacent source-list ranges containing ordered items for merging.
block: range in the destination list to which two runs are merged.
- )
on mergeSort(theList, l, r) -- Sort items l thru r of theList.
set listLength to (count theList)
if (listLength < 2) then return
-- Convert negative and/or transposed range indices.
if (l < 0) then set l to listLength + l + 1
if (r < 0) then set r to listLength + r + 1
if (l > r) then set {l, r} to {r, l}
-- Script object containing the input list and the sort range indices.
script main
property lst : theList
property l : missing value
property r : missing value
end script
set {main's l, main's r} to {l, r}
-- Just swap adjacent items as necessary on the first pass.
-- (Short insertion sorts would be better, to create larger initial runs.)
repeat with j from (l + 1) to r by 2
set i to j - 1
set lv to main's lst's item i
set rv to main's lst's item j
if (lv > rv) then
set main's lst's item i to rv
set main's lst's item j to lv
end if
end repeat
set rangeLength to r - l + 1
if (rangeLength < 3) then return -- That's all if fewer than three items to sort.
-- Script object to alternate with the one above as the source and destination for the
-- merges. Its list need only contain the items from the sort range as ordered so far.
script aux
property lst : main's lst's items l thru r
property l : 1
property r : rangeLength
end script
-- Work out how many merging passes will be needed and set the script objects' initial
-- source and destination roles so that the final pass will merge back to the original list.
set passesToDo to 0
set blockSize to 2
repeat while (blockSize < rangeLength)
set passesToDo to passesToDo + 1
set blockSize to blockSize + blockSize
end repeat
set {srce, dest} to {{main, aux}, {aux, main}}'s item (passesToDo mod 2 + 1)
-- Do the remaining passes, doubling the run and block sizes on each pass.
-- (The end set in each pass will usually be truncated.)
set blockSize to 2
repeat passesToDo times -- Per pass.
set runSize to blockSize
set blockSize to blockSize + blockSize
set k to (dest's l) - 1 -- Destination traversal index.
repeat with leftStart from srce's l to srce's r by blockSize -- Per merge.
set blockEnd to k + blockSize
if (blockEnd comes after dest's r) then set blockEnd to dest's r
set i to leftStart -- Left run traversal index.
set leftEnd to leftStart + runSize - 1
if (leftEnd comes before srce's r) then
set j to leftEnd + 1 -- Right run traversal index.
set rightEnd to leftEnd + runSize
if (rightEnd comes after srce's r) then set rightEnd to srce's r
-- Merge process:
set lv to srce's lst's item i
set rv to srce's lst's item j
repeat with k from (k + 1) to blockEnd
if (lv > rv) then
set dest's lst's item k to rv
if (j = rightEnd) then exit repeat -- Right run used up.
set j to j + 1
set rv to srce's lst's item j
else
set dest's lst's item k to lv
if (i = leftEnd) then -- Left run used up.
set i to j
exit repeat
end if
set i to i + 1
set lv to srce's lst's item i
end if
end repeat
end if
-- Use up the remaining items from the not-yet-exhausted run.
repeat with k from (k + 1) to blockEnd
set dest's lst's item k to srce's lst's item i
set i to i + 1
end repeat
end repeat -- Per merge.
-- Switch source and destination scripts for the next pass.
tell srce
set srce to dest
set dest to it
end tell
end repeat -- Per pass.
return -- nothing
end mergeSort property sort : mergeSort
-- Demo: local aList set aList to {22, 15, 98, 82, 22, 4, 58, 70, 80, 38, 49, 48, 46, 54, 93, 8, 54, 2, 72, 84, 86, 76, 53, 37, 90} sort(aList, 1, -1) -- Sort items 1 thru -1 of aList. return aList</lang>
- Output:
<lang applescript>{2, 4, 8, 15, 22, 22, 37, 38, 46, 48, 49, 53, 54, 54, 58, 70, 72, 76, 80, 82, 84, 86, 90, 93, 98}</lang>
ARM Assembly
<lang ARM Assembly> /* 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" </lang>
Astro
<lang python>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</lang>
ATS
A mergesort for linear lists
This algorithm modifies the links in the list, rather than allocate new cons-pairs. It requires no garbage collector.
<lang ats>(*------------------------------------------------------------------*) (* Mergesort in ATS2, for linear lists. *) (*------------------------------------------------------------------*)
- include "share/atspre_staload.hats"
staload UN = "prelude/SATS/unsafe.sats"
- define NIL list_vt_nil ()
- define :: list_vt_cons
(*------------------------------------------------------------------*)
(* Destructive stable merge. *) extern fun {a : vt@ype} list_vt_merge {m, n : int}
(lst1 : list_vt (a, m),
lst2 : list_vt (a, n))
:<!wrt> list_vt (a, m + n)
(* Order predicate for list_vt_merge. You have to implement this to
suit your needs. *)
extern fun {a : vt@ype} list_vt_merge$lt : (&a, &a) -<> bool
(* Destructive stable mergesort. *) extern fun {a : vt@ype} list_vt_mergesort {n : int}
(lst : list_vt (a, n)) :<!wrt> list_vt (a, n)
(* Order predicate for list_vt_mergesort. You have to implement this
to suit your needs. *)
extern fun {a : vt@ype} list_vt_mergesort$lt : (&a, &a) -<> bool
(*------------------------------------------------------------------*)
implement {a} list_vt_merge {m, n} (lst1, lst2) =
let macdef lt = list_vt_merge$lt<a>
fun
loop {m, n : nat} .<m + n>.
(lst1 : list_vt (a, m),
lst2 : list_vt (a, n),
lst_merged : &List_vt a? >> list_vt (a, m + n))
:<!wrt> void =
case+ lst1 of
| ~ NIL => lst_merged := lst2
| @ elem1 :: tail1 =>
begin
case+ lst2 of
| ~ NIL =>
let
prval () = fold@ lst1
in
lst_merged := lst1
end
| @ elem2 :: tail2 =>
if ~(elem2 \lt elem1) then
let
val () = lst_merged := lst1
prval () = fold@ lst2
val () = loop (tail1, lst2, tail1)
prval () = fold@ lst_merged
in
end
else
let
val () = lst_merged := lst2
prval () = fold@ lst1
val () = loop (lst1, tail2, tail2)
prval () = fold@ lst_merged
in
end
end
prval () = lemma_list_vt_param lst1 (* Proves 0 <= m. *)
prval () = lemma_list_vt_param lst2 (* Proves 0 <= n. *)
prval () = prop_verify {0 <= m} ()
prval () = prop_verify {0 <= n} ()
var lst_merged : List_vt a?
val () = loop {m, n} (lst1, lst2, lst_merged)
in
lst_merged
end
(*------------------------------------------------------------------*)
implement {a} list_vt_mergesort {n} lst =
let
implement
list_vt_merge$lt<a> (x, y) =
list_vt_mergesort$lt<a> (x, y)
(* You can make SMALL larger than 1 and write small_sort as a fast
stable sort for small lists. *)
#define SMALL 1
fn
small_sort {m : pos | m <= SMALL}
(lst : list_vt (a, m),
m : int m)
:<!wrt> list_vt (a, m) =
lst
fun
recurs {m : pos} .<m>.
(lst : list_vt (a, m),
m : int m)
:<!wrt> list_vt (a, m) =
if m <= SMALL then
small_sort (lst, m)
else
let
prval () = prop_verify {2 <= m} ()
val i = m / 2
val @(lst1, lst2) = list_vt_split_at<a> (lst, i)
val lst1 = recurs (lst1, i)
val lst2 = recurs (lst2, m - i)
in
list_vt_merge<a> (lst1, lst2)
end
prval () = lemma_list_vt_param lst (* Proves 0 <= n. *)
prval () = prop_verify {0 <= n} ()
in
case+ lst of
| NIL => lst
| _ :: _ => recurs (lst, length lst)
end
(*------------------------------------------------------------------*)
extern fun list_vt_mergesort_int {n : int}
(lst : list_vt (int, n)) :<!wrt> list_vt (int, n)
implement list_vt_mergesort_int {n} lst =
let
implement
list_vt_mergesort$lt<int> (x, y) =
x < y
in
list_vt_mergesort<int> {n} lst
end
implement main0 () =
let
val lst = $list_vt (22, 15, 98, 82, 22, 4, 58, 70, 80, 38, 49,
48, 46, 54, 93, 8, 54, 2, 72, 84, 86, 76,
53, 37, 90)
val () = println! ("before : ", $UN.castvwtp1{List int} lst)
val lst = list_vt_mergesort_int lst
val () = println! ("after : ", $UN.castvwtp1{List int} lst)
in
list_vt_free<int> lst
end
(*------------------------------------------------------------------*)</lang>
- Output:
$ patscc -O3 -DATS_MEMALLOC_LIBC mergesort_task_for_list_vt.dats && ./a.out before : 22, 15, 98, 82, 22, 4, 58, 70, 80, 38, 49, 48, 46, 54, 93, 8, 54, 2, 72, 84, 86, 76, 53, 37, 90 after : 2, 4, 8, 15, 22, 22, 37, 38, 46, 48, 49, 53, 54, 54, 58, 70, 72, 76, 80, 82, 84, 86, 90, 93, 98
Footnote: Rather than directly write a mergesort for "ordinary" non-linear lists, I would write a routine to do the following:
- make a copy of the list;
- cast the copy to a linear list;
- sort the linear list;
- cast the result to non-linear list, and return the casted result.
This way, new cons-pairs are allocated only once.
The same thing can be done in other languages, of course. An interesting thing about this ATS implementation, though, is it proves the result is of the same length as the input. It does not, however, prove that the result satisfies the order predicate.
A mergesort for non-linear lists of integers, guaranteeing a sorted result
The following program not only sorts a list of integers, but verifies that the result is sorted. It is the simplest implementation I could think of that does that. It works by having a special kind of list that can be consed only in sorted order.
The length of the result also is verified. However, there is no proof that the result contains the same data as the input.
<lang ats>//-------------------------------------------------------------------- // // A mergesort for 32-bit signed integers. // //--------------------------------------------------------------------
- include "share/atspre_staload.hats"
(*------------------------------------------------------------------*)
- define ENTIER_MAX 2147483647
(* We do not include the most negative two's-complement number. *) stadef entier (i : int) = ~ENTIER_MAX <= i && i <= ENTIER_MAX sortdef entier = {i : int | entier i}
typedef entier (i : int) = [entier i] int i typedef entier = [i : entier] entier i
datatype sorted_entier_list (int, int) = | sorted_entier_list_nil (0, ENTIER_MAX) | {n : nat}
{i, j : entier | ~(j < i)}
sorted_entier_list_cons (n + 1, i) of
(entier i, sorted_entier_list (n, j))
typedef sorted_entier_list (n : int) =
[i : entier] sorted_entier_list (n, i)
typedef sorted_entier_list =
[n : int] sorted_entier_list n
infixr ( :: ) :::
- define NIL list_nil ()
- define :: list_cons
- define SNIL sorted_entier_list_nil ()
- define ::: sorted_entier_list_cons
(*------------------------------------------------------------------*)
extern prfn lemma_sorted_entier_list_param
{n : int}
(lst : sorted_entier_list n)
:<prf> [0 <= n] void
extern fn sorted_entier_list_length
{n : int}
(lst : sorted_entier_list n)
:<> [0 <= n] int n
extern fn sorted_entier_list_merge
{m, n : int}
{i, j : entier}
(lst1 : sorted_entier_list (m, i),
lst2 : sorted_entier_list (n, j))
:<> sorted_entier_list (m + n, min (i, j))
extern fn entier_list_mergesort
{n : int}
(lst : list (entier, n)) (* An ordinary list. *)
:<!wrt> sorted_entier_list n
extern fn sorted_entier_list2list
{n : int}
(lst : sorted_entier_list n)
:<> list (entier, n)
overload length with sorted_entier_list_length overload merge with sorted_entier_list_merge overload mergesort with entier_list_mergesort overload to_list with sorted_entier_list2list
(*------------------------------------------------------------------*)
primplement lemma_sorted_entier_list_param {n} lst =
case+ lst of | SNIL => () | _ ::: _ => ()
implement sorted_entier_list_length {n} lst =
(* This implementation is tail-recursive. *)
let
fun
count {m : nat | m <= n} .<n - m>.
(lst : sorted_entier_list (n - m),
m : int m)
:<> [0 <= n] int n =
case+ lst of
| SNIL => m
| _ ::: tail => count {m + 1} (tail, succ m)
prval () = lemma_sorted_entier_list_param lst in count (lst, 0) end
implement sorted_entier_list_merge (lst1, lst2) =
(* This implementation is *NOT* tail recursive. It will use O(m+n)
stack space. *)
let
fun
recurs {m, n : nat}
{i, j : entier} .<m + n>.
(lst1 : sorted_entier_list (m, i),
lst2 : sorted_entier_list (n, j))
:<> sorted_entier_list (m + n, min (i, j)) =
case+ lst1 of
| SNIL => lst2
| i ::: tail1 =>
begin
case+ lst2 of
| SNIL => lst1
| j ::: tail2 =>
if ~(j < i) then
i ::: recurs (tail1, lst2)
else
j ::: recurs (lst1, tail2)
end
prval () = lemma_sorted_entier_list_param lst1 prval () = lemma_sorted_entier_list_param lst2 in recurs (lst1, lst2) end
implement entier_list_mergesort lst =
let
fun
recurs {m : nat} .<m>.
(lst : list (entier, m),
m : int m)
:<!wrt> sorted_entier_list m =
if m = 1 then
let
val+ head :: NIL = lst
in
head ::: SNIL
end
else if m = 0 then
SNIL
else
let
val m_left = m \g1int_ndiv 2
val m_right = m - m_left
val @(left, right) = list_split_at (lst, m_left)
val left = recurs (list_vt2t left, m_left)
and right = recurs (right, m_right)
in
left \merge right
end
prval () = lemma_list_param lst in recurs (lst, length lst) end
implement sorted_entier_list2list lst =
(* This implementation is *NOT* tail recursive. It will use O(n)
stack space. *)
let
fun
recurs {n : nat} .<n>.
(lst : sorted_entier_list n)
:<> list (entier, n) =
case+ lst of
| SNIL => NIL
| head ::: tail => head :: recurs tail
prval () = lemma_sorted_entier_list_param lst in recurs lst end
(*------------------------------------------------------------------*)
fn print_Int_list
{n : int}
(lst : list (Int, n))
: void =
let
fun
loop {n : nat} .<n>.
(lst : list (Int, n))
: void =
case+ lst of
| NIL => ()
| head :: tail =>
begin
print! (" ");
print! (head);
loop tail
end
prval () = lemma_list_param lst
in
loop lst
end
implement main0 () =
let
val example_list =
$list (22, 15, 98, 82, 22, 4, 58, 70, 80, 38, 49, 48, 46, 54,
93, 8, 54, 2, 72, 84, 86, 76, 53, 37, 90)
val sorted_list = mergesort example_list
in
print! ("unsorted ");
print_Int_list example_list;
println! ();
print! ("sorted ");
print_Int_list (to_list sorted_list);
println! ()
end
(*------------------------------------------------------------------*)</lang>
- Output:
patscc -O3 -DATS_MEMALLOC_GCBDW mergesort_task_verified.dats -lgc && ./a.out unsorted 22 15 98 82 22 4 58 70 80 38 49 48 46 54 93 8 54 2 72 84 86 76 53 37 90 sorted 2 4 8 15 22 22 37 38 46 48 49 53 54 54 58 70 72 76 80 82 84 86 90 93 98
Postscript. One might try adding a line such as
val x = 3 ::: 2 ::: SNIL
to the program and see that the compiler will report it as erroneous, on grounds that "2 is not less than 3" is unsatisfied.
AutoHotkey_L
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 <lang AutoHotkey>#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
}</lang>
AutoHotkey
Contributed by Laszlo on the ahk forum <lang AutoHotkey>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)
}
}
}</lang>
BBC BASIC
<lang BBCBASIC>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</lang> Usage would look something like this example which sorts a series of 1000 random integers: <lang BBCBASIC>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</lang>
BCPL
<lang bcpl>get "libhdr"
let mergesort(A, n) be if n >= 2 $( let m = n / 2
mergesort(A, m) mergesort(A+m, n-m) merge(A, n, m)
$) and merge(A, n, m) be $( let i, j = 0, m
let x = getvec(n)
for k=0 to n-1
x!k := A!valof
test j~=n & (i=m | A!j < A!i)
$( j := j + 1
resultis j - 1
$)
else
$( i := i + 1
resultis i - 1
$)
for i=0 to n-1 do a!i := x!i
freevec(x)
$)
let write(s, A, len) be $( writes(s)
for i=0 to len-1 do writed(A!i, 4)
wrch('*N')
$)
let start() be $( let array = table 4,65,2,-31,0,99,2,83,782,1
let length = 10
write("Before: ", array, length)
mergesort(array, length)
write("After: ", array, length)
$)</lang>
- Output:
Before: 4 65 2 -31 0 99 2 83 782 1 After: -31 0 1 2 2 4 65 83 99 782
C
<lang c>#include <stdio.h>
- include <stdlib.h>
void merge (int *a, int n, int m) {
int i, j, k;
int *x = malloc(n * sizeof (int));
for (i = 0, j = m, k = 0; k < n; k++) {
x[k] = j == n ? a[i++]
: i == m ? a[j++]
: a[j] < a[i] ? a[j++]
: a[i++];
}
for (i = 0; i < n; i++) {
a[i] = x[i];
}
free(x);
}
void merge_sort (int *a, int n) {
if (n < 2)
return;
int m = n / 2;
merge_sort(a, m);
merge_sort(a + m, n - m);
merge(a, n, m);
}
int main () {
int a[] = {4, 65, 2, -31, 0, 99, 2, 83, 782, 1};
int n = sizeof a / sizeof a[0];
int i;
for (i = 0; i < n; i++)
printf("%d%s", a[i], i == n - 1 ? "\n" : " ");
merge_sort(a, n);
for (i = 0; i < n; i++)
printf("%d%s", a[i], i == n - 1 ? "\n" : " ");
return 0;
}</lang>
- Output:
4 65 2 -31 0 99 2 83 782 1 -31 0 1 2 2 4 65 83 99 782
C#
<lang csharp>namespace RosettaCode {
using System;
public class MergeSort<T> where T : IComparable {
#region Constants
public const UInt32 INSERTION_LIMIT_DEFAULT = 12;
public const Int32 MERGES_DEFAULT = 6;
#endregion
#region Properties
public UInt32 InsertionLimit { get; }
protected UInt32[] Positions { get; set; }
private Int32 merges;
public Int32 Merges {
get { return merges; }
set {
// A minimum of 2 merges are required
if (value > 1)
merges = value;
else
throw new ArgumentOutOfRangeException($"value = {value} must be greater than one", nameof(Merges));
if (Positions == null || Positions.Length != merges)
Positions = new UInt32[merges];
}
}
#endregion
#region Constructors
public MergeSort(UInt32 insertionLimit, Int32 merges) {
InsertionLimit = insertionLimit;
Merges = merges;
}
public MergeSort()
: this(INSERTION_LIMIT_DEFAULT, MERGES_DEFAULT) {
}
#endregion
#region Sort Methods
public void Sort(T[] entries) {
// Allocate merge buffer
var entries2 = new T[entries.Length];
Sort(entries, entries2, 0, entries.Length - 1);
}
// Top-Down K-way Merge Sort
public void Sort(T[] entries1, T[] entries2, Int32 first, Int32 last) {
var length = last + 1 - first;
if (length < 2) return;
if (length < Merges || length < InsertionLimit) {
InsertionSort<T>.Sort(entries1, first, last);
return;
}
var left = first;
var size = ceiling(length, Merges);
for (var remaining = length; remaining > 0; remaining -= size, left += size) {
var right = left + Math.Min(remaining, size) - 1;
Sort(entries1, entries2, left, right);
}
Merge(entries1, entries2, first, last);
Array.Copy(entries2, first, entries1, first, length);
}
#endregion
#region Merge Methods
public void Merge(T[] entries1, T[] entries2, Int32 first, Int32 last) {
Array.Clear(Positions, 0, Merges);
// This implementation has a quadratic time dependency on the number of merges
for (var index = first; index <= last; index++)
entries2[index] = remove(entries1, first, last);
}
private T remove(T[] entries, Int32 first, Int32 last) {
T entry = default;
Int32? found = default;
var length = last + 1 - first;
var index = 0;
var left = first;
var size = ceiling(length, Merges);
for (var remaining = length; remaining > 0; remaining -= size, left += size, index++) {
var position = Positions[index];
if (position < Math.Min(remaining, size)) {
var next = entries[left + position];
if (!found.HasValue || entry.CompareTo(next) > 0) {
found = index;
entry = next;
}
}
}
// Remove entry
Positions[found.Value]++;
return entry;
}
#endregion
#region Math Methods
private static Int32 ceiling(Int32 numerator, Int32 denominator) {
return (numerator + denominator - 1) / denominator;
}
#endregion
}
#region Insertion Sort
static class InsertionSort<T> where T : IComparable {
public static void Sort(T[] entries, Int32 first, Int32 last) {
for (var next = first + 1; next <= last; next++)
insert(entries, first, next);
}
/// <summary>Bubble next entry up to its sorted location, assuming entries[first:next - 1] are already sorted.</summary>
private static void insert(T[] entries, Int32 first, Int32 next) {
var entry = entries[next];
while (next > first && entries[next - 1].CompareTo(entry) > 0)
entries[next] = entries[--next];
entries[next] = entry;
}
}
#endregion
}</lang> Example: <lang csharp> 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));
}
}</lang>
- Output:
1 2 2 3 4 5 6 6 7
C++
<lang cpp>#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>());
}</lang>
Clojure
<lang lisp> (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)))))
</lang>
COBOL
Cobol cannot do recursion, so this version simulates recursion. The working storage is therefore pretty complex, so I have shown the whole program, not just the working procedure division parts. <lang COBOL> 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.</lang>
CoffeeScript
<lang coffeescript># This is a simple version of mergesort that returns brand-new arrays.
- A more sophisticated version would do more in-place optimizations.
merge_sort = (arr) ->
if arr.length <= 1
return (elem for elem in arr)
m = Math.floor(arr.length / 2)
arr1 = merge_sort(arr.slice 0, m)
arr2 = merge_sort(arr.slice m)
result = []
p1 = p2 = 0
while true
if p1 >= arr1.length
if p2 >= arr2.length
return result
result.push arr2[p2]
p2 += 1
else if p2 >= arr2.length or arr1[p1] < arr2[p2]
result.push arr1[p1]
p1 += 1
else
result.push arr2[p2]
p2 += 1
do ->
console.log merge_sort [2,4,6,8,1,3,5,7,9,10,11,0,13,12]</lang>
- Output:
> coffee mergesort.coffee [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
Common Lisp
<lang lisp>(defun merge-sort (result-type sequence predicate)
(let ((split (floor (length sequence) 2)))
(if (zerop split)
(copy-seq sequence)
(merge result-type (merge-sort result-type (subseq sequence 0 split) predicate)
(merge-sort result-type (subseq sequence split) predicate)
predicate))))</lang>
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
<lang 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]</lang>
Curry
Copied from Curry: Example Programs <lang curry>-- 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</lang>
D
Arrays only, not in-place. <lang d>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;
}</lang>
Alternative Version
This in-place version allocates the auxiliary memory on the stack, making life easier for the garbage collector, but with risk of stack overflow (same output): <lang d>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);
}</lang>
Dart
<lang dart>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;
}
}</lang>
Delphi
See Pascal.
E
<lang e>def merge(var xs :List, var ys :List) {
var result := []
while (xs =~ [x] + xr && ys =~ [y] + yr) {
if (x <= y) {
result with= x
xs := xr
} else {
result with= y
ys := yr
}
}
return result + xs + ys
}
def sort(list :List) {
if (list.size() <= 1) { return list }
def split := list.size() // 2
return merge(sort(list.run(0, split)),
sort(list.run(split)))
}</lang>
EasyLang
<lang>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[]</lang>
Eiffel
<lang Eiffel> class MERGE_SORT [G -> COMPARABLE]
create sort
feature
sort (ar: ARRAY [G]) -- Sorted array in ascending order. require ar_not_empty: not ar.is_empty do create sorted_array.make_empty mergesort (ar, 1, ar.count) sorted_array := ar ensure sorted_array_not_empty: not sorted_array.is_empty sorted: is_sorted (sorted_array, 1, sorted_array.count) end
sorted_array: ARRAY [G]
feature {NONE}
mergesort (ar: ARRAY [G]; l, r: INTEGER) -- Sorting part of mergesort. local m: INTEGER do if l < r then m := (l + r) // 2 mergesort (ar, l, m) mergesort (ar, m + 1, r) merge (ar, l, m, r) end end
merge (ar: ARRAY [G]; l, m, r: INTEGER) -- Merge part of mergesort. require positive_index_l: l >= 1 positive_index_m: m >= 1 positive_index_r: r >= 1 ar_not_empty: not ar.is_empty local merged: ARRAY [G] h, i, j, k: INTEGER do i := l j := m + 1 k := l create merged.make_filled (ar [1], 1, ar.count) from until i > m or j > r loop if ar.item (i) <= ar.item (j) then merged.force (ar.item (i), k) i := i + 1 elseif ar.item (i) > ar.item (j) then merged.force (ar.item (j), k) j := j + 1 end k := k + 1 end if i > m then from h := j until h > r loop merged.force (ar.item (h), k + h - j) h := h + 1 end elseif j > m then from h := i until h > m loop merged.force (ar.item (h), k + h - i) h := h + 1 end end from h := l until h > r loop ar.item (h) := merged.item (h) h := h + 1 end ensure is_partially_sorted: is_sorted (ar, l, r) end
is_sorted (ar: ARRAY [G]; l, r: INTEGER): BOOLEAN -- Is 'ar' sorted in ascending order? require ar_not_empty: not ar.is_empty l_in_range: l >= 1 r_in_range: r <= ar.count local i: INTEGER do Result := True from i := l until i = r loop if ar [i] > ar [i + 1] then Result := False end i := i + 1 end end
end </lang> Test: <lang Eiffel> 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 </lang>
- Output:
unsorted 2 5 66 -2 0 7 sorted -2 0 2 5 7 66
Elixir
<lang elixir>defmodule Sort do
def merge_sort(list) when length(list) <= 1, do: list
def merge_sort(list) do
{left, right} = Enum.split(list, div(length(list), 2))
:lists.merge( merge_sort(left), merge_sort(right))
end
end</lang> Example:
iex(10)> Sort.merge_sort([5,3,9,4,1,6,8,2,7]) [1, 2, 3, 4, 5, 6, 7, 8, 9]
Erlang
Below are two versions. Both take advantage of built-in Erlang functions, lists:split and list:merge. The multi-process version spawns a new process each time it splits. This was slightly faster on a test system with only two cores, so it may not be the best implementation, however it does illustrate how easy it can be to add multi-threaded/process capabilities to a program.
Single-threaded version: <lang erlang>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)).</lang>
Multi-process version: <lang erlang>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([]).</lang>
another multi-process version (number of processes == number of processor cores):
<lang erlang>
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.
</lang>
ERRE
<lang ERRE> PROGRAM MERGESORT_DEMO
! Example of merge sort usage.
CONST SIZE%=100,S1%=50
DIM DTA%[SIZE%],FH%[S1%],STACK%[20,2]
PROCEDURE MERGE(START%,MIDDLE%,ENDS%)
LOCAL FHSIZE%
FHSIZE%=MIDDLE%-START%+1
FOR I%=0 TO FHSIZE%-1 DO
FH%[I%]=DTA%[START%+I%]
END FOR
I%=0 J%=MIDDLE%+1 K%=START%
REPEAT
IF FH%[I%]<=DTA%[J%] THEN
DTA%[K%]=FH%[I%]
I%=I%+1
K%=K%+1
ELSE
DTA%[K%]=DTA%[J%]
J%=J%+1
K%=K%+1
END IF
UNTIL I%=FHSIZE% OR J%>ENDS%
WHILE I%<FHSIZE% DO
DTA%[K%]=FH%[I%]
I%=I%+1
K%=K%+1
END WHILE
END PROCEDURE
PROCEDURE MERGE_SORT(LEV->LEV)
! ***************************************************************** ! This procedure Merge Sorts the chunk of DTA% bounded by ! Start% & Ends%. ! *****************************************************************
LOCAL MIDDLE%
IF ENDS%=START% THEN LEV=LEV-1 EXIT PROCEDURE END IF
IF ENDS%-START%=1 THEN
IF DTA%[ENDS%]<DTA%[START%] THEN
SWAP(DTA%[START%],DTA%[ENDS%])
END IF
LEV=LEV-1
EXIT PROCEDURE
END IF
MIDDLE%=START%+(ENDS%-START%)/2
STACK%[LEV,0]=START% STACK%[LEV,1]=ENDS% STACK%[LEV,2]=MIDDLE% START%=START% ENDS%=MIDDLE% MERGE_SORT(LEV+1->LEV) START%=STACK%[LEV,0] ENDS%=STACK%[LEV,1] MIDDLE%=STACK%[LEV,2]
STACK%[LEV,0]=START% STACK%[LEV,1]=ENDS% STACK%[LEV,2]=MIDDLE% START%=MIDDLE%+1 ENDS%=ENDS% MERGE_SORT(LEV+1->LEV) START%=STACK%[LEV,0] ENDS%=STACK%[LEV,1] MIDDLE%=STACK%[LEV,2]
MERGE(START%,MIDDLE%,ENDS%)
LEV=LEV-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 </lang>
Euphoria
<lang euphoria>function merge(sequence left, sequence right)
sequence result
result = {}
while length(left) > 0 and length(right) > 0 do
if compare(left[1], right[1]) <= 0 then
result = append(result, left[1])
left = left[2..$]
else
result = append(result, right[1])
right = right[2..$]
end if
end while
return result & left & right
end function
function mergesort(sequence m)
sequence left, right
integer middle
if length(m) <= 1 then
return m
else
middle = floor(length(m)/2)
left = mergesort(m[1..middle])
right = mergesort(m[middle+1..$])
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)</lang>
- Output:
{385,599,284,650,457,804,724,300,434,722}
{284,300,385,434,457,599,650,722,724,804}
F#
<lang fsharp>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)</lang>
Factor
<lang factor>: mergestep ( accum seq1 seq2 -- accum seq1 seq2 ) 2dup [ first ] bi@ < [ [ [ first ] [ rest-slice ] bi [ suffix ] dip ] dip ] [ [ first ] [ rest-slice ] bi [ swap [ suffix ] dip ] dip ] if ;
- merge ( seq1 seq2 -- merged )
[ { } ] 2dip [ 2dup [ length 0 > ] bi@ and ] [ mergestep ] while append append ;
- mergesort ( seq -- sorted )
dup length 1 > [ dup length 2 / floor [ head ] [ tail ] 2bi [ mergesort ] bi@ merge ] [ ] if ;</lang>
<lang factor>( scratchpad ) { 4 2 6 5 7 1 3 } mergesort . { 1 2 3 4 5 6 7 }</lang>
Forth
This is an in-place mergesort which works on arrays of integers. <lang forth>: 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</lang>
Fortran
<lang fortran> 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
</lang>
FreeBASIC
Uses 'top down' C-like algorithm in Wikipedia article: <lang freebasic>' 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</lang>
- 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
<lang funl>def
sort( [] ) = [] sort( [x] ) = [x] sort( xs ) = val (l, r) = xs.splitAt( xs.length()\2 ) merge( sort(l), sort(r) )
merge( [], xs ) = xs merge( xs, [] ) = xs merge( x:xs, y:ys ) | x <= y = x : merge( xs, y:ys ) | otherwise = y : merge( x:xs, ys )
println( sort([94, 37, 16, 56, 72, 48, 17, 27, 58, 67]) ) println( sort(['Sofía', 'Alysha', 'Sophia', 'Maya', 'Emma', 'Olivia', 'Emily']) )</lang>
- Output:
[16, 17, 27, 37, 48, 56, 58, 67, 72, 94] [Alysha, Emily, Emma, Maya, Olivia, Sofía, Sophia]
Go
<lang go>package main
import "fmt"
var a = []int{170, 45, 75, -90, -802, 24, 2, 66} var s = make([]int, len(a)/2+1) // scratch space for merge step
func main() {
fmt.Println("before:", a)
mergeSort(a)
fmt.Println("after: ", a)
}
func mergeSort(a []int) {
if len(a) < 2 {
return
}
mid := len(a) / 2
mergeSort(a[:mid])
mergeSort(a[mid:])
if a[mid-1] <= a[mid] {
return
}
// merge step, with the copy-half optimization
copy(s, a[:mid])
l, r := 0, mid
for i := 0; ; i++ {
if s[l] <= a[r] {
a[i] = s[l]
l++
if l == mid {
break
}
} else {
a[i] = a[r]
r++
if r == len(a) {
copy(a[i+1:], s[l:mid])
break
}
}
}
return
}</lang>
Groovy
This is the standard algorithm, except that in the looping phase of the merge we work backwards through the left and right lists to construct the merged list, to take advantage of the Groovy List.pop() method. However, this results in a partially merged list in reverse sort order; so we then reverse it to put in back into correct order. This could play havoc with the sort stability, but we compensate by picking aggressively from the right list (ties go to the right), rather than aggressively from the left as is done in the standard algorithm. <lang groovy>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)
}</lang> Test: <lang groovy>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]))</lang> The presence of decimal and integer versions of the same numbers, demonstrates, but of course does not prove, that the sort remains stable.
- Output:
.............................................................[4, 12, 14, 23, 24, 24, 31, 35, 38, 46, 51, 57, 57, 58, 76, 78, 89, 92, 95, 97, 99] ....................................................................[0, 1, 4, 5, 7, 8, 12, 14, 18, 20, 31, 33, 44, 62, 70, 73, 75, 76, 78, 81, 82, 84, 88] ....[1, 10, 10.0, 10.00] ....[1, 10, 10.00, 10.0] ....[1, 10.0, 10, 10.00] ....[1, 10.0, 10.00, 10] ....[1, 10.00, 10, 10.0] ....[1, 10.00, 10.0, 10]
Tail recursion version
It is possible to write a version based on tail recursion, similar to that written in Haskell, OCaml or F#. This version also takes into account stack overflow problems induced by recursion for large lists using closure trampolines: <lang groovy>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] </lang>
which uses List.collate(), alternatively one could write a purely recursive split() closure as:
<lang groovy>
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() </lang>
Haskell
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. <lang haskell>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)</lang>
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 <lang haskell>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)</lang> 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: <lang haskell>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</lang>
In this code, mergeAll, mergePairs, and merge are as above, except using the specialized cmp function in merge.
Icon and Unicon
<lang Icon>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</lang>
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
<lang io>List do (
merge := method(lst1, lst2,
result := list()
while(lst1 isNotEmpty or lst2 isNotEmpty,
if(lst1 first <= lst2 first) then(
result append(lst1 removeFirst)
) else (
result append(lst2 removeFirst)
)
)
result)
mergeSort := method(
if (size > 1) then(
half_size := (size / 2) ceil
return merge(slice(0, half_size) mergeSort,
slice(half_size, size) mergeSort)
) else (return self)
)
mergeSortInPlace := method(
copy(mergeSort)
)
)
lst := list(9, 5, 3, -1, 15, -2) lst mergeSort println # ==> list(-2, -1, 3, 5, 9, 15) lst mergeSortInPlace println # ==> list(-2, -1, 3, 5, 9, 15)</lang>
Isabelle
<lang Isabelle>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 </lang>
J
Recursive Solution <lang j>mergesort=: {{
if. 2>#y do. y return.end.
middle=. <.-:#y
X=. mergesort middle{.y
Y=. mergesort middle}.y
X merge Y
}}
merge=: Template:R=. y</lang>
Non-Recursive Solution
(This uses the same merge):
<lang J>mergesort=: {{
stride=. 1
N=. #r=. y
while. stride < N do.
stride=. 2*mid=. stride
r=. ;(-stride) (mid&}. <@merge (mid<.#) {.])\ r
end.
}}</lang>
Example use: <lang J> mergesort 18 2 8 1 5 14 9 19 11 13 16 0 3 10 17 15 12 4 7 6 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19</lang>
But don't forget to use J's primitives /: or \: if you really need a sort-function.
Java
<lang java5>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;
}
}</lang>
JavaScript
<lang javascript>function merge(left, right, arr) {
var a = 0;
while (left.length && right.length) {
arr[a++] = (right[0] < left[0]) ? right.shift() : left.shift();
}
while (left.length) {
arr[a++] = left.shift();
}
while (right.length) {
arr[a++] = right.shift();
}
}
function mergeSort(arr) {
var len = arr.length;
if (len === 1) { return; }
var mid = Math.floor(len / 2),
left = arr.slice(0, mid),
right = arr.slice(mid);
mergeSort(left); mergeSort(right); merge(left, right, arr);
}
var arr = [1, 5, 2, 7, 3, 9, 4, 6, 8]; mergeSort(arr); // arr will now: 1, 2, 3, 4, 5, 6, 7, 8, 9
// here is improved faster version, also often faster than QuickSort!
function mergeSort2(a) {
if (a.length <= 1) return const mid = Math.floor(a.length / 2), left = a.slice(0, mid), right = a.slice(mid) mergeSort2(left) mergeSort2(right) let ia = 0, il = 0, ir = 0 while (il < left.length && ir < right.length) a[ia++] = left[il] < right[ir] ? left[il++] : right[ir++] while (il < left.length) a[ia++] = left[il++] while (ir < right.length) a[ia++] = right[ir++]
} </lang>
jq
The sort function defined here will sort any JSON array. <lang jq># 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;</lang>
Example: <lang jq> ( [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)</lang>
- Output:
true true true
Julia
<lang julia>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))</lang>
- Output:
# unordered: [8, 6, 7, 1, -1, 0, -4, 7, -7, 0] -> ordered: [-7, -4, -1, 0, 0, 1, 6, 7, 7, 8]
Kotlin
<lang kotlin>fun mergeSort(list: List<Int>): List<Int> {
if (list.size <= 1) {
return list
}
val left = mutableListOf<Int>() val right = mutableListOf<Int>()
val middle = list.size / 2
list.forEachIndexed { index, number ->
if (index < middle) {
left.add(number)
} else {
right.add(number)
}
}
fun merge(left: List<Int>, right: List<Int>): List<Int> = mutableListOf<Int>().apply {
var indexLeft = 0
var indexRight = 0
while (indexLeft < left.size && indexRight < right.size) {
if (left[indexLeft] <= right[indexRight]) {
add(left[indexLeft])
indexLeft++
} else {
add(right[indexRight])
indexRight++
}
}
while (indexLeft < left.size) {
add(left[indexLeft])
indexLeft++
}
while (indexRight < right.size) {
add(right[indexRight])
indexRight++
}
}
return merge(mergeSort(left), mergeSort(right))
}
fun main(args: Array<String>) {
val numbers = listOf(5, 2, 3, 17, 12, 1, 8, 3, 4, 9, 7)
println("Unsorted: $numbers")
println("Sorted: ${mergeSort(numbers)}")
}</lang>
- 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
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.
<lang scheme> {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] </lang>
Liberty BASIC
<lang lb> 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</lang>
Logo
<lang 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</lang>
Logtalk
<lang logtalk>msort([], []) :- !. msort([X], [X]) :- !. msort([X, Y| Xs], Ys) :-
split([X, Y| Xs], X1s, X2s), msort(X1s, Y1s), msort(X2s, Y2s), merge(Y1s, Y2s, Ys).
split([], [], []). split([X| Xs], [X| Ys], Zs) :-
split(Xs, Zs, Ys).
merge([X| Xs], [Y| Ys], [X| Zs]) :-
X @=< Y, !, merge(Xs, [Y| Ys], Zs).
merge([X| Xs], [Y| Ys], [Y| Zs]) :-
X @> Y, !, merge([X | Xs], Ys, Zs).
merge([], Xs, Xs) :- !. merge(Xs, [], Xs).</lang>
Lua
<lang Lua>local function merge(left_container, left_container_begin, left_container_end, right_container, right_container_begin, right_container_end, result_container, result_container_begin, comparator) while left_container_begin <= left_container_end do if right_container_begin > right_container_end then for i = left_container_begin, left_container_end do result_container[result_container_begin] = left_container[i] result_container_begin = result_container_begin + 1 end
return end
if comparator(right_container[right_container_begin], left_container[left_container_begin]) then result_container[result_container_begin] = right_container[right_container_begin] right_container_begin = right_container_begin + 1 else result_container[result_container_begin] = left_container[left_container_begin] left_container_begin = left_container_begin + 1 end
result_container_begin = result_container_begin + 1 end
for i = right_container_begin, right_container_end do result_container[result_container_begin] = right_container[i] result_container_begin = result_container_begin + 1 end end
local function mergesort_impl(container, container_begin, container_end, comparator) local range_length = (container_end - container_begin) + 1 if range_length < 2 then return end local copy = {} local copy_len = 0
for it = container_begin, container_end do copy_len = copy_len + 1 copy[copy_len] = container[it] end
local middle = bit.rshift(range_length, 1) -- or math.floor(range_length / 2) mergesort_impl(copy, 1, middle, comparator) mergesort_impl(copy, middle + 1, copy_len, comparator) merge(copy, 1, middle, copy, middle + 1, copy_len, container, container_begin, comparator) end
local function mergesort_default_comparator(a, b) return a < b end
function table.mergesort(container, comparator) if not comparator then comparator = mergesort_default_comparator end
mergesort_impl(container, 1, #container, comparator) end</lang>
<lang Lua>function getLower(a,b)
local i,j=1,1
return function()
if not b[j] or a[i] and a[i]<b[j] then
i=i+1; return a[i-1]
else
j=j+1; return b[j-1]
end
end
end
function merge(a,b)
local res={}
for v in getLower(a,b) do res[#res+1]=v end
return 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</lang>
Lucid
[1] <lang lucid>msort(a) = if iseod(first next a) then a else merge(msort(b0),msort(b1)) fi
where
p = false fby not p;
b0 = a whenever p;
b1 = a whenever not p;
just(a) = ja
where
ja = a fby if iseod ja then eod else next a fi;
end;
merge(x,y) = if takexx then xx else yy fi
where
xx = (x) upon takexx;
yy = (y) upon not takexx;
takexx = if iseod(yy) then true elseif
iseod(xx) then false else xx <= yy fi;
end;
end;</lang>
M2000 Interpreter
<lang M2000 Interpreter> module checkit { \\ merge sort group merge { function sort(right as stack) { if len(right)<=1 then =right : exit left=.sort(stack up right, len(right) div 2 ) right=.sort(right) \\ stackitem(right) is same as stackitem(right,1) if stackitem(left, len(left))<=stackitem(right) then \\ !left take items from left for merging \\ so after this left and right became empty stacks =stack:=!left, !right exit end if =.merge(left, right) } function sortdown(right as stack) { if len(right)<=1 then =right : exit left=.sortdown(stack up right, len(right) div 2 ) right=.sortdown(right) if stackitem(left, len(left))>stackitem(right) then =stack:=!left, !right : exit end if =.mergedown(left, right) } \\ left and right are pointers to stack objects \\ here we pass by value the pointer not the data function merge(left as stack, right as stack) { result=stack while len(left) > 0 and len(right) > 0 if stackitem(left,1) <= stackitem(right) then result=stack:=!result, !(stack up left, 1) else result=stack:=!result, !(stack up right, 1) end if end while if len(right) > 0 then result=stack:= !result,!right if len(left) > 0 then result=stack:= !result,!left =result } function mergedown(left as stack, right as stack) { result=stack while len(left) > 0 and len(right) > 0 if stackitem(left,1) > stackitem(right) then result=stack:=!result, !(stack up left, 1) else result=stack:=!result, !(stack up right, 1) end if end while if len(right) > 0 then result=stack:= !result,!right if len(left) > 0 then result=stack:= !result,!left =result } } k=stack:=7, 5, 2, 6, 1, 4, 2, 6, 3 print merge.sort(k) print len(k)=0 ' we have to use merge.sort(stack(k)) to pass a copy of k
\\ input array (arr is a pointer to array) arr=(10,8,9,7,5,6,2,3,0,1) \\ stack(array pointer) return a stack with a copy of array items \\ array(stack pointer) return an array, empty the stack
arr2=array(merge.sort(stack(arr))) Print type$(arr2) Dim a() \\ a() is an array as a value, so we just copy arr2 to a() a()=arr2 \\ to prove we add 1 to each element of arr2 arr2++ Print a() ' 0,1,2,3,4,5,6,7,8,9 Print arr2 ' 1,2,3,4,5,6,7,8,9,11 p=a() ' we get a pointer \\ a() has a double pointer inside \\ so a() get just the inner pointer a()=array(merge.sortdown(stack(p))) \\ so now p (which use the outer pointer) \\ still points to a() print p ' p point to a()
} checkit </lang>
Maple
<lang>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;</lang>
- Output:
[0,0,2,3,3,8,17,36,40,72]
Mathematica / Wolfram Language
<lang Mathematica>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], rightrightIndex++,
rightIndex > Length[right], leftleftIndex++,
leftleftIndex <= rightrightIndex, leftleftIndex++,
True, rightrightIndex++],
{Length[left] + Length[right]}]
]</lang>
MATLAB
<lang MATLAB>function list = mergeSort(list)
if numel(list) <= 1
return
else
middle = ceil(numel(list) / 2);
left = list(1:middle);
right = list(middle+1:end);
left = mergeSort(left);
right = mergeSort(right);
if left(end) <= right(1)
list = [left right];
return
end
%merge(left,right)
counter = 1;
while (numel(left) > 0) && (numel(right) > 0)
if(left(1) <= right(1))
list(counter) = left(1);
left(1) = [];
else
list(counter) = right(1);
right(1) = [];
end
counter = counter + 1;
end
if numel(left) > 0
list(counter:end) = left;
elseif numel(right) > 0
list(counter:end) = right;
end
%end merge
end %if
end %mergeSort</lang> Sample Usage: <lang MATLAB>>> mergeSort([4 3 1 5 6 2])
ans =
1 2 3 4 5 6</lang>
Maxima
<lang maxima>merge(a, b) := block(
[c: [ ], i: 1, j: 1, p: length(a), q: length(b)],
while i <= p and j <= q do (
if a[i] < b[j] then (
c: endcons(a[i], c),
i: i + 1
) else (
c: endcons(b[j], c),
j: j + 1
)
),
if i > p then append(c, rest(b, j - 1)) else append(c, rest(a, i - 1))
)$
mergesort(u) := block(
[n: length(u), k, a, b],
if n <= 1 then u else (
a: rest(u, k: quotient(n, 2)),
b: rest(u, k - n),
merge(mergesort(a), mergesort(b))
)
)$</lang>
MAXScript
<lang MAXScript>fn mergesort arr = ( local left = #() local right = #() local result = #() if arr.count < 2 then return arr else ( local mid = arr.count/2 for i = 1 to mid do ( append left arr[i] ) for i = (mid+1) to arr.count do ( append right arr[i] ) left = mergesort left right = mergesort right if left[left.count] <= right[1] do ( join left right return left ) result = _merge left right return result ) )
fn _merge a b = ( local result = #() while a.count > 0 and b.count > 0 do ( if a[1] <= b[1] then ( append result a[1] a = for i in 2 to a.count collect a[i] ) else ( append result b[1] b = for i in 2 to b.count collect b[i] ) ) if a.count > 0 do ( join result a ) if b.count > 0 do ( join result b ) return result )</lang> Output: <lang MAXScript> 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)
</lang>
Mercury
This version of a sort will sort a list of any type for which there is an ordering predicate defined. Both a function form and a predicate form are defined here with the function implemented in terms of the predicate. Some of the ceremony has been elided. <lang mercury>
- - 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] ).
</lang>
Modula-2
Iterative
Divides the input into blocks of 2 entries, and sorts each block by swapping if necessary. Then merges blocks of 2 into blocks of 4, blocks of 4 into blocks of 8, and so on. <lang modula2> DEFINITION MODULE MSIterat;
PROCEDURE IterativeMergeSort( VAR a : ARRAY OF INTEGER);
END MSIterat. </lang> <lang modula2> IMPLEMENTATION MODULE MSIterat;
IMPORT Storage;
PROCEDURE IterativeMergeSort( VAR a : ARRAY OF INTEGER); VAR
n, bufLen, len, endBuf : CARDINAL; k, nL, nR, b, h, i, j, startR, endR: CARDINAL; temp : INTEGER; (* array element *) pbuf : POINTER TO ARRAY CARDINAL OF INTEGER;
BEGIN
n := HIGH(a) + 1; (* length of array *)
IF (n < 2) THEN RETURN; END;
(* Sort blocks of length 2 by swapping elements if necessary.
Start at high end of array; ignore a[0] if n is odd.*)
k := n;
REPEAT
DEC(k, 2);
IF (a[k] > a[k + 1]) THEN
temp := a[k]; a[k] := a[k + 1]; a[k + 1] := temp;
END;
UNTIL (k < 2);
IF (n = 2) THEN RETURN; END;
(* Set up a buffer for temporary storage when merging. *)
(* TopSpeed Modula-2 doesn't seem to have dynamic arrays,
so we use a workaround *)
bufLen := n DIV 2;
Storage.ALLOCATE( pbuf, bufLen*SIZE(INTEGER));
nR := 2; (* length of right-hand block when merging *)
REPEAT
len := 2*nR; (* maximum length of a merged block in this iteration *)
k := n; (* start at the high end of the array *)
WHILE (k > nR) DO
IF (k >= len) THEN
nL := nR; DEC(k, len);
ELSE
nL := k - nR; k := 0; END;
(* Merging 2 adjacent blocks, already sorted.
k = start index of left block;
nL, nR = lengths of left and right blocks *)
startR := k + nL; endR := startR + nR;
(* Skip elements in left block that are already in correct place *)
temp := a[startR]; (* first (smallest) element in right block *)
j := k;
WHILE (j < startR) AND (a[j] <= temp) DO INC(j); END;
endBuf := startR - j; (* length of buffer actually used *)
IF (endBuf > 0) THEN (* if endBuf = 0 then already sorted *)
(* Copy from left block to buffer, omitting elements
that are already in correct place *)
h := j;
FOR b := 0 TO endBuf - 1 DO
pbuf^[b] := a[h]; INC(h);
END;
(* Fill in values from right block or buffer *)
b := 0;
i := startR;
(* j = startR - endBuf from above *)
WHILE (b < endBuf) AND (i < endR) DO
IF (pbuf^[b] <= a[i]) THEN
a[j] := pbuf^[b]; INC(b)
ELSE
a[j] := a[i]; INC(i); END;
INC(j);
END;
(* If now b = endBuf then the merge is complete.
Else just copy the remaining elements in the buffer. *)
WHILE (b < endBuf) DO
a[j] := pbuf^[b]; INC(j); INC(b);
END;
END;
END;
nR := len;
UNTIL (nR >= n);
Storage.DEALLOCATE( pbuf, bufLen*SIZE(INTEGER));
END IterativeMergeSort;
END MSIterat. </lang> <lang modula2> MODULE MSItDemo; (* Demo of iterative merge sort *)
IMPORT IO, Lib; FROM MSIterat IMPORT IterativeMergeSort;
(* Procedure to display the values in the demo array *) PROCEDURE Display( VAR a : ARRAY OF INTEGER); VAR
j, nrInLine : CARDINAL;
BEGIN
nrInLine := 0; FOR j := 0 TO HIGH(a) DO IO.WrCard( a[j], 5); INC( nrInLine); IF (nrInLine = 10) THEN IO.WrLn; nrInLine := 0; END; END; IF (nrInLine > 0) THEN IO.WrLn; END;
END Display;
(* Main routine *) CONST
ArrayLength = 50;
VAR
arr : ARRAY [0..ArrayLength - 1] OF INTEGER; m : CARDINAL;
BEGIN
Lib.RANDOMIZE; FOR m := 0 TO ArrayLength - 1 DO arr[m] := Lib.RANDOM( 1000); END; IO.WrStr( 'Before:'); IO.WrLn; Display( arr); IterativeMergeSort( arr); IO.WrStr( 'After:'); IO.WrLn; Display( arr);
END MSItDemo. </lang>
- Output:
Before: 236 542 526 549 869 632 446 518 909 270 826 562 469 258 681 604 921 772 548 328 147 679 71 239 772 106 477 556 451 64 941 207 87 486 280 206 380 689 964 376 298 635 552 887 387 70 287 77 610 605 After: 64 70 71 77 87 106 147 206 207 236 239 258 270 280 287 298 328 376 380 387 446 451 469 477 486 518 526 542 548 549 552 556 562 604 605 610 632 635 679 681 689 772 772 826 869 887 909 921 941 964
Recursive on linked list
According to Wikipedia, "merge sort is often the best choice for sorting a linked list". The code below shows a general procedure for merge-sorting a linked list. As in the improved Delphi version, only the pointers are moved. To carry out the Rosetta Code task, the demo program sorts an array of records on an integer-valued field.
The method for splitting a linked list is taken from "Merge sort algorithm for a singly linked list" on Techie Delight. Two pointers step through the list, one at twice the speed of the other. When the fast pointer reaches the end, the slow pointer marks the halfway point. <lang modula2> DEFINITION MODULE MergSort;
TYPE MSCompare = PROCEDURE( ADDRESS, ADDRESS) : INTEGER; TYPE MSGetNext = PROCEDURE( ADDRESS) : ADDRESS; TYPE MSSetNext = PROCEDURE( ADDRESS, ADDRESS);
PROCEDURE DoMergeSort( VAR start : ADDRESS;
Compare : MSCompare;
GetNext : MSGetNext;
SetNext : MSSetNext);
(*
Procedures to be supplied by the caller: Compare(a1, a2) returns -1 if a1^ is to be placed before a2^; +1 if after; 0 if no priority. GetNext(a) returns address of next item after a^. SetNext(a, n) sets address of next item after a^ to n. If a^ is last item, then address of next item is NIL. It can be assumed that a, a1, a2 are not NIL.
- )
END MergSort. </lang> <lang modula2> IMPLEMENTATION MODULE MergSort;
PROCEDURE DoMergeSort( VAR start : ADDRESS;
Compare : MSCompare;
GetNext : MSGetNext;
SetNext : MSSetNext);
VAR
p1, p2, q : ADDRESS;
BEGIN
(* If list has < 2 items, do nothing *) IF (start = NIL) THEN RETURN; END; p1 := GetNext( start); IF (p1 = NIL) THEN RETURN; END;
(* If list has only 2 items, we'll not use recursion *)
p2 := GetNext( p1);
IF (p2 = NIL) THEN
IF (Compare( start, p1) > 0) THEN
q := start; SetNext( p1, q); SetNext( q, NIL);
start := p1;
END;
RETURN;
END;
(* List has > 2 items: split list in half *) p1 := start; REPEAT p1 := GetNext( p1); p2 := GetNext( p2); IF (p2 <> NIL) THEN p2 := GetNext( p2); END; UNTIL (p2 = NIL); (* Now p1 points to last item in first half of list *) p2 := GetNext( p1); SetNext( p1, NIL); p1 := start;
(* Recursive calls to sort each half; p1 and p2 will be updated *) DoMergeSort( p1, Compare, GetNext, SetNext); DoMergeSort( p2, Compare, GetNext, SetNext);
(* Merge the sorted halves *)
IF Compare( p1, p2) < 0 THEN
start := p1; p1 := GetNext( p1);
ELSE
start := p2; p2 := GetNext( p2);
END;
q := start;
WHILE (p1 <> NIL) AND (p2 <> NIL) DO
IF Compare( p1, p2) < 0 THEN
SetNext( q, p1); q := p1; p1 := GetNext( p1);
ELSE
SetNext( q, p2); q := p2; p2 := GetNext( p2);
END;
END;
IF (p1 = NIL) THEN SetNext( q, p2) ELSE SetNext( q, p1) END;
END DoMergeSort; END MergSort. </lang> <lang modula2> MODULE MergDemo;
IMPORT IO, Lib, MergSort;
TYPE PTestRec = POINTER TO TestRec; TYPE TestRec = RECORD
Value : INTEGER; Next : PTestRec;
END;
PROCEDURE Compare( a1, a2 : ADDRESS) : INTEGER; VAR
p1, p2 : PTestRec;
BEGIN
p1 := a1; p2 := a2; IF (p1^.Value < p2^.Value) THEN RETURN -1 ELSIF (p1^.Value > p2^.Value) THEN RETURN 1 ELSE RETURN 0; END;
END Compare;
PROCEDURE GetNext( a : ADDRESS) : ADDRESS; VAR
p : PTestRec;
BEGIN
p := a; RETURN p^.Next;
END GetNext;
PROCEDURE SetNext( a, n : ADDRESS); VAR
p : PTestRec;
BEGIN
p := a; p^.Next := n;
END SetNext;
(* Display the values in the linked list *) PROCEDURE Display( p : PTestRec); VAR
nrInLine : CARDINAL;
BEGIN
nrInLine := 0; WHILE (p <> NIL) DO IO.WrCard( p^.Value, 5); p := p^.Next; INC( nrInLine); IF (nrInLine = 10) THEN IO.WrLn; nrInLine := 0; END; END; IF (nrInLine > 0) THEN IO.WrLn; END;
END Display;
(* Main routine *) CONST ArraySize = 50; VAR
arr : ARRAY [0..ArraySize - 1] OF TestRec; j : CARDINAL; start, p : PTestRec;
BEGIN
(* Fill values with random integers *)
FOR j := 0 TO ArraySize - 1 DO
arr[j].Value := Lib.RANDOM( 1000);
END;
(* Set up the links *)
IF (ArraySize > 1) THEN (* FOR loop 0 TO -1 crashes program *)
FOR j := 0 TO ArraySize - 2 DO
arr[j].Next := ADR( arr[j + 1]);
END;
END;
arr[ArraySize - 1].Next := NIL;
(* Demonstrate merge sort on the linked list *)
start := ADR( arr[0]);
IO.WrStr( 'Before:'); IO.WrLn;
Display( start);
MergSort.DoMergeSort( start, Compare, GetNext, SetNext);
IO.WrStr( 'After:'); IO.WrLn;
Display( start);
END MergDemo. </lang>
- Output:
Before: 683 68 458 645 223 801 485 101 255 590 381 149 29 298 226 937 866 130 297 153 551 159 760 403 380 770 296 701 399 775 236 758 249 314 230 106 626 804 956 149 706 625 651 727 323 38 66 534 85 663 After: 29 38 66 68 85 101 106 130 149 149 153 159 223 226 230 236 249 255 296 297 298 314 323 380 381 399 403 458 485 534 551 590 625 626 645 651 663 683 701 706 727 758 760 770 775 801 804 866 937 956
Nemerle
This is a translation of a Standard ML example from Wikipedia. <lang Nemerle>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);
}
}</lang>
- Output:
[1, 2, 3, 4, 5, 6, 7, 8, 9] [a, c, f, l, t, w, y]
NetRexx
<lang NetRexx>/* NetRexx */ options replace format comments java crossref savelog symbols binary
import java.util.List
placesList = [String -
"UK London", "US New York", "US Boston", "US Washington" - , "UK Washington", "US Birmingham", "UK Birmingham", "UK Boston" -
]
lists = [ -
placesList - , mergeSort(String[] Arrays.copyOf(placesList, placesList.length)) -
]
loop ln = 0 to lists.length - 1
cl = lists[ln] loop ct = 0 to cl.length - 1 say cl[ct] end ct say end ln
return
method mergeSort(m = String[]) public constant binary returns String[]
rl = String[m.length] al = List mergeSort(Arrays.asList(m)) al.toArray(rl)
return rl
method mergeSort(m = List) public constant binary returns ArrayList
result = ArrayList(m.size)
left = ArrayList()
right = ArrayList()
if m.size > 1 then do
middle = m.size % 2
loop x_ = 0 to middle - 1
left.add(m.get(x_))
end x_
loop x_ = middle to m.size - 1
right.add(m.get(x_))
end x_
left = mergeSort(left)
right = mergeSort(right)
if (Comparable left.get(left.size - 1)).compareTo(Comparable right.get(0)) <= 0 then do
left.addAll(right)
result.addAll(m)
end
else do
result = merge(left, right)
end
end
else do
result.addAll(m)
end
return result
method merge(left = List, right = List) public constant binary returns ArrayList
result = ArrayList()
loop label mx while left.size > 0 & right.size > 0
if (Comparable left.get(0)).compareTo(Comparable right.get(0)) <= 0 then do
result.add(left.get(0))
left.remove(0)
end
else do
result.add(right.get(0))
right.remove(0)
end
end mx
if left.size > 0 then do
result.addAll(left)
end
if right.size > 0 then do
result.addAll(right)
end
return result
</lang>
- 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
<lang nim>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</lang>
- Output:
@[-31, 0, 2, 2, 4, 65, 83, 99, 782]
OCaml
<lang ocaml>let rec split_at n xs =
match n, xs with
0, xs ->
[], xs
| _, [] ->
failwith "index too large"
| n, x::xs when n > 0 ->
let xs', xs = split_at (pred n) xs in
x::xs', xs
| _, _ ->
invalid_arg "negative argument"
let rec merge_sort cmp = function
[] -> []
| [x] -> [x]
| xs ->
let xs, ys = split_at (List.length xs / 2) xs in
List.merge cmp (merge_sort cmp xs) (merge_sort cmp ys)
let _ =
merge_sort compare [8;6;4;2;1;3;5;7;9]</lang>
Oz
<lang oz>declare
fun {MergeSort Xs}
case Xs
of nil then nil
[] [X] then [X]
else
Middle = {Length Xs} div 2
Left Right
{List.takeDrop Xs Middle ?Left ?Right}
in
{List.merge {MergeSort Left} {MergeSort Right} Value.'<'}
end
end
in
{Show {MergeSort [3 1 4 1 5 9 2 6 5]}}</lang>
PARI/GP
Note also that the built-in vecsort and listsort use a merge sort internally.
<lang parigp>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 };</lang>
Pascal
<lang pascal>program MergeSortDemo;
{$IFDEF FPC}
{$MODE DELPHI}
{$ENDIF}
type
TIntArray = array of integer;
function merge(left, right: TIntArray): TIntArray;
var
i, j: integer;
begin
j := 0;
setlength(Result, length(left) + length(right));
while (length(left) > 0) and (length(right) > 0) do
begin
if left[0] <= right[0] then
begin
Result[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
Result[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
Result[j + i] := left[i];
j := j + length(left);
if length(right) > 0 then
for i := low(right) to high(right) do
Result[j + i] := right[i];
end;
function mergeSort(m: TIntArray): TIntArray;
var
left, right: TIntArray;
i, middle: integer;
begin
setlength(Result, length(m));
if length(m) = 1 then
Result[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);
Result := 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.</lang>
- Output:
./MergeSort The data before sorting: 6 1 2 1 5 2 1 5 The data after sorting: 1 1 1 2 2 5 5 6
improvement
uses "only" one halfsized temporary array for merging, which are set to the right size in before. small sized fields are sorted via insertion sort. Only an array of Pointers is sorted, so no complex data transfers are needed.Sort for X,Y or whatever is easy to implement.
Works with ( Turbo -) Delphi too. <lang pascal>{$IFDEF FPC}
{$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. </lang>
- 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
<lang perl>sub merge_sort {
my @x = @_;
return @x if @x < 2;
my $m = int @x / 2;
my @a = merge_sort(@x[0 .. $m - 1]);
my @b = merge_sort(@x[$m .. $#x]);
for (@x) {
$_ = !@a ? shift @b
: !@b ? shift @a
: $a[0] <= $b[0] ? shift @a
: shift @b;
}
@x;
}
my @a = (4, 65, 2, -31, 0, 99, 83, 782, 1); @a = merge_sort @a; print "@a\n";</lang> Also note, the built-in function sort uses mergesort.
Phix
with javascript_semantics function merge(sequence left, sequence right) sequence result = {} while length(left)>0 and length(right)>0 do if left[1]<=right[1] then result = append(result, left[1]) left = left[2..$] else result = append(result, right[1]) right = right[2..$] end if end while return result & left & right end function function mergesort(sequence m) if length(m)<=1 then return m end if integer middle = floor(length(m)/2) sequence left = mergesort(m[1..middle]), right = mergesort(m[middle+1..$]) if left[$]<=right[1] then return left & right elsif right[$]<=left[1] then return right & left end if return merge(left, right) end function constant s = shuffle(tagset(10)) ? s ? mergesort(deep_copy(s))
- Output:
{8,1,2,5,10,3,9,6,7,4}
{1,2,3,4,5,6,7,8,9,10}
PHP
<lang php>function mergesort($arr){ if(count($arr) == 1 ) return $arr; $mid = count($arr) / 2;
$left = array_slice($arr, 0, $mid); $right = array_slice($arr, $mid);
$left = mergesort($left); $right = mergesort($right); return merge($left, $right); }
function merge($left, $right){ $res = array(); while (count($left) > 0 && count($right) > 0){ if($left[0] > $right[0]){ $res[] = $right[0]; $right = array_slice($right , 1); }else{ $res[] = $left[0]; $left = array_slice($left, 1); } } while (count($left) > 0){ $res[] = $left[0]; $left = array_slice($left, 1); } while (count($right) > 0){ $res[] = $right[0]; $right = array_slice($right, 1); } return $res; }
$arr = array( 1, 5, 2, 7, 3, 9, 4, 6, 8); $arr = mergesort($arr); echo implode(',',$arr);</lang>
- Output:
1,2,3,4,5,6,7,8,9
Picat
<lang Picat>% 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).</lang>
PicoLisp
PicoLisp's built-in sort routine uses merge sort. This is a high level implementation. <lang lisp>(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))</lang>
PL/I
<lang pli>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;</lang>
PowerShell
<lang PowerShell> function MergeSort([object[]] $SortInput) { # The base case exits for minimal lists that are sorted by definition if ($SortInput.Length -le 1) {return $SortInput}
# Divide and conquer [int] $midPoint = $SortInput.Length/2 # The @() operators ensure a single result remains typed as an array [object[]] $left = @(MergeSort @($SortInput[0..($midPoint-1)])) [object[]] $right = @(MergeSort @($SortInput[$midPoint..($SortInput.Length-1)]))
# Merge [object[]] $result = @() while (($left.Length -gt 0) -and ($right.Length -gt 0)) { if ($left[0] -lt $right[0]) { $result += $left[0] # Use an if/else rather than accessing the array range as $array[1..0] if ($left.Length -gt 1){$left = $left[1..$($left.Length-1)]} else {$left = @()} } else { $result += $right[0] # Without the if/else, $array[1..0] would return the whole array when $array.Length == 1 if ($right.Length -gt 1){$right = $right[1..$($right.Length-1)]} else {$right = @()} } }
# If we get here, either $left or $right is an empty array (or both are empty!). Since the # rest of the unmerged array is already sorted, we can simply string together what we have. # This line outputs the concatenated result. An explicit 'return' statement is not needed. $result + $left + $right } </lang>
Prolog
<lang prolog>% 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).</lang>
PureBasic
A non-optimized version with lists. <lang PureBasic>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</lang>
- 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
<lang python>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))</lang>
Pre-2.6, merge() could be implemented like this: <lang python>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</lang>
using only recursions <lang python>def merge(x, y):
if x==[]: return y if y==[]: return x return [x[0]] + merge(x[1:], y) if x[0]<y[0] else [y[0]] + merge(x, y[1:])
def sort(a, n):
m = n//2 return a if n<=1 else merge(sort(a[:m], m), sort(a[m:], n-m))
a = list(map(int, input().split())) print(sort(a, len(a)))</lang>
Quackery
<lang Quackery>[ [] temp put
[ dup [] != while
over [] != while
over 0 peek
over 0 peek
> not if dip
[ 1 split
temp take
rot join
temp put ]
again ]
join
temp take swap join ] is merge ( [ [ --> [ )
[ dup size 2 < if done
dup size 2 / split swap recurse swap recurse merge ] is mergesort ( [ --> [ )</lang>
R
<lang r>mergesort <- function(m) {
merge_ <- function(left, right)
{
result <- c()
while(length(left) > 0 && length(right) > 0)
{
if(left[1] <= right[1])
{
result <- c(result, left[1])
left <- left[-1]
} else
{
result <- c(result, right[1])
right <- right[-1]
}
}
if(length(left) > 0) result <- c(result, left)
if(length(right) > 0) result <- c(result, right)
result
}
len <- length(m)
if(len <= 1) m else
{
middle <- length(m) / 2
left <- m[1:floor(middle)]
right <- m[floor(middle+1):len]
left <- mergesort(left)
right <- mergesort(right)
if(left[length(left)] <= right[1])
{
c(left, right)
} else
{
merge_(left, right)
}
}
} mergesort(c(4, 65, 2, -31, 0, 99, 83, 782, 1)) # -31 0 1 2 4 65 83 99 782</lang>
Racket
<lang racket>
- lang racket
(define (merge xs ys)
(cond [(empty? xs) ys]
[(empty? ys) xs]
[(match* (xs ys)
[((list* a as) (list* b bs))
(cond [(<= a b) (cons a (merge as ys))]
[ (cons b (merge xs bs))])])]))
(define (merge-sort xs)
(match xs
[(or (list) (list _)) xs]
[_ (define-values (ys zs) (split-at xs (quotient (length xs) 2)))
(merge (merge-sort ys) (merge-sort zs))]))
</lang> This variation is bottom up: <lang racket>
- 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))])])]))
</lang>
Raku
(formerly Perl 6)
<lang perl6>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;</lang>
- Output:
input = 6 7 2 1 8 9 5 3 4 output = 1 2 3 4 5 6 7 8 9
REBOL
msort: function [a compare] [msort-do merge] [
if (length? a) < 2 [return a]
; define a recursive Msort-do function
msort-do: function [a b l] [mid] [
either l < 4 [
if l = 3 [msort-do next b next a 2]
merge a b 1 next b l - 1
] [
mid: make integer! l / 2
msort-do b a mid
msort-do skip b mid skip a mid l - mid
merge a b mid skip b mid l - mid
]
]
; function Merge is the key part of the algorithm
merge: func [a b lb c lc] [
until [
either (compare first b first c) [
change/only a first b
b: next b
a: next a
zero? lb: lb - 1
] [
change/only a first c
c: next c
a: next a
zero? lc: lc - 1
]
]
loop lb [
change/only a first b
b: next b
a: next a
]
loop lc [
change/only a first c
c: next c
a: next a
]
]
msort-do a copy a length? a
a
]
REXX
Note: the array elements can be anything: integers, floating point (exponentiated), character strings ··· <lang rexx>/*REXX pgm sorts a stemmed array (numbers and/or chars) using the merge─sort algorithm.*/ call init /*sinfully initialize the @ array. */ call show 'before sort' /*show the "before" array elements. */
say copies('▒', 75) /*display a separator line to the term.*/
call merge # /*invoke the merge sort for the array*/ call show ' after sort' /*show the "after" array elements. */ exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ init: @.=; @.1= '---The seven deadly sins---' ; @.4= "avarice" ; @.7= 'gluttony'
@.2= '===========================' ; @.5= "wrath" ; @.8= 'sloth'
@.3= 'pride' ; @.6= "envy" ; @.9= 'lust'
do #=1 until @.#==; end; #= #-1; return /*#: # of entries in @ array.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/ show: do j=1 for #; say right('element',20) right(j,length(#)) arg(1)":" @.j; end; return /*──────────────────────────────────────────────────────────────────────────────────────*/ merge: procedure expose @. !.; parse arg n, L; if L== then do; !.=; L= 1; end
if n==1 then return; h= L + 1
if n==2 then do; if @.L>@.h then do; _=@.h; @.h=@.L; @.L=_; end; return; end
m= n % 2 /* [↑] handle case of two items.*/
call merge n-m, L+m /*divide items to the left ···*/
call merger m, L, 1 /* " " " " right ···*/
i= 1; j= L + m
do k=L while k<j /*whilst items on right exist ···*/
if j==L+n | !.i<=@.j then do; @.k= !.i; i= i + 1; end
else do; @.k= @.j; j= j + 1; end
end /*k*/
return
/*──────────────────────────────────────────────────────────────────────────────────────*/ merger: procedure expose @. !.; parse arg n,L,T
if n==1 then do; !.T= @.L; return; end
if n==2 then do; h= L + 1; q= T + 1; !.q= @.L; !.T= @.h; return; end
m= n % 2 /* [↑] handle case of two items.*/
call merge m, L /*divide items to the left ···*/
call merger n-m, L+m, m+T /* " " " " right ···*/
i= L; j= m + T
do k=T while k<j /*whilst items on left exist ···*/
if j==T+n | @.i<=!.j then do; !.k= @.i; i= i + 1; end
else do; !.k= !.j; j= j + 1; end
end /*k*/
return</lang>
- 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
<lang ruby>def merge_sort(m)
return m if m.length <= 1 middle = m.length / 2 left = merge_sort(m[0...middle]) right = merge_sort(m[middle..-1]) merge(left, right)
end
def merge(left, right)
result = [] until left.empty? || right.empty? result << (left.first<=right.first ? left.shift : right.shift) end result + left + 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]</lang>
Here's a version that monkey patches the Array class, with an example that demonstrates it's a stable sort <lang ruby>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"]]</lang>
Rust
<lang rust> 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..]); } } </lang>
The sort algorithm : <lang rust> 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); } </lang>
Version without recursion call (faster) : <lang rust> 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; } } </lang>
Scala
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. <lang scala> 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) }
} </lang>
Scheme
<lang scheme>(define (merge-sort l gt?)
(define (merge left right)
(cond
((null? left)
right)
((null? right)
left)
((gt? (car left) (car right))
(cons (car right)
(merge left (cdr right))))
(else
(cons (car left)
(merge (cdr left) right)))))
(define (take l n)
(if (zero? n)
(list)
(cons (car l)
(take (cdr l) (- n 1)))))
(let ((half (quotient (length l) 2)))
(if (zero? half)
l
(merge (merge-sort (take l half) gt?)
(merge-sort (list-tail l half) gt?)))))</lang>
(merge-sort '(1 3 5 7 9 8 6 4 2) >)
Seed7
<lang seed7>const proc: mergeSort2 (inout array elemType: arr, in integer: lo, in integer: hi, inout array elemType: scratch) is func
local
var integer: mid is 0;
var integer: k is 0;
var integer: t_lo is 0;
var integer: t_hi is 0;
begin
if lo < hi then
mid := (lo + hi) div 2;
mergeSort2(arr, lo, mid, scratch);
mergeSort2(arr, succ(mid), hi, scratch);
t_lo := lo;
t_hi := succ(mid);
for k range lo to hi do
if t_lo <= mid and (t_hi > hi or arr[t_lo] <= arr[t_hi]) then
scratch[k] := arr[t_lo];
incr(t_lo);
else
scratch[k] := arr[t_hi];
incr(t_hi);
end if;
end for;
for k range lo to hi do
arr[k] := scratch[k];
end for;
end if;
end func;
const proc: mergeSort2 (inout array elemType: arr) is func
local var array elemType: scratch is 0 times elemType.value; begin scratch := length(arr) times elemType.value; mergeSort2(arr, 1, length(arr), scratch); end func;</lang>
Original source: [2]
Sidef
<lang ruby>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)</lang>
Standard ML
<lang sml>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]</lang>
Swift
<lang Swift>// Merge Sort in Swift 4.2 // Source: https://github.com/raywenderlich/swift-algorithm-club/tree/master/Merge%20Sort // NOTE: by use of generics you can make it sort arrays of any type that conforms to // Comparable protocol, however this is not always optimal
import Foundation
func mergeSort(_ array: [Int]) -> [Int] {
guard array.count > 1 else { return array }
let middleIndex = array.count / 2
let leftPart = mergeSort(Array(array[0..<middleIndex])) let rightPart = mergeSort(Array(array[middleIndex..<array.count]))
func merge(left: [Int], right: [Int]) -> [Int] {
var leftIndex = 0
var rightIndex = 0
var merged = [Int]()
merged.reserveCapacity(left.count + right.count)
while leftIndex < left.count && rightIndex < right.count {
if left[leftIndex] < right[rightIndex] {
merged.append(left[leftIndex])
leftIndex += 1
} else if left[leftIndex] > right[rightIndex] {
merged.append(right[rightIndex])
rightIndex += 1
} else {
merged.append(left[leftIndex])
leftIndex += 1
merged.append(right[rightIndex])
rightIndex += 1
}
}
while leftIndex < left.count {
merged.append(left[leftIndex])
leftIndex += 1
}
while rightIndex < right.count {
merged.append(right[rightIndex])
rightIndex += 1
}
return merged
}
return merge(left: leftPart, right: rightPart)
}</lang>
Tailspin
The standard recursive merge sort <lang tailspin> templates mergesort
templates merge
@: $(2);
[ $(1)... -> \(
when <?($@merge<[](0)>)
| ..$@merge(1)> do
$ !
otherwise
^@merge(1) !
$ -> #
\),
$@...] !
end merge
$ -> #
when <[](0..1)> do $! otherwise def half: $::length ~/ 2; [$(1..$half) -> mergesort, $($half+1..last) -> mergesort] -> merge !
end mergesort
[4,5,3,8,1,2,6,7,9,8,5] -> mergesort -> !OUT::write </lang>
- 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. <lang tailspin> templates mergesort
templates merge
@: $(2);
$(1)... -> \(
when <?($@merge<[](0)>)
| ..$@merge(1)> do
$ !
otherwise
^@merge(1) !
$ -> #
\) !
$@... !
end merge
templates mergePairs
when <[](1)> do
$(1) !
when <[](2..)> do
[$(1..2) -> merge] !
$(3..last) -> #
end mergePairs
templates mergeAll
when <[](0)> do
$ !
when <[](1)> do
$(1) !
otherwise
[ $ -> mergePairs ] -> #
end mergeAll
$ -> [ $... -> [ $ ] ] -> mergeAll !
end mergesort
[4,5,3,8,1,2,6,7,9,8,5] -> mergesort -> !OUT::write </lang>
- Output:
[1, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9]
Tcl
<lang tcl>package require Tcl 8.5
proc mergesort m {
set len [llength $m]
if {$len <= 1} {
return $m
}
set middle [expr {$len / 2}]
set left [lrange $m 0 [expr {$middle - 1}]]
set right [lrange $m $middle end]
return [merge [mergesort $left] [mergesort $right]]
}
proc merge {left right} {
set result [list]
while {[set lleft [llength $left]] > 0 && [set lright [llength $right]] > 0} {
if {[lindex $left 0] <= [lindex $right 0]} {
set left [lassign $left value]
} else {
set right [lassign $right value]
}
lappend result $value
}
if {$lleft > 0} {
lappend result {*}$left
}
if {$lright > 0} {
set result [concat $result $right] ;# another way append elements
}
return $result
}
puts [mergesort {8 6 4 2 1 3 5 7 9}] ;# => 1 2 3 4 5 6 7 8 9</lang> Also note that Tcl's built-in lsort command uses the mergesort algorithm.
Unison
<lang Unison>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)</lang>
UnixPipes
<lang bash>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</lang>
Ursala
<lang Ursala>#import std
mergesort "p" = @iNCS :-0 ~&B^?a\~&YaO "p"?abh/~&alh2faltPrXPRC ~&arh2falrtPXPRC
- show+
example = mergesort(lleq) <'zoh','zpb','hhh','egi','bff','cii','yid'></lang>
- 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. <lang Ursala>mergesort "p" = "p"-<</lang>
V
merge uses the helper mergei to merge two lists. The mergei takes a stack of the form [mergedlist] [list1] [list2] it then extracts one element from list2, splits the list1 with it, joins the older merged list, first part of list1 and the element that was used for splitting (taken from list2) into the new merged list. the new list1 is the second part of the split on older list1. new list2 is the list remaining after the element e2 was extracted from it. <lang v>[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].</lang>
[8 7 6 5 4 2 1 3 9] msort puts
Vlang
<lang vlang>fn main() {
mut a := [170, 45, 75, -90, -802, 24, 2, 66]
println("before: $a")
a = merge_sort(a)
println("after: $a")
}
fn merge_sort(m []int) []int {
if m.len <= 1{
return m
} else {
mid := m.len / 2
mut left := merge_sort(m[..mid])
mut right := merge_sort(m[mid..])
if m[mid-1] <= m[mid] {
left << right
return left
}
return merge(mut left, mut right)
}
}
fn merge(mut left []int,mut right []int) []int {
mut result := []int{}
for left.len > 0 && right.len > 0 {
if left[0] <= right[0]{
result << left[0]
left = left[1..]
} else {
result << right[0]
right = right[1..]
}
}
if left.len > 0 {
result << left
}
if right.len > 0 {
result << right
}
return result
}</lang>
Wren
<lang ecmascript>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()
}</lang>
- 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.
<lang ecmascript>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()
}</lang>
- Output:
As above.
XPL0
This is based on an example in "Fundamentals of Computer Algorithms" by Horowitz & Sahni. <lang XPL0>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, ^ )]; ]</lang>
- Output:
-5 1 1 2 3 4 4 5 6 9
Yabasic
<lang yabasic> dim b(9)
sub copyArray(a(), inicio, final, b())
dim b(final - 1)
for k = inicio to final - 1
b(k) = a(k)
next
end sub
// La mitad izquierda es a(inicio to mitad-1). // La mitad derecha es a(mitad to final-1). // El resultado es b(inicio to final-1). sub topDownMerge(a(), inicio, mitad, final, b())
i = inicio
j = mitad
// Si bien hay elementos en los recorridos izquierdo o derecho ...
for k = inicio to final - 1
// Si existe un inicio de recorrido izquierdo y es <= inicio de recorrido derecho existente.
if (i < mitad) and (j >= final or a(i) <= a(j)) then
b(k) = a(i)
i = i + 1
else
b(k) = a(j)
j = j + 1
end if
next
end sub
// Ordenar la matriz a() usando la matriz b() como fuente. // inicio es inclusivo; final es exclusivo (a(final) no está en el conjunto). sub topDownSplitMerge(b(), inicio, final, a())
if (final - inicio) < 2 then return : fi // Si la diferencia = 1, considérelo ordenado // dividir la ejecución de más de 1 elemento en mitades mitad = int((final + inicio) / 2) // mitad = punto medio // recursively sort both runs from array a() into b() topDownSplitMerge(a(), inicio, mitad, b()) // ordenar la parte izquierda topDownSplitMerge(a(), mitad, final, b()) // ordenar la parte derecha // fusionar las ejecuciones resultantes de la matriz b() en a() topDownMerge(b(), inicio, mitad, final, a())
end sub
// El array a() tiene los elementos para ordenar; array b() es una matriz de trabajo (inicialmente vacía). sub topDownMergeSort(a(), b(), n)
copyArray(a(), 0, n, b()) // duplicar la matriz a() en b() topDownSplitMerge(b(), 0, n, a()) // ordenar los datos de b() en a()
end sub
sub printArray(a())
for i = 1 to arraysize(a(),1)
print a(i) using "####";
next
print
end sub
//--------------------------
label a1
data 4, 65, 2, -31, 0, 99, 2, 83, 782, 1
label a2
data 7, 5, 2, 6, 1, 4, 2, 6, 3
dim a(9) restore a1 for i = 0 to 9
read p a(i) = p
next i
dim a2(8) restore a2 for i = 0 to 8
read p a2(i) = p
next i
print "unsort "; printArray(a()) topDownMergeSort (a(), b(), 10) print " sort "; printArray(a()) print print "unsort "; printArray(a2()) topDownMergeSort (a2(), b(), 9) print " sort "; printArray(a2()) end </lang>
ZED
Source -> http://ideone.com/uZEPL4 Compiled -> http://ideone.com/SJ5EGu
This is a bottom up version of merge sort: <lang zed>(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</lang>
zkl
Pretty wasteful memory wise, probably not suitable for large sorts.
<lang zkl>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,*])));
}</lang> <lang zkl>merge_sort(T(1,3,5,7,9,8,6,4,2)).println(); merge_sort("big fjords vex quick waltz nymph").concat().println();</lang>
- Output:
L(1,2,3,4,5,6,7,8,9)
abcdefghiijklmnopqrstuvwxyz
Or, for lists only: <lang zkl>fcn mergeSort(L){
if (L.len()<2) return(L.copy()); n:=L.len()/2; self.fcn(L[0,n]).merge(self.fcn(L[n,*]));
}</lang> <lang zkl>mergeSort(T(1,3,5,7,9,8,6,4,2)).println(); mergeSort("big fjords vex quick waltz nymph".split("")).concat().println();</lang>
- Output:
L(1,2,3,4,5,6,7,8,9)
abcdefghiijklmnopqrstuvwxyz
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