Sorting algorithms/Merge sort: Difference between revisions
| Line 589: | Line 589: | ||
This is an in-place mergesort which works on arrays of integers. |
This is an in-place mergesort which works on arrays of integers. |
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<lang forth> |
<lang forth> |
||
: |
: merge-step ( right mid left -- right mid+ left+ ) |
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| ⚫ | |||
: merge-step |
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over @ over @ < if |
over @ over @ < if |
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over @ >r |
over @ >r |
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| Line 599: | Line 596: | ||
>r cell+ 2dup = if rdrop dup else r> then |
>r cell+ 2dup = if rdrop dup else r> then |
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then cell+ ; |
then cell+ ; |
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: merge ( right mid left -- ) |
: merge ( right mid left -- right left ) |
||
begin 2dup > while merge-step repeat |
dup >r begin 2dup > while merge-step repeat 2drop r> ; |
||
| ⚫ | |||
: mergesort ( right left |
: mergesort ( right left -- right left ) |
||
2dup cell+ <= if exit then |
2dup cell+ <= if exit then |
||
swap 2dup mid recurse rot recurse merge ; |
|||
swap recurse |
|||
-rot recurse |
|||
rot 3dup merge nip ; |
|||
: sort ( addr len -- ) cells over + swap mergesort 2drop ; |
: sort ( addr len -- ) cells over + swap mergesort 2drop ; |
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| Line 613: | Line 609: | ||
create test 8 , 1 , 5 , 3 , 9 , 0 , 2 , 7 , 6 , 4 , |
create test 8 , 1 , 5 , 3 , 9 , 0 , 2 , 7 , 6 , 4 , |
||
: . |
: .array ( addr len -- ) 0 do dup i cells + @ . loop drop ; |
||
test 10 sort . |
test 10 2dup sort .array \ 0 1 2 3 4 5 6 7 8 9 |
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</lang> |
</lang> |
||
Revision as of 15:46, 6 November 2009
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.
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
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> The output of this example is:
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.
MODE DATA = CHAR;
PROC merge sort = ([]DATA m)[]DATA: (
IF LWB m >= UPB m THEN
m
ELSE
INT middle = ( UPB m + LWB m ) OVER 2;
[]DATA left = merge sort(m[:middle]);
[]DATA right = merge sort(m[middle+1:]);
flex merge(left, right)[AT LWB m]
FI
);
# FLEX version: A demonstration of FLEX for manipulating arrays #
PROC flex merge = ([]DATA in left, in right)[]DATA:(
[UPB in left + UPB in right]DATA result;
FLEX[0]DATA left := in left;
FLEX[0]DATA right := in right;
FOR index TO UPB result DO
# change the direction of this comparison to change the direction of the sort #
IF LWB right > UPB right THEN
result[index:] := left;
stop iteration
ELIF LWB left > UPB left THEN
result[index:] := right;
stop iteration
ELIF left[1] <= right[1] THEN
result[index] := left[1];
left := left[2:]
ELSE
result[index] := right[1];
right := right[2:]
FI
OD;
stop iteration:
result
);
[32]CHAR char array data := "big fjords vex quick waltz nymph";
print((merge sort(char array data), new line));
Output:
abcdefghiijklmnopqrstuvwxyz
Optimised version:
- avoids FLEX array copies and manipulations
- avoids type DATA memory copies, useful in cases where DATA is a large STRUCT
PROC opt merge sort = ([]REF DATA m)[]REF DATA: (
IF LWB m >= UPB m THEN
m
ELSE
INT middle = ( UPB m + LWB m ) OVER 2;
[]REF DATA left = opt merge sort(m[:middle]);
[]REF DATA right = opt merge sort(m[middle+1:]);
opt merge(left, right)[AT LWB m]
FI
);
PROC opt merge = ([]REF DATA left, right)[]REF DATA:(
[UPB left - LWB left + 1 + UPB right - LWB right + 1]REF DATA result;
INT index left:=LWB left, index right:=LWB right;
FOR index TO UPB result DO
# change the direction of this comparison to change the direction of the sort #
IF index right > UPB right THEN
result[index:] := left[index left:];
stop iteration
ELIF index left > UPB left THEN
result[index:] := right[index right:];
stop iteration
ELIF left[index left] <= right[index right] THEN
result[index] := left[index left]; index left +:= 1
ELSE
result[index] := right[index right]; index right +:= 1
FI
OD;
stop iteration:
result
);
# create an array of pointers to the data being sorted #
[UPB char array data]REF DATA data; FOR i TO UPB char array data DO data[i] := char array data[i] OD;
[]REF CHAR result = opt merge sort(data);
FOR i TO UPB result DO print((result[i])) OD; print(new line)
Output:
abcdefghiijklmnopqrstuvwxyz
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>
C
<lang c>#include <stdio.h>
- include <stdlib.h>
- include <string.h>
int *locmerge(int *l, unsigned int ll, int *r, unsigned int lr) {
int *result; unsigned int il, ir, ires; il = ir = ires = 0;
result = malloc(sizeof(int)*(ll+lr));
while ( (ll > 0) && ( lr > 0 ) ) {
if ( l[il] <= r[ir] ) {
result[ires++] = l[il++]; ll--;
} else {
result[ires++] = r[ir++]; lr--;
}
}
if ( ll > 0 ) {
memcpy(&result[ires], &l[il], sizeof(int)*ll);
}
if ( lr > 0 ) {
memcpy(&result[ires], &r[ir], sizeof(int)*lr);
}
return result;
}
int *mergesort(int *list, unsigned int l)
{
unsigned int middle; int *tleft, *tright, *result, *left, *right;
if ( l < 2 ) return list;
middle = l / 2;
tleft = malloc(sizeof(int)*(l - middle));
tright = malloc(sizeof(int)*middle);
memcpy(tleft, list, sizeof(int)*(l-middle));
memcpy(tright, list+(l-middle), sizeof(int)*middle);
left = mergesort(tleft, l-middle);
right = mergesort(tright, middle);
if (list[l-middle-1] <= list[l-middle])
result = list;
else
result = locmerge(left, l-middle, right, middle);
if ( tleft == left ) {
free(left);
} else {
free(left); free(tleft);
}
if ( tright == right ) {
free(right);
} else {
free(right); free(tright);
}
return result;
}</lang>
Usage:
<lang c>int main() {
int *tobesorted; int i;
tobesorted = malloc(sizeof(int)*50);
for(i=0; i < 50; i++) {
tobesorted[i] = 50 - i;
printf("%d\n", tobesorted[i]);
}
printf("----\n");
int *r = mergesort(tobesorted, 50);
for(i=0; i < 50; i++) printf("%d\n", r[i]);
free(r);
return 0;
}</lang>
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>
C#
<lang csharp>using System; using System.Collections.Generic;
namespace RosettaCode.MergeSort {
public static class MergeSorter
{
public static List<T> Sort<T>(List<T> list) where T : IComparable
{
if (list.Count <= 1) return list;
List<T> left = list.GetRange(0, list.Count / 2);
List<T> right = list.GetRange(left.Count, list.Count - left.Count);
return Merge(Sort(left), Sort(right));
}
public static List<T> Merge<T>(List<T> left, List<T> right) where T : IComparable
{
List<T> result = new List<T>();
while (left.Count > 0 && right.Count > 0)
{
if (left[0].CompareTo(right[0]) <= 0)
{
result.Add(left[0]);
left.RemoveAt(0);
}
else
{
result.Add(right[0]);
right.RemoveAt(0);
}
}
result.AddRange(left);
result.AddRange(right);
return result;
}
}
}</lang>
As in the Ada example above, the following code provides a usage example:
<lang csharp>using System; using System.Collections.Generic;
namespace RosettaCode.MergeSort {
class Program
{
static void Main(string[] args)
{
List<int> testList = new List<int> { 1, 5, 2, 7, 3, 9, 4, 6 };
printList(testList);
printList(MergeSorter.Sort(testList));
}
private static void printList<T>(List<T> list)
{
foreach (var t in list)
{
Console.Write(t + " ");
}
Console.WriteLine();
}
}
}</lang>
Again, as in the Ada example the output is:
1 5 2 7 3 9 4 6 1 2 3 4 5 6 7 9
Clojure
(defn merge* [left right]
(cond (nil? left) right
(nil? right) left
true (let [[l & *left] left
[r & *right] right]
(if (<= l r) (cons l (merge* *left right))
(cons r (merge* left *right))))))
(defn merge-sort [L]
(let [[l & *L] L]
(if (nil? *L)
L
(let [[left right] (split-at (/ (count L) 2) L)]
(merge* (merge-sort left) (merge-sort right))))))
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)
D
module mergesort ;
version(Tango) {
import tango.io.Stdout ;
import tango.util.collection.LinkSeq ;
alias LinkSeq!(int) LNK ;
// Tango LinkSeq version
void mergesort1(T)(T m) {
if (m.length <= 1)
return m ;
int mid = m.length / 2 ;
T left = m.subset(0, mid) ;
T right = m.subset(mid, m.length - mid) ;
mergesort1(left) ;
mergesort1(right) ;
merge1(m, left, right) ;
}
void merge1(T)(T m, T left, T right) {
m.clear ;
while(left.length > 0 && right.length > 0)
if (left.head <= right.head)
m.append(left.take()) ;
else
m.append(right.take()) ;
while(left.length > 0)
m.append(left.take()) ;
while(right.length > 0)
m.append(right.take()) ;
}
alias Stdout print ;
} else { // not Version Tango
import std.stdio ;
alias writef print ;
}
// D array version
T[] mergesort2(T)(inout T[] m) {
if (m.length <= 1)
return m ;
int mid = m.length / 2 ;
T[] left, right;
left = m[0..mid] ;
right = m[mid..$] ;
left.mergesort2() ;
right.mergesort2() ;
m.merge2(left, right) ;
return m ;
}
void merge2(T)(inout T[] merged, inout T[] left, inout T[] right) {
T[] m = new T[left.length + right.length];
int headL = 0 ;
int headR = 0 ;
int tailM = 0 ;
while (headL < left.length && headR < right.length)
if(left[headL] <= right[headR])
m[tailM++] = left[headL++] ;
else
m[tailM++] = right[headR++] ;
if (headL < left.length)
m[tailM..$] = left[headL..$] ;
else if (headR < right.length)
m[tailM..$] = right[headR..$] ;
merged = m ;
}
void dump(T)(T l) {
foreach(e ; l)
print(e," ") ;
print("\n") ;
}
void main() {
int[] arr = [8,6,4,2,1,3,5,7,9] ;
version(Tango) {
LNK lnk = new LNK ;
foreach(e;arr)
lnk.append(e);
dump(lnk) ;
mergesort1(lnk) ;
dump(lnk) ;
}
dump(arr) ;
mergesort2(arr) ;
dump(arr) ;
}
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)))
}
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>subroutine Merge(A,NA,B,NB,C,NC)
integer, intent(in) :: NA,NB,NC ! Normal usage: NA+NB = NC
integer, intent(in out) :: A(NA) ! B overlays C(NA+1:NC)
integer, intent(in) :: B(NB)
integer, intent(in out) :: C(NC)
integer :: I,J,K
I = 1; J = 1; K = 1;
do while(I <= NA .and. J <= NB)
if (A(I) <= B(J)) then
C(K) = A(I)
I = I+1
else
C(K) = B(J)
J = J+1
endif
K = K + 1
enddo
do while (I <= NA)
C(K) = A(I)
I = I + 1
K = K + 1
enddo
return
end subroutine merge
recursive subroutine MergeSort(A,N,T)
integer, intent(in) :: N
integer, dimension(N), intent(in out) :: A
integer, dimension((N+1)/2), intent (out) :: T
integer :: NA,NB,V
if (N < 2) return
if (N == 2) then
if (A(1) > A(2)) then
V = A(1)
A(1) = A(2)
A(2) = V
endif
return
endif
NA=(N+1)/2
NB=N-NA
call MergeSort(A,NA,T) call MergeSort(A(NA+1),NB,T)
if (A(NA) > A(NA+1)) then
T(1:NA)=A(1:NA)
call Merge(T,NA,A(NA+1),NB,A,N)
endif
return
end subroutine MergeSort
program TestMergeSort
integer, parameter :: N = 8 integer, dimension(N) :: A = (/ 1, 5, 2, 7, 3, 9, 4, 6 /) integer, dimension ((N+1)/2) :: T call MergeSort(A,N,T) write(*,'(A,/,10I3)')'Sorted array :',A
end program TestMergeSort</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:xs') ys@(y:ys') | x <= y = x : merge xs' ys
| otherwise = y : merge xs ys'
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>
Java
<lang java>import java.util.LinkedList; public class Merge<E extends Comparable<E>> { public LinkedList<E> mergeSort(LinkedList<E> m){ if(m.size() <= 1) return m;
int middle= m.size() / 2; LinkedList<E> left= new LinkedList<E>(); for(int i= 0;i < middle;i++) left.add(m.get(i)); LinkedList<E> right= new LinkedList<E>(); for(int i= middle;i < m.size();i++) right.add(m.get(i));
right= mergeSort(right); left= mergeSort(left); LinkedList<E> result= merge(left, right);
return result; }
public LinkedList<E> merge(LinkedList<E> left, LinkedList<E> right){ LinkedList<E> result= new LinkedList<E>();
while(left.size() > 0 && right.size() > 0){ //change the direction of this comparison to change the direction of the sort if(left.peek().compareTo(right.peek()) <= 0) result.add(left.remove()); else result.add(right.remove()); }
if(left.size() > 0) result.addAll(left); if(right.size() > 0) result.addAll(right); return result; } }</lang>
JavaScript
<lang javascript>function sort(a) {
var mid = a.length>>1;
if (mid==0) return a;
var less = sort(a.slice(0,mid));
var more = sort(a.slice(mid));
var merged = [];
do {
if (more[0] < less[0]) { var t=less; less=more; more=t; }
merged.push(less.shift());
} while (less.length > 0);
return merged.concat(more);
}</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
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;
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>
PL/I
<lang PL/1>
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>
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>
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 = []
while left and right:
# change the direction of this comparison to change the direction of the sort
if left[0] <= right[0]:
result.append(left.pop(0))
else:
result.append(right.pop(0))
if left:
result.extend(left)
if right:
result.extend(right)
return result</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>
Ruby
<lang ruby>def merge_sort(m)
if m.length <= 1
return m
end
middle = m.length / 2 left = m[0,middle] right = m[middle..-1]
left = merge_sort(left) right = merge_sort(right) merge(left, right)
end
def merge(left, right)
result = []
until left.empty? || right.empty?
# change the direction of this comparison to change the direction of the sort
if left.first <= right.first
result << left.shift
else
result << right.shift
end
end
unless left.empty?
result += left
end
unless right.empty?
result += right
end
result
end</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)
if length <= 1
self
else
unless comparitor
comparitor = lambda {|a, b| a <=> b}
end
middle = length / 2
left = self[0, middle].mergesort(&comparitor)
right = self[middle..-1].mergesort(&comparitor)
merge(left, right, comparitor)
end
end
protected
def merge(left, right, comparitor)
if left.empty?
right
elsif right.empty?
left
elsif comparitor.call(left.first, right.first) <= 0
[left.first] + merge(left[1..-1], right, comparitor)
else
[right.first] + merge(left, right[1..-1], comparitor)
end
end
end
ary = [7,6,5,9,8,4,3,1,2,0] ary.mergesort # => [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] 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"]] ary.mergesort {|a, b| a[1] <=> b[1]}
- => [["US", "Birmingham"], ["UK", "Birmingham"], ["UK", "London"], ["US", "New York"]]</lang>
Scheme
<lang scheme>(define (merge-sort l gt?)
(letrec
(
(merge
(lambda (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))))))
(take
(lambda (l num)
(if (zero? num)
(list)
(cons (car l) (take (cdr l) (- num 1))))))
(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]
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>
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.
UnixPipes
split() {
(while read a b ; do
echo $a > $1 ; echo $b > $2
done)
}
mergesort() {
xargs -n 2 | (read a b; test -n "$b" && (
lc="1.$1" ; gc="2.$1"
(echo $a $b;cat)|split >(mergesort $lc >$lc) >( mergesort $gc >$gc)
sort -m $lc $gc
rm -f $lc $gc;
) || echo $a)
}
cat to.sort | mergesort
Ursala
<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.
[merge
[mergei
uncons [swap [>] split] dip
[[*m] e2 [*a1] b1 a2 : [*m *a1 e2] b1 a2] view].
[a b : [] a b] view
[size zero?] [pop concat]
[mergei]
tailrec].
[msort
[splitat [arr a : [arr a take arr a drop]] view i].
[splitarr dup size 2 / >int splitat].
[small?] []
[splitarr]
[merge]
binrec].
[8 7 6 5 4 2 1 3 9] msort puts