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This page uses content from Wikipedia. The original article was at Insertion sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)

An O(n²) sorting algorithm which moves elements one at a time into the correct position. The algorithm consists of inserting one element at a time into the previously sorted part of the array, moving higher ranked elements up as necessary. To start off, the first (or smallest, or any arbitrary) element of the unsorted array is considered to be the sorted part.

Although insertion sort is an O(n²) algorithm, its simplicity, low overhead, good locality of reference and efficiency make it a good choice in two cases (i) small n, (ii) as the final finishing-off algorithm for O(n logn) algorithms such as mergesort and quicksort.

The algorithm is as follows (from wikipedia):

function insertionSort(array A)
    for i from 1 to length[A]-1 do
        value := A[i] 
        j := i-1
        while j >= 0 and A[j] > value do
            A[j+1] := A[j]
            j := j-1
        done
        A[j+1] = value
    done

Writing the algorithm for integers will suffice.

ACL2

<lang Lisp>(defun insert (x xs)

  (cond ((endp xs) (list x))
        ((< x (first xs))
         (cons x xs))
        (t (cons (first xs)
                 (insert x (rest xs))))))

(defun isort (xs)

  (if (endp xs)
      nil
      (insert (first xs)
              (isort (rest xs)))))</lang>

ActionScript

<lang ActionScript>function insertionSort(array:Array) { for(var i:int = 1; i < array.length;i++) { var value = array[i]; var j:int = i-1; while(j >= 0 && array[j] > value) { array[j+1] = array[j]; j--; } array[j+1] = value; } return array; }</lang>

Ada

<lang ada>type Data_Array is array(Natural range <>) of Integer;

procedure Insertion_Sort(Item : in out Data_Array) is

  First : Natural := Item'First;
  Last  : Natural := Item'Last;
  Value : Integer;
  J     : Integer;

begin

  for I in (First + 1)..Last loop
     Value := Item(I);
     J := I - 1;
     while J in Item'range and then Item(J) > Value loop
        Item(J + 1) := Item(J);
        J := J - 1;
     end loop;
     Item(J + 1) := Value;
  end loop;

end Insertion_Sort;</lang>

ALGOL 68

Translation of: Ada

Works with: ALGOL 68 version Revision 1 - no extensions to language used

Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny

Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8-8d

<lang algol68>MODE DATA = REF CHAR;

PROC in place insertion sort = (REF[]DATA item)VOID: BEGIN

  INT first := LWB item;
  INT last  := UPB item;
  INT j;
  DATA value;
  FOR i FROM first + 1 TO last DO
     value := item[i];
     j := i - 1;
  #  WHILE j >= LWB item AND j <= UPB item ANDF item[j] > value DO // example of ANDF extension #
     WHILE ( j >= LWB item AND j <= UPB item | item[j]>value | FALSE ) DO # no extension! #
        item[j + 1] := item[j];
        j -:=  1
     OD;
     item[j + 1] := value
  OD

END # in place insertion sort #;

[32]CHAR data := "big fjords vex quick waltz nymph"; [UPB data]DATA ref data; FOR i TO UPB data DO ref data[i] := data[i] OD; in place insertion sort(ref data); FOR i TO UPB ref data DO print(ref data[i]) OD; print(new line); print((data))</lang> Output:

abcdefghiijklmnopqrstuvwxyz
big fjords vex quick waltz nymph

AutoHotkey

contributed by Laszlo on the ahk forum <lang AutoHotkey>MsgBox % InsertionSort("") MsgBox % InsertionSort("xxx") MsgBox % InsertionSort("3,2,1") MsgBox % InsertionSort("dog,000000,xx,cat,pile,abcde,1,cat,zz,xx,z")

InsertionSort(var) { ; SORT COMMA SEPARATED LIST

  StringSplit a, var, `,                ; make array, size = a0
  Loop % a0-1 {
     i := A_Index+1, v := a%i%, j := i-1
     While j>0 and a%j%>v
        u := j+1, a%u% := a%j%, j--
     u := j+1, a%u% := v
  }
  Loop % a0                             ; construct string from sorted array
     sorted .= "," . a%A_Index%
  Return SubStr(sorted,2)               ; drop leading comma

}</lang>

AWK

Sort standard input (storing lines into an array) and output to standard output <lang awk>{

 line[NR] = $0

} END { # sort it with insertion sort

 for(i=1; i <= NR; i++) {
   value = line[i]
   j = i - 1
   while( ( j > 0) && ( line[j] > value ) ) {
     line[j+1] = line[j]
     j--
   }
   line[j+1] = value
 }
 #print it
 for(i=1; i <= NR; i++) {
   print line[i]
 }

}</lang>

BASIC

Translation of: REALbasic

Works with: QBasic

This version should work on any BASIC that can accept arrays as function arguments. <lang qbasic>DECLARE SUB InsertionSort (theList() AS INTEGER)

DIM n(10) AS INTEGER, L AS INTEGER, o AS STRING FOR L = 0 TO 10

   n(L) = INT(RND * 32768)

NEXT InsertionSort n() FOR L = 1 TO 10

   PRINT n(L); ";";

   DIM insertionElementIndex AS INTEGER
   FOR insertionElementIndex = 1 TO UBOUND(theList)
       DIM insertionElement AS INTEGER
       insertionElement = theList(insertionElementIndex)
       DIM j AS INTEGER
       j = insertionElementIndex - 1
       DO WHILE (j >= 0)
           'necessary for BASICs without short-circuit evaluation
           IF (insertionElement < theList(j)) THEN
               theList(j + 1) = theList(j)
               j = j - 1
           ELSE
               EXIT DO
           END IF
       LOOP
       theList(j + 1) = insertionElement
   NEXT

END SUB</lang>

Sample output:

1486 ; 9488 ; 9894 ; 17479 ; 18989 ; 23119 ; 23233 ; 24927 ; 25386 ; 26689 ;

BBC BASIC

<lang BBCBASIC>DEF PROC_InsertionSort(Size%) FOR I%=2 TO Size%

  Temp%=data%(I%)
  J%=I%
  WHILE J%>1 AND Temp%<data%(J%-1)
     data%(J%)=data%(J%-1)
     J%=J%-1
  ENDWHILE
  IF J% <> I% data%(J%)=Temp%

NEXT I% ENDPROC</lang>

C

<lang c>#include <stddef.h>

static void insertion_sort(int *a, const size_t n) {

   size_t i, j;
   int value;
   for (i = 1; i < n; i++) {
       value = a[i];
       for (j = i; j > 0 && value < a[j - 1]; j--) {
           a[j] = a[j - 1];
       }
       a[j] = value;
   }

}

int main(void) {

   int a[] = {4, 65, 2, -31, 0, 99, 2, 83, 782, 1};
   insertion_sort(a, sizeof a / sizeof a[0]);
   return 0;

}</lang>

C++

Uses binary search via std::upper_bound() to find the insertion position in logarithmic time, then performs the insertion via std::rotate(), in linear time.

<lang cpp>#include <algorithm>

template<typename Iter> void insertion_sort(Iter beg, Iter end) {

   for (Iter i = beg; i != end; ++i)
       std::rotate(std::upper_bound(beg, i, *i), i, i+1);

}</lang>

C#

<lang csharp>using System;

namespace insertionsort {

   class Program
   {
       static void Main(string[] args)
       {
           int[] A = new int[] { 3, 9, 4, 6, 8, 1, 7, 2, 5 };
           insertionSort(ref A);
           Console.WriteLine(string.Join(",", A));
       }

       public static void insertionSort (ref int[] A){
           for (int i = 0; i < A.Length; i++)
           {
               int value = A[i], j = i-1;
               while (j >= 0 && A[j] > value)
               {
                   A[j + 1] = A[j];
                   j--;
               }
               A[j + 1] = value;
           }
       }
   }

} </lang>

Clojure

Translated from the Haskell example: <lang lisp>(defn in-sort! [data]

 (letfn [(insert ([raw x](insert [] raw x))

([sorted [y & raw] x] (if (nil? y) (conj sorted x) (if (<= x y ) (concat sorted [x,y] raw) (recur (conj sorted y) raw x )))))]

   (reduce insert [] data)))

Usage: (in-sort! [6,8,5,9,3,2,1,4,7])
Returns: [1 2 3 4 5 6 7 8 9]</lang>

CMake

<lang cmake># insertion_sort(var [value1 value2...]) sorts a list of integers. function(insertion_sort var)

 math(EXPR last "${ARGC} - 1")         # Sort ARGV[1..last].
 foreach(i RANGE 2 ${last})
   # Extend the sorted area to ARGV[1..i].
   set(b ${i})
   set(v ${ARGV${b}})
   # Insert v == ARGV[b] in sorted order. While b > 1, check if b is
   # too high, then decrement b. After loop, set ARGV[b] = v.
   while(b GREATER 1)
     math(EXPR a "${b} - 1")
     set(u ${ARGV${a}})
     # Now u == ARGV[a]. Pretend v == ARGV[b]. Compare.
     if(u GREATER ${v})
       # ARGV[a] and ARGV[b] are in wrong order. Fix by moving ARGV[a]
       # to ARGV[b], making room for later insertion of v.
       set(ARGV${b} ${u})
     else()
       break()
     endif()
     math(EXPR b "${b} - 1")
   endwhile()
   set(ARGV${b} ${v})
 endforeach(i)

 set(answer)
 foreach(i RANGE 1 ${last})
   list(APPEND answer ${ARGV${i}})
 endforeach(i)
 set("${var}" "${answer}" PARENT_SCOPE)

endfunction(insertion_sort)</lang>

<lang cmake>insertion_sort(result 33 11 44 22 66 55) message(STATUS "${result}") # -- 11;22;33;44;55;66</lang>

COBOL

This exerpt contains just enough of the procedure division to show the sort itself. The appropriate data division entries can be inferred. See also the entry for the Bubble sort for a full program. <lang COBOL> C-PROCESS SECTION.

          PERFORM E-INSERTION VARYING WB-IX-1 FROM 1 BY 1
                              UNTIL WB-IX-1 > WC-SIZE.

...

      E-INSERTION SECTION.
      E-000.
          MOVE WB-ENTRY(WB-IX-1) TO WC-TEMP.
          SET WB-IX-2 TO WB-IX-1.

          PERFORM F-PASS UNTIL WB-IX-2 NOT > 1 OR
                               WC-TEMP NOT < WB-ENTRY(WB-IX-2 - 1).

          IF WB-IX-1 NOT = WB-IX-2
             MOVE WC-TEMP TO WB-ENTRY(WB-IX-2).

      E-999.
          EXIT.

      F-PASS SECTION.
      F-000.
          MOVE WB-ENTRY(WB-IX-2 - 1) TO WB-ENTRY(WB-IX-2).
          SET WB-IX-2                DOWN BY 1.

      F-999.
          EXIT.</lang>

Common Lisp

<lang lisp>(defun span (predicate list)

 (let ((tail (member-if-not predicate list)))
   (values (ldiff list tail) tail)))

(defun less-than (x)

 (lambda (y) (< y x)))

(defun insert (list elt)

 (multiple-value-bind (left right) (span (less-than elt) list)
   (append left (list elt) right)))

(defun insertion-sort (list)

 (reduce #'insert list :initial-value nil))</lang>

D

<lang d>void insertionSort(T)(T[] data) pure nothrow {

   foreach (i, value; data[1 .. $]) {
       auto j = i + 1;
       for ( ; j > 0 && value < data[j - 1]; j--)
           data[j] = data[j - 1];
       data[j] = value;
   }

}

void main() {

   import std.stdio;
   auto items = [28, 44, 46, 24, 19, 2, 17, 11, 25, 4];
   items.insertionSort();
   writeln(items);

}</lang>

Output:

[2, 4, 11, 17, 19, 24, 25, 28, 44, 46]

Delphi

Array sort

Dynamic array is a 0-based array of variable length

Static array is an arbitrary-based array of fixed length <lang Delphi>program TestInsertionSort;

{$APPTYPE CONSOLE}

{.$DEFINE DYNARRAY} // remove '.' to compile with dynamic array

type

 TItem = Integer;   // declare ordinal type for array item

{$IFDEF DYNARRAY}

 TArray = array of TItem;          // dynamic array

{$ELSE}

 TArray = array[0..15] of TItem;   // static array

{$ENDIF}

procedure InsertionSort(var A: TArray); var

 I, J: Integer;
 Item: TItem;

begin

 for I:= 1 + Low(A) to High(A) do begin
   Item:= A[I];
   J:= I - 1;
   while (J >= Low(A)) and (A[J] > Item) do begin
     A[J + 1]:= A[J];
     Dec(J);
   end;
   A[J + 1]:= Item;
 end;

end;

var

 A: TArray;
 I: Integer;

begin {$IFDEF DYNARRAY}

 SetLength(A, 16);

{$ENDIF}

 for I:= Low(A) to High(A) do
   A[I]:= Random(100);
 for I:= Low(A) to High(A) do
   Write(A[I]:3);
 Writeln;
 InsertionSort(A);
 for I:= Low(A) to High(A) do
   Write(A[I]:3);
 Writeln;
 Readln;

end.</lang> Output:

  0  3 86 20 27 67 31 16 37 42  8 47  7 84  5 29
  0  3  5  7  8 16 20 27 29 31 37 42 47 67 84 86

String sort

// string is 1-based variable-length array of Char <lang Delphi>procedure InsertionSort(var S: string); var

 I, J, L: Integer;
 Ch: Char;

begin

 L:= Length(S);
 for I:= 2 to L do begin
   Ch:= S[I];
   J:= I - 1;
   while (J > 0) and (S[J] > Ch) do begin
     S[J + 1]:= S[J];
     Dec(J);
   end;
   S[J + 1]:= Ch;
 end;

end;</lang>

// in : S = 'the quick brown fox jumps over the lazy dog'
// out: S = '        abcdeeefghhijklmnoooopqrrsttuuvwxyz'

E

Some lines in this example are too long (more than 80 characters). Please fix the code if it's possible and remove this message.

A direct conversion of the pseudocode.

<lang e>def insertionSort(array) {

   for i in 1..!(array.size()) {
       def value := array[i]
       var j := i-1
       while (j >= 0 && array[j] > value) {
           array[j + 1] := array[j]
           j -= 1
       }
       array[j+1] := value
  }

}</lang>

Test case:

<lang e>? def a := [71, 53, 22, 24, 83, 54, 39, 78, 65, 26, 60, 75, 67, 27, 52, 59, 93, 62, 85, 99, 88, 10, 91, 85, 13, 17, 14, 96, 55, 10, 61, 94, 27, 50, 75, 40, 47, 63, 10, 23].diverge() > insertionSort(a) > a

value: [10, 10, 10, 13, 14, 17, 22, 23, 24, 26, 27, 27, 39, 40, 47, 50, 52, 53, 54, 55, 59, 60, 61, 62, 63, 65, 67, 71, 75, 75, 78, 83, 85, 85, 88, 91, 93, 94, 96, 99].diverge()</lang>

Eiffel

Works with: EiffelStudio version 6.6 (with provisional loop syntax)

This solution is shown in the routine sort of the class MY_SORTED_SET.

For a more complete explanation of the Eiffel sort examples, see the Bubble sort.

<lang eiffel>class

   MY_SORTED_SET [G -> COMPARABLE]

inherit

   TWO_WAY_SORTED_SET [G]
       redefine
           sort
       end

create

   make

feature

   sort
           -- Insertion sort
       local
           l_j: INTEGER
           l_value: like item
       do
           across 2 |..| count as ii loop
               from
                   l_j := ii.item - 1
                   l_value := Current.i_th (ii.item)
               until
                   l_j < 1 or Current.i_th (l_j) <= l_value
               loop
                   Current.i_th (l_j + 1) := Current.i_th (l_j)
                   l_j := l_j - 1
               end
               Current.i_th (l_j + 1) := l_value
           end
       end

end</lang>

Emacs Lisp

(defun min-or-max-of-2-numbers (n1 n2 rel)

 "n1 and n2 are two numbers, rel can be '< or '> according to

what sort of sorting is wanted, this function returns the greater or smaller number n1 or n2"

 (cond
  ((eval (list rel n1 n2)) n1)
  (t n2)))

(defun min-or-max-of-a-list (lon rel)

 "lon is a list of numbers, rel is '< or '>, this fonction

returns the higher or lower number of the list"

 (if (cdr lon)
     (min-or-max-of-2-numbers (car lon)

(min-or-max-of-a-list (cdr lon) rel) rel)

   (car lon)))

(defun remove-number-from-list (n lon)

 "lon is a list of numbers, n is a number belonging to the list,

this function returns the same list but the number n. If n is present twice or more, it will be removed only once"

 (if lon
     (cond
      ((= (car lon) n) (cdr lon))
      (t (cons (car lon) (remove-number-from-list n (cdr lon)))))
   nil))

(defun sort-insertion (lon rel)

 "lon is a list of numbers, rel can be '< or '>, this function

returns a list containing the same elements but which is sorted according to rel"

 (if lon
     (cons (min-or-max-of-a-list lon rel)

(sort-insertion (remove-number-from-list (min-or-max-of-a-list lon rel) lon) rel))

   nil))

let's try it

(sort-insertion (list 1 2 3 9 8 7 25 12 3 2 1) '>)

</lang>

Erlang

<lang Erlang>-module(sort). -export([insertion/1]).

insertion(L) -> lists:foldl(fun insert/2, [], L).

insert(X,[]) -> [X]; insert(X,L=[H|_]) when X =< H -> [X|L]; insert(X,[H|T]) -> [H|insert(X, T)].</lang>

And the calls: <lang erlang>1> c(sort). {ok,sort} 2> sort:insertion([5,3,9,4,1,6,8,2,7]). [1,2,3,4,5,6,7,8,9]</lang>

Euphoria

<lang euphoria>function insertion_sort(sequence s)

   object temp
   integer j
   for i = 2 to length(s) do
       temp = s[i]
       j = i-1
       while j >= 1 and compare(s[j],temp) > 0 do
           s[j+1] = s[j]
           j -= 1
       end while
       s[j+1] = temp
   end for
   return s

end function

include misc.e constant s = {4, 15, "delta", 2, -31, 0, "alfa", 19, "gamma", 2, 13, "beta", 782, 1}

puts(1,"Before: ") pretty_print(1,s,{2}) puts(1,"\nAfter: ") pretty_print(1,insertion_sort(s),{2})</lang>

Output:

Before: {
  4,
  15,
  "delta",
  2,
  -31,
  0,
  "alfa",
  19,
  "gamma",
  2,
  13,
  "beta",
  782,
  1
}
After: {
  -31,
  0,
  1,
  2,
  2,
  4,
  13,
  15,
  19,
  782,
  "alfa",
  "beta",
  "delta",
  "gamma"
}

Forth

<lang forth>: insert ( start end -- start )

 dup @ >r ( r: v )	\ v = a[i]
 begin
   2dup <			\ j>0
 while
   r@ over cell- @ <		\ a[j-1] > v
 while
   cell-			\ j--
   dup @ over cell+ !		\ a[j] = a[j-1]
 repeat then
 r> swap ! ;		\ a[j] = v

sort ( array len -- )

 1 ?do dup i cells + insert loop drop ;

create test 7 , 3 , 0 , 2 , 9 , 1 , 6 , 8 , 4 , 5 , test 10 sort test 10 cells dump</lang>

Fortran

Works with: Fortran version 90 and later

<lang fortran>PURE SUBROUTINE Insertion_Sort(a)

 REAL, INTENT(in out), DIMENSION(:) :: a
 REAL :: temp
 INTEGER :: i, j
  
 DO i = 2, SIZE(a)
    j = i - 1
    temp = a(i)
    DO WHILE (j>=1 .AND. a(j)>temp)
       a(j+1) = a(j)
       j = j - 1
    END DO
    a(j+1) = temp
 END DO

END SUBROUTINE Insertion_Sort</lang> In ISO Fortran 90 and above the intrinsic function CSHIFT can be used to shift the elements in the array but in practice is slower than the above example <lang fortran>DO i = 2, SIZE(a)

  j = i - 1
  DO WHILE (j>=1 .AND. a(j) > a(i))
     j = j - 1
  END DO
  a(j+1:i) = cshift(a(j+1:i),-1)

END DO</lang>

Alternate Fortran 77 version

<lang fortran> SUBROUTINE SORT(N,A)

     IMPLICIT NONE
     INTEGER N,I,J
     DOUBLE PRECISION A(N),X
     DO 30 I=2,N
     X=A(I)
     J=I
  10 J=J-1
     IF(J.EQ.0 .OR. A(J).LE.X) GO TO 20
     A(J+1)=A(J)
     GO TO 10
  20 A(J+1)=X
  30 CONTINUE
     END</lang>

GAP

<lang gap>InsertionSort := function(L)

 local n, i, j, x;
 n := Length(L);
 for i in [ 2 .. n ] do
   x := L[i];
   j := i - 1;
   while j >= 1 and L[j] > x do
     L[j + 1] := L[j];
     j := j - 1;
   od;
   L[j + 1] := x;
 od;

end;

s := "BFKRIMPOQACNESWUTXDGLVZHYJ"; InsertionSort(s); s;

"ABCDEFGHIJKLMNOPQRSTUVWXYZ"</lang>

Go

<lang go>package main

import "fmt"

func main() {

   var list insert = []int{31, 41, 59, 26, 53, 58, 97, 93, 23, 84}
   fmt.Println("unsorted:", list)

   list.sort()
   fmt.Println("sorted!  ", list)

}

type insert []int

func (a insert) sort() {

   for i := 1; i < len(a); i++ {
       value := a[i]
       j := i - 1
       for j >= 0 && a[j] > value {
           a[j+1] = a[j]
           j = j - 1
       }
       a[j+1] = value
   }

}</lang> Output:

unsorted: [31 41 59 26 53 58 97 93 23 84]
sorted!   [23 26 31 41 53 58 59 84 93 97]

Groovy

Solution: <lang groovy>def insertionSort = { list ->

   def size = list.size()
   (1..<size).each { i ->
       def value = list[i]
       def j = i - 1
       for (; j >= 0 && list[j] > value; j--) {
           print "."; list[j+1] = list[j]
       }
       print "."; list[j+1] = value
   }
   list

}</lang>

Test: <lang groovy>println (insertionSort([23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78,4])) println (insertionSort([88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70,12,7,1]))</lang>

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]

Haskell

<lang haskell>import Data.List (insert)

insertionSort :: Ord a => [a] -> [a] insertionSort = foldr insert []

-- Example use: -- *Main> insertionSort [6,8,5,9,3,2,1,4,7] -- [1,2,3,4,5,6,7,8,9]</lang>

HicEst

<lang hicest>DO i = 2, LEN(A)

  value = A(i)
  j = i - 1
1 IF( j > 0 ) THEN
    IF( A(j) > value ) THEN
      A(j+1) = A(j)
      j = j - 1
      GOTO 1 ! no WHILE in HicEst
    ENDIF
  ENDIF
  A(j+1) = value

ENDDO</lang>

Icon and Unicon

<lang Icon>procedure main() #: demonstrate various ways to sort a list and string

  demosort(insertionsort,[3, 14, 1, 5, 9, 2, 6, 3],"qwerty")

end

procedure insertionsort(X,op) #: return sorted X local i,temp

  op := sortop(op,X)                # select how and what we sort
  
  every i := 2 to *X do {
     temp := X[j := i]
     while op(temp,X[1 <= (j -:= 1)]) do 
        X[j+1] := X[j]
     X[j+1] := temp
     }
  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.

Abbreviated sample output:

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

J

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

Solution inspired by the Common LISP solution: <lang J>isort=:((>: # ]) , [ , < #])/</lang> Example of use: <lang J> isort 32 4 1 34 95 3 2 120 _38 _38 1 2 3 4 32 34 95 120</lang>

Java

<lang java5>public static void insertSort(int[] A){

 for(int i = 1; i < A.length; i++){
   int value = A[i];
   int j = i - 1;
   while(j >= 0 && A[j] > value){
     A[j + 1] = A[j];
     j = j - 1;
   }
   A[j + 1] = value;
 }

}</lang>

Using some built-in algorithms (warning: not stable, due to the lack of an "upper bound" binary search function)

Translation of: C++

<lang java5>public static <E extends Comparable<? super E>> void insertionSort(List<E> a) {

 for (int i = 1; i < a.size(); i++) {
   int j = Math.abs(Collections.binarySearch(a.subList(0, i), a.get(i)) + 1);
   Collections.rotate(a.subList(j, i+1), j - i);
 }

} public static <E extends Comparable<? super E>> void insertionSort(E[] a) {

 for (int i = 1; i < a.length; i++) {
   E x = a[i];
   int j = Math.abs(Arrays.binarySearch(a, 0, i, x) + 1);
   System.arraycopy(a, j, a, j+1, i-j);
   a[j] = x;
 }

}</lang>

JavaScript

<lang javascript> function insertionSort (a) {

   for (var i = 0; i < a.length; i++) {
       var k = a[i];
       for (var j = i; j > 0 && k < a[j - 1]; j--)
           a[j] = a[j - 1];
       a[j] = k;
   }
   return a;

}

var a = [4, 65, 2, -31, 0, 99, 83, 782, 1]; insertionSort(a); document.write(a.join(" ")); </lang>

Io

<lang io> List do(

 insertionSortInPlace := method(
   for(j, 1, size - 1,
     key := at(j)
     i := j - 1

     while(i >= 0 and at(i) > key,
       atPut(i + 1, at(i))
       i = i - 1
     )
     atPut(i + 1, key)
   )
 )

)

lst := list(7, 6, 5, 9, 8, 4, 3, 1, 2, 0) lst insertionSortInPlace println # ==> list(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)</lang>

A shorter, but slightly less efficient, version: <lang io>List do(

   insertionSortInPlace := method(
       # In fact, we could've done slice(1, size - 1) foreach(...)
       # but creating a new list in memory can only make it worse.
       foreach(idx, key,
           newidx := slice(0, idx) map(x, x > key) indexOf(true)
           if(newidx, insertAt(removeAt(idx), newidx))
       )
   self)

)

lst := list(7, 6, 5, 9, 8, 4, 3, 1, 2, 0) lst insertionSortInPlace println # ==> list(0, 1, 2, 3, 4, 5, 6, 7, 8, 9) </lang>

Liberty BASIC

<lang lb> itemCount = 20

   dim A(itemCount)
   for i = 1 to itemCount
       A(i) = int(rnd(1) * 100)
   next i

   print "Before Sort"
   gosub [printArray]

'--- Insertion sort algorithm

   for i = 2 to itemCount
       value = A(i)
       j = i-1
       while j >= 0 and A(j) > value
           A(j+1) = A(j)
           j = j-1
       wend
       A(j+1) = value
   next

'--- end of (Insertion sort algorithm)

   print "After Sort"
   gosub [printArray]

end

[printArray]

   for i = 1 to itemCount
       print using("###", A(i));
   next i
   print

return</lang>

Lua

<lang lua>function bins(tb, val, st, en)

 local st, en = st or 1, en or #tb
 local mid = math.floor((st + en)/2)
 if en == st then return tb[st] > val and st or st+1
 else return tb[mid] > val and bins(tb, val, st, mid) or bins(tb, val, mid+1, en)
 end

end function isort(t)

 local ret = {t[1], t[2]}
 for i = 3, #t do
   table.insert(ret, bins(ret, t[i]), t[i])
 end
 return ret

end

print(unpack(isort{4,5,2,7,8,3}))</lang>

Mathematica

<lang Mathematica>insertionSort[a_List] := Module[{A = a},

 For[i = 2, i <= Length[A], i++,
  value = Ai;    j = i - 1;
  While[j >= 1 && Aj > value, Aj + 1 = Aj; j--;];
  Aj + 1 = value;];

A ]</lang>

insertionSort@{ 2, 1, 3, 5}
{1, 2, 3, 5}

MATLAB / Octave

This is a direct translation of the pseudo-code above, except that it has been modified to compensate for MATLAB's 1 based arrays. <lang MATLAB>function list = insertionSort(list)

   for i = (2:numel(list))
       
       value = list(i);
       j = i - 1;
       
       while (j >= 1) && (list(j) > value)
           list(j+1) = list(j);
           j = j-1;
       end
       
       list(j+1) = value;
                  
   end %for

end %insertionSort</lang>

Sample Usage: <lang MATLAB>>> insertionSort([4 3 1 5 6 2])

ans =

    1     2     3     4     5     6</lang>

Modula-3

Translation of: Ada

<lang modula3>MODULE InsertSort;

PROCEDURE IntSort(VAR item: ARRAY OF INTEGER) =

 VAR j, value: INTEGER;
 BEGIN
   FOR i := FIRST(item) + 1 TO LAST(item) DO
     value := item[i];
     j := i - 1;
     WHILE j >= FIRST(item) AND item[j] > value DO
       item[j + 1] := item[j];
       DEC(j);
     END;
     item[j + 1] := value;
   END;
 END IntSort;

END InsertSort.</lang>

Nemerle

From the psuedocode. <lang Nemerle>using System.Console; using Nemerle.English;

module InsertSort {

   public static Sort(this a : array[int]) : void
   {
       mutable value = 0; mutable j = 0;
       foreach (i in [1 .. (a.Length - 1)])
       {
           value = a[i]; j = i - 1;
           while (j >= 0 and a[j] > value)
           {
               a[j + 1] = a[j];
               j = j - 1;
           }
           a[j + 1] = value;
       }
   }
   
   Main() : void
   {
       def arr = array[1, 4, 8, 3, 8, 3, 5, 2, 6];
       arr.Sort();
       foreach (i in arr) Write($"$i  ");
   }

}</lang>

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 -
 , insertionSort(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 insertionSort(A = String[]) public constant binary returns String[]

 rl = String[A.length]
 al = List insertionSort(Arrays.asList(A))
 al.toArray(rl)

 return rl

method insertionSort(A = List) public constant binary returns ArrayList

 loop i_ = 1 to A.size - 1
   value = A.get(i_)
   j_ = i_ - 1
   loop label j_ while j_ >= 0
     if (Comparable A.get(j_)).compareTo(Comparable value) <= 0 then leave j_
     A.set(j_ + 1, A.get(j_))
     j_ = j_ - 1
     end j_
     A.set(j_ + 1, value)
   end i_

 return ArrayList(A)

</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

Objeck

<lang objeck> bundle Default {

 class Insert {
   function : Main(args : String[]) ~ Nil {
     values := [9, 7, 10, 2, 9, 7, 4, 3, 10, 2, 7, 10];
     InsertionSort(values);
     each(i : values) {
       values[i]->PrintLine();
     };
   }
     
   function : InsertionSort (a : Int[]) ~ Nil {
     each(i : a) {
       value := a[i];
       j := i - 1;
       while(j >= 0 & a[j] > value) {
         a[j + 1] := a[j];
         j -= 1;
       };
       a[j + 1] := value;
     };
   }
 }

} </lang>

OCaml

<lang ocaml>let rec insert x = function

 [] -> [x]

| y :: ys ->

  if x <= y then x :: y :: ys
  else y :: insert x ys

let insertion_sort lst = List.fold_right insert lst [];;

insertion_sort [6;8;5;9;3;2;1;4;7];;</lang>

Oz

Direct translation of pseudocode. In-place sorting of mutable arrays. <lang oz>declare

 proc {InsertionSort A}
    Low = {Array.low A}
    High = {Array.high A}
 in
    for I in Low+1..High do
       Value = A.I
       J = {NewCell I-1}
    in
       for while:@J >= Low andthen A.@J > Value do
          A.(@J+1) := A.@J
          J := @J - 1
       end
       A.(@J+1) := Value
    end
 end

 Arr = {Tuple.toArray unit(3 1 4 1 5 9 2 6 5)}

in

 {InsertionSort Arr}
 {Show {Array.toRecord unit Arr}}</lang>

Qi

Based on the scheme version. <lang qi>(define insert

 X []     -> [X]
 X [Y|Ys] -> [X Y|Ys] where (<= X Y)
 X [Y|Ys] -> [Y|(insert X Ys)])

(define insertion-sort

 []     -> []
 [X|Xs] -> (insert X (insertion-sort Xs)))

(insertion-sort [6 8 5 9 3 2 1 4 7]) </lang>

PARI/GP

<lang parigp>insertionSort(v)={

 for(i=1,#v-1,
   my(j=i-1,x=v[i]);
   while(j && v[j]>x,
     v[j+1]=v[j];
     j--
   );
   v[j+1]=x
 );
 v

};</lang>

Pascal

See Delphi

Perl

<lang perl> sub insertion_sort {

   my (@list) = @_;
   foreach my $i (1 .. $#list) {
       my $j = $i;
       my $k = $list[$i];
       while ( $j > 0 && $k < $list[$j - 1]) {
           $list[$j] = $list[$j - 1];
           $j--;
       }
       $list[$j] = $k;
   }
   return @list;

}

my @a = insertion_sort(4, 65, 2, -31, 0, 99, 83, 782, 1); print "@a\n"; </lang> Output:

-31 0 1 2 4 65 83 99 782

Perl 6

<lang perl6>sub insertion_sort ( @a is copy ) {

   for 1 .. @a.end -> $i {
       my $value = @a[$i];
       my $j;
       loop ( $j = $i-1; $j >= 0 and @a[$j] > $value; $j-- ) {
           @a[$j+1] = @a[$j];
       }
       @a[$j+1] = $value;
   }
   return @a;

}

my @data = 22, 7, 2, -5, 8, 4; say 'input = ' ~ @data; say 'output = ' ~ @data.&insertion_sort; </lang>

Output:

input  = 22 7 2 -5 8 4
output = -5 2 4 7 8 22

PHP

<lang php>function insertionSort(&$arr){ for($i=0;$i<count($arr);$i++){ $val = $arr[$i]; $j = $i-1; while($j>=0 && $arr[$j] > $val){ $arr[$j+1] = $arr[$j]; $j--; } $arr[$j+1] = $val; } }

$arr = array(4,2,1,6,9,3,8,7); insertionSort($arr); echo implode(',',$arr);</lang>

1,2,3,4,6,7,8,9

PicoLisp

<lang PicoLisp>(de insertionSort (Lst)

  (for (I (cdr Lst)  I  (cdr I))
     (for (J Lst  (n== J I)  (cdr J))
        (T (> (car J) (car I))
           (rot J (offset I J)) ) ) )
  Lst )</lang>

Output:

: (insertionSort (5 3 1 7 4 1 1 20))
-> (1 1 1 3 4 5 7 20)

PL/I

<lang pli> INSSORT: PROCEDURE (A);

  DCL  A(*)        FIXED BIN(31);
  DCL (I, J, V, N) FIXED BIN(31);

  N = HBOUND(A,1); M = LBOUND(A,1);
  DO I=M+1 TO N;
     V=A(I);
     J=I-1;
     DO WHILE (J > M-1);
        if A(J) <= V then leave;
        A(J+1)=A(J); J=J-1;
     END;
     A(J+1)=V;
  END;
  RETURN;

END INSSORT; </lang>

Prolog

<lang prolog>insert_sort(L1,L2) :-

 insert_sort_intern(L1,[],L2).

insert_sort_intern([],L,L). insert_sort_intern([H|T],L1,L) :-

 insert(L1,H,L2),
 insert_sort_intern(T,L2,L).

insert([],X,[X]). insert([H|T],X,[X,H|T]) :-

 X =< H,
 !.

insert([H|T],X,[H|T2]) :-

 insert(T,X,T2).</lang>

% Example use:
%    ?- insert_sort([2,23,42,3,10,1,34,5],L).
%    L = [1,2,3,5,10,23,34,42] ? 
%    yes

Functional approach

Works with SWI-Prolog.
Insertion sort inserts elements of a list in a sorted list. So we can use foldl to sort a list. <lang Prolog>% insertion sort isort(L, LS) :- foldl(insert, [], L, LS).

% foldl(Pred, Init, List, R). foldl(_Pred, Val, [], Val). foldl(Pred, Val, [H | T], Res) :- call(Pred, Val, H, Val1), foldl(Pred, Val1, T, Res).

% insertion in a sorted list insert([], N, [N]).

insert([H | T], N, [N, H|T]) :- N =< H, !.

insert([H | T], N, [H|L1]) :- insert(T, N, L1). </lang> Example use:

 ?- isort([2,23,42,3,10,1,34,5],L).
L = [1,2,3,5,10,23,34,42]

PureBasic

<lang PureBasic>Procedure insertionSort(Array a(1))

 Protected low, high
 Protected firstIndex, lastIndex = ArraySize(a())
 
 If lastIndex > firstIndex + 1
   low = firstIndex + 1
   While low <= lastIndex
     high = low
     While high > firstIndex
       If a(high) < a(high - 1)
         Swap a(high), a(high - 1)
       Else
         Break
       EndIf
       high - 1
     Wend
     low + 1
   Wend
 EndIf

EndProcedure</lang>

Python

<lang python>def insertion_sort(l):

   for i in xrange(1, len(l)):
       j = i-1 
       key = l[i]
       while (l[j] > key) and (j >= 0):
          l[j+1] = l[j]
          j -= 1
       l[j+1] = key</lang>

Insertion sort with binary search

<lang python>def insertion_sort_bin(seq):

   for i in range(1, len(seq)):
       key = seq[i]
       # invariant: ``seq[:i]`` is sorted        
       # find the least `low' such that ``seq[low]`` is not less then `key'.
       #   Binary search in sorted sequence ``seq[low:up]``:
       low, up = 0, i
       while up > low:
           middle = (low + up) // 2
           if seq[middle] < key:
               low = middle + 1              
           else:
               up = middle
       # insert key at position ``low``
       seq[:] = seq[:low] + [key] + seq[low:i] + seq[i + 1:]</lang>

This is also built-in to the standard library:

<lang python>import bisect def insertion_sort_bin(seq):

   for i in range(1, len(seq)):
       bisect.insort(seq, seq.pop(i), 0, i)</lang>

R

Direct translation of pseudocode. <lang r>insertionsort <- function(x) {

  for(i in 2:(length(x)))
  {
     value <- x[i]
     j <- i - 1
     while(j >= 1 && x[j] > value)
     {
        x[j+1] <- x[j]
        j <- j-1
     }
     x[j+1] <- value
  }
  x

} insertionsort(c(4, 65, 2, -31, 0, 99, 83, 782, 1)) # -31 0 1 2 4 65 83 99 782</lang>

REALbasic

<lang vb>Sub InsertionSort(theList() as Integer)

 for insertionElementIndex as Integer = 1 to UBound(theList)
   dim insertionElement as Integer = theList(insertionElementIndex)
   dim j as Integer = insertionElementIndex - 1
   while (j >= 0) and (insertionElement < theList(j))
     theList(j + 1) = theList(j)
     j = j - 1
   wend
   theList(j + 1) = insertionElement
 next

End Sub</lang>

REXX

<lang rexx>/*REXX program sorts an array using the insertion-sort method. */

call gen@ /*generate array elements. */ call show@ 'before sort' /*show before array elements*/ call insertionSort highItem /*invoke the insertion sort.*/ call show@ ' after sort' /*show after array elements*/ exit

/*─────────────────────────────────────INSERTIONSORT subroutine────*/ insertionSort: procedure expose @.; parse arg highItem

 do i=2 to highItem
 value=@.i

    do j=i-1 by -1 while j\==0 & @.j>value
    jp1=j+1
    @.jp1=@.j
    end

 jp1=j+1
 @.jp1=value
 end

return

/*─────────────────────────────────────GEN@ subroutine─────────────*/ gen@: @.= /*assign default value. */

@.1="---Monday's Child Is Fair of Face (by Mother Goose)---" @.2="Monday's child is fair of face;" @.3="Tuesday's child is full of grace;" @.4="Wednesday's child is full of woe;" @.5="Thursday's child has far to go;" @.6="Friday's child is loving and giving;" @.7="Saturday's child works hard for a living;" @.8="But the child that is born on the Sabbath day" @.9="Is blithe and bonny, good and gay."

 do highItem=1 while @.highItem\==  /*find how many entries.    */
 end

highItem=highItem-1 /*adjust highItem slightly. */ return

/*─────────────────────────────────────SHOW@ subroutine────────────*/ show@: widthH=length(highItem) /*maximum width of any line.*/

 do j=1 for highItem
 say 'element' right(j,widthH) arg(1)':' @.j
 end

say copies('─',80) /*show a seperator line. */ return</lang>

Output:

element 1 before sort: ---Monday's Child Is Fair of Face  (by Mother Goose)---
element 2 before sort: Monday's child is fair of face;
element 3 before sort: Tuesday's child is full of grace;
element 4 before sort: Wednesday's child is full of woe;
element 5 before sort: Thursday's child has far to go;
element 6 before sort: Friday's child is loving and giving;
element 7 before sort: Saturday's child works hard for a living;
element 8 before sort: But the child that is born on the Sabbath day
element 9 before sort: Is blithe and bonny, good and gay.
────────────────────────────────────────────────────────────────────────────────

element 1  after sort: ---Monday's Child Is Fair of Face  (by Mother Goose)---
element 2  after sort: But the child that is born on the Sabbath day
element 3  after sort: Friday's child is loving and giving;
element 4  after sort: Is blithe and bonny, good and gay.
element 5  after sort: Monday's child is fair of face;
element 6  after sort: Saturday's child works hard for a living;
element 7  after sort: Thursday's child has far to go;
element 8  after sort: Tuesday's child is full of grace;
element 9  after sort: Wednesday's child is full of woe;
────────────────────────────────────────────────────────────────────────────────

Ruby

<lang ruby>class Array

 def insertionsort!
   1.upto(length - 1) do |i|
     value = self[i]
     j = i - 1
     while j >= 0 and self[j] > value
       self[j+1] = self[j]
       j -= 1
     end
     self[j+1] = value
   end
   self
 end

end ary = [7,6,5,9,8,4,3,1,2,0] ary.insertionsort!

=> [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]</lang>

Alternative version which doesn't swap elements but rather removes and inserts the value at the correct place: <lang ruby>class Array

 def insertionsort!
   return if length < 2

   1.upto(length - 1) do |i|
     value = delete_at i
     j = i - 1
     j -= 1 while j >= 0 && value < self[j]
     insert(j + 1, value)
   end
   self
 end

end

ary = [7,6,5,9,8,4,3,1,2,0] ary.insertionsort!

=> [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]</lang>

Scala

<lang scala>def insert(list: List[Int], value: Int) = list.span(_ < value) match {

 case (lower, upper) => lower ::: value :: upper

} def insertSort(list: List[Int]) = list.foldLeft(List[Int]())(insert)</lang>

Scheme

<lang scheme>(define (insert x lst)

 (if (null? lst)
     (list x)
     (let ((y (car lst))
           (ys (cdr lst)))
       (if (<= x y)
           (cons x lst)
           (cons y (insert x ys))))))

(define (insertion-sort lst)

 (if (null? lst)
     '()
     (insert (car lst)
             (insertion-sort (cdr lst)))))

(insertion-sort '(6 8 5 9 3 2 1 4 7))</lang>

Seed7

<lang seed7>const proc: insertionSort (inout array elemType: arr) is func

 local
   var integer: i is 0;
   var integer: j is 0;
   var elemType: help is elemType.value;
 begin
   for i range 2 to length(arr) do
     j := i;
     help := arr[i];
     while j > 1 and arr[pred(j)] > help do
       arr[j] := arr[pred(j)];
       decr(j);
     end while;
     arr[j] := help;
   end for;
 end func;</lang>

Original source: [1]

SNOBOL4

<lang snobol>* read data into an array A = table() i = 0 readln A = trim(input) :s(readln) aSize = i - 1

sort array
i = 1 loop1 value = A j = i - 1 loop2 gt(j,0) gt(A<j>,value) :f(done2) A<j + 1> = A<j> j = j - 1 :(loop2) done2 A<j + 1> = value i = ?lt(i,aSize) i + 1 :s(loop1) i = 1
output sorted data
while output = A; i = ?lt(i,aSize) i + 1 :s(while) end</lang>

Standard ML
<lang sml>fun insertion_sort cmp = let
fun insert (x, []) = [x] | insert (x, y::ys) = case cmp (x, y) of GREATER => y :: insert (x, ys) | _ => x :: y :: ys
in
foldl insert []
end;
insertion_sort Int.compare [6,8,5,9,3,2,1,4,7];</lang>
TI-83 BASIC
Store input in L₁, run prgmSORTINS, get output in L₂.
:L₁→L₂ :0→A :Lbl L :A+1→A :A→B :While B>0 :If L₂(B)<L₂(B+1) :Goto B :L₂(B)→C :L₂(B+1)→L₂(B) :C→L₂(B+1) :B-1→B :End :Lbl B :If A<(dim(L₂)-1) :Goto L :DelVar A :DelVar B :DelVar C :Stop
Tcl
<lang tcl>package require Tcl 8.5
proc insertionsort {m} {
for {set i 1} {$i < [llength $m]} {incr i} { set val [lindex $m $i] set j [expr {$i - 1}] while {$j >= 0 && [lindex $m $j] > $val} { lset m [expr {$j + 1}] [lindex $m $j] incr j -1 } lset m [expr {$j + 1}] $val } return $m
}
puts [insertionsort {8 6 4 2 1 3 5 7 9}] ;# => 1 2 3 4 5 6 7 8 9</lang>
TI-83 BASIC
Input into L₁, run prgmSORTINS, output in L₂.
:"INSERTION" :L₁→L₂ :0→A :Lbl L :A+1→A :A→B :While B>0 :If L₂(B)≤L₂(B+1) :Goto B :L₂(B)→C :L₂(B+1)→L₂(B) :C→L₂(B+1) :B-1→B :End :Lbl B :If A<(dim(L₂)-1) :Goto L :DelVar A :DelVar B :DelVar C :Return
UnixPipes
<lang bash>selectionsort() {
read a test -n "$a" && ( selectionsort | sort -nm <(echo $a) -)
}</lang> <lang bash>cat to.sort | selectionsort</lang>
Ursala
<lang Ursala>#import nat
insort = ~&i&& @hNCtX ~&r->lx ^\~&rt nleq-~rlrSPrhlPrSCPTlrShlPNCTPQ@rhPlD</lang> test program: <lang Ursala>#cast %nL
example = insort <45,82,69,82,104,58,88,112,89,74></lang> output:
<45,58,69,74,82,82,88,89,104,112>
Yorick
Based on pseudocode, except using 1-based arrays. <lang yorick>func insertionSort(&A) {
for(i = 2; i <= numberof(A); i++) { value = A(i); j = i - 1; while(j >= 1 && A(j) > value) { A(j+1) = A(j); j--; } A(j+1) = value; }
}</lang>