Sorting algorithms/Merge sort
You are encouraged to solve this task according to the task description, using any language you may know.
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For 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) (technically n*lg(n)--lg is log base 2) sort. It is notable for having no worst case. It is always O(n*log(n)). 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) 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. <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; </ada>
<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;
</ada> The following code provides an usage example for the generic package defined above. <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; </ada> The output of this example is:
1 5 2 7 3 9 4 6 1 2 3 4 5 6 7 9
Clojure
This solution is pilfered from the Haskell version.
(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
(defun merge-sort (result-type sequence predicate) (let ((split (floor (length sequence) 2))) (if (zerop split) (copy-seq sequence) (merge result-type (merge-sort result-type (subseq sequence 0 split) predicate) (merge-sort result-type (subseq sequence split) predicate) predicate))))
merge
is a standard Common Lisp function.
> (merge-sort 'list (list 1 3 5 7 9 8 6 4 2) #'<) (1 2 3 4 5 6 7 8 9)
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))) }
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'
mergeSort [] = [] mergeSort [x] = [x] mergeSort xs = merge (mergeSort $ take n xs) (mergeSort $ drop n xs) where n = length xs `div` 2
Java
<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; } }</java>
JavaScript
<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);
}</javascript>
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 less? 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
<ocaml>let rec split_at n xs =
match n, xs with 0, xs -> [], xs | _, [] -> failwith "index too large" | n, x::xs when x > 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]</ocaml>
Python
<python>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 merge(left, right)
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</python>
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?)))))
(merge-sort (list 1 3 5 7 9 8 6 4 2) >)
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
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