# Sorting algorithms/Insertion sort

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Sorting algorithms/Insertion 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:

O(n logn) sorts

O(n log2n) sorts
Shell Sort

 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:

1.   small   n,
2.   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.

## 11l

Translation of: Python
```F insertion_sort(&l)
L(i) 1 .< l.len
V j = i - 1
V key = l[i]
L j >= 0 & l[j] > key
l[j + 1] = l[j]
j--
l[j + 1] = key

V arr = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0]
insertion_sort(&arr)
print(arr)```
Output:
```[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
```

## 360 Assembly

Translation of: PL/I

These programs use two ASSIST macros (XDECO, XPRNT) to keep the code as short as possible.

### Basic

```*        Insertion sort            16/06/2016
INSSORT  CSECT
USING  INSSORT,R13        base register
B      72(R15)            skip savearea
DC     17F'0'             savearea
STM    R14,R12,12(R13)    prolog
ST     R13,4(R15)         "
ST     R15,8(R13)         "
LR     R13,R15            "
LA     R6,2               i=2
LA     R9,A+L'A           @a(2)
LOOPI    C      R6,N               do i=2 to n
BH     ELOOPI             leave i
L      R2,0(R9)           a(i)
ST     R2,V               v=a(i)
LR     R7,R6              j=i
BCTR   R7,0               j=i-1
LR     R8,R9              @a(i)
S      R8,=A(L'A)         @a(j)
LOOPJ    LTR    R7,R7              do j=i-1 to 1 by -1 while j>0
BNH    ELOOPJ             leave j
L      R2,0(R8)           a(j)
C      R2,V               a(j)>v
BNH    ELOOPJ             leave j
MVC    L'A(L'A,R8),0(R8)  a(j+1)=a(j)
BCTR   R7,0               j=j-1
S      R8,=A(L'A)         @a(j)
B      LOOPJ              next j
ELOOPJ   MVC    L'A(L'A,R8),V      a(j+1)=v;
LA     R6,1(R6)           i=i+1
LA     R9,L'A(R9)         @a(i)
B      LOOPI              next i
ELOOPI   LA     R9,PG              pgi=0
LA     R6,1               i=1
LA     R8,A               @a(1)
LOOPXI   C      R6,N               do i=1 to n
BH     ELOOPXI            leave i
L      R1,0(R8)           a(i)
XDECO  R1,XDEC            edit a(i)
MVC    0(4,R9),XDEC+8     output a(i)
LA     R9,4(R9)           pgi=pgi+1
LA     R6,1(R6)           i=i+1
LA     R8,L'A(R8)         @a(i)
B      LOOPXI             next i
ELOOPXI  XPRNT  PG,L'PG            print buffer
L      R13,4(0,R13)       epilog
LM     R14,R12,12(R13)    "
XR     R15,R15            "
BR     R14                exit
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'
V        DS     F                  variable
N        DC     A((V-A)/L'A)       n=hbound(a)
PG       DC     CL80' '            buffer
XDEC     DS     CL12               for xdeco
YREGS                     symbolics for registers
END    INSSORT```
Output:
``` -31   0   1   2   2   4  45  58  65  69  74  82  82  83  88  89  99 104 112 782
```

### Assembler Structured Macros

No harmful gotos [:)Dijkstra], no labels. It's cleaner, but is it clearer?

```*        Insertion sort        16/06/2016
INSSORTS CSECT
USING  INSSORTS,R13       base register
B      72(R15)            skip savearea
DC     17F'0'             savearea
STM    R14,R12,12(R13)    prolog
ST     R13,4(R15)         "
ST     R15,8(R13)         "
LR     R13,R15            "
LA     R6,2               i=2
LA     R9,A+L'A           @a(2)
DO     WHILE=(C,R6,LE,N)  do while i<=n
L      R2,0(R9)           a(i)
ST     R2,V               v=a(i)
LR     R7,R6              j=i
BCTR   R7,0               j=i-1
LR     R8,R9              @a(i)
S      R8,=A(L'A)         @a(j)
L      R2,0(R8)           a(j)
DO     WHILE=(C,R7,GT,0,AND,C,R2,GT,V)  do while j>0 & a(j)>v
MVC    L'A(L'A,R8),0(R8)  a(j+1)=a(j)
BCTR   R7,0               j=j-1
S      R8,=A(L'A)         @a(j)
L      R2,0(R8)           a(j)
ENDDO  ,                  next j
MVC    L'A(L'A,R8),V      a(j+1)=v;
LA     R6,1(R6)           i=i+1
LA     R9,L'A(R9)         @a(i)
ENDDO  ,                  next i
LA     R9,PG              pgi=0
LA     R6,1               i=1
LA     R8,A               @a(1)
DO     WHILE=(C,R6,LE,N)  do while i<=n
L      R1,0(R8)           a(i)
XDECO  R1,XDEC            edit a(i)
MVC    0(4,R9),XDEC+8     output a(i)
LA     R9,4(R9)           pgi=pgi+1
LA     R6,1(R6)           i=i+1
LA     R8,L'A(R8)         @a(i)
ENDDO  ,                  next i
XPRNT  PG,L'PG            print buffer
L      R13,4(0,R13)       epilog
LM     R14,R12,12(R13)    "
XR     R15,R15            "
BR     R14                exit
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'
V    DS     F                  variable
N    DC     A((V-A)/L'A)       n=hbound(a)
PG   DC     CL80' '            buffer
XDEC DS     CL12               for xdeco
YREGS                     symbolics for registers
END    INSSORTS```
Output:

Same as previous

## AArch64 Assembly

Works with: as version Raspberry Pi 3B version Buster 64 bits
```/* ARM assembly AARCH64 Raspberry PI 3B */
/*  program insertionSort64.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
.equ NBELEMENTS, (. - TableNumber) / 8
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConv:       .skip 24
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main
main:                                              // entry of program
mov x1,0                                       // first element
mov x2,NBELEMENTS                              // number of élements
bl insertionSort
bl displayTable

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
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

/******************************************************************/
/*     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:
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
/******************************************************************/
/*         insertion sort                                              */
/******************************************************************/
/* x0 contains the address of table */
/* x1 contains the first element    */
/* x2 contains the number of element */
insertionSort:
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
add x3,x1,1                // index i
1:                             // start loop 1
ldr x4,[x0,x3,lsl 3]       // load value A[i]
sub x5,x3,1                // index j
2:                             // start loop 2
ldr x6,[x0,x5,lsl 3]       // load value A[j]
cmp x6,x4                  // compare value
ble 3f
add x5,x5,1                // increment index j
str x6,[x0,x5,lsl 3]       // store value A[j+1}
sub x5,x5,2                // j = j - 1
cmp x5,x1                  // compare first element
bge 2b                     // loop 2
3:
add x5,x5,1                // increment index j
str x4,[x0,x5,lsl 3]       // store value A[i}
add x3,x3,1                // increment index i
cmp x3,x2                  // end ?
blt 1b                     // loop 1

100:
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

/******************************************************************/
/*      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]
bl conversion10S                  // décimal conversion
bl strInsertAtCharInc            // insert result at @ character
bl affichageMess                 // display message
cmp x3,NBELEMENTS - 1
ble 1b
bl affichageMess
mov x0,x2
100:
ldp x2,x3,[sp],16               // restaur  2 registers
ldp x1,lr,[sp],16               // restaur  2 registers
/********************************************************/
/*        File Include fonctions                        */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"```

## ACL2

```(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)))))
```

## Action!

```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 InsertionSort(INT ARRAY a INT size)
INT i,j,value

FOR i=1 TO size-1
DO
value=a(i)
j=i-1
WHILE j>=0 AND a(j)>value
DO
a(j+1)=a(j)
j==-1
OD
a(j+1)=value
OD
RETURN

PROC Test(INT ARRAY a INT size)
PrintE("Array before sort:")
PrintArray(a,size)
InsertionSort(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```
Output:
```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

```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;
}
```

```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;
```

## ALGOL 68

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
```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))```
Output:
```abcdefghiijklmnopqrstuvwxyz
big fjords vex quick waltz nymph
```

## ALGOL W

External in-place insertion sort routine for integers. From the pseudo code but with variable bounds.

```% insertion sorts in-place the array A. As Algol W procedures can't find the bounds %
% of an array parameter, the lower and upper bounds must be specified in lb and ub  %
procedure insertionSortI ( integer array A ( * ); integer value lb, ub ) ;
for i := lb + 1 until ub do begin
integer v, j;
v := A( i );
j := i - 1;
while j >= lb and A( j ) > v do begin
A( j + 1 ) := A( j );
j := j - 1
end while_j_ge_0_and_Aj_gt_v ;
A( j + 1 ) := v
end insertionSortI ;```

Test the insertionSortI procedure.

```begin
% external in-place insertion sort procedure %
procedure insertionSortI ( integer array A( * ); integer value lb, ub ) ;
algol "ISORTI" ;

integer array d ( 1 :: 8 );
integer p;
p := 1;
for i := 34, 2, -1, 0, 0, 9, -56, 3 do begin
d( p ) := i;
p := p + 1
end for_i ;
insertionSortI( d, 1, 8 );
write( i_w := 1, d( 1 ) );
for i := 2 until 8 do writeon( i_w := 1, d( i ) )
end.```
Output:
```-56  -1  0  0  2  3  9  34
```

## AppleScript

```-- In-place insertion sort
on insertionSort(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}

-- The list as a script property to allow faster references to its items.
script o
property lst : theList
end script

-- Set up a minor optimisation whereby the latest instance of the highest value so far isn't
-- put back into the list until either it's superseded or the end of the sort is reached.
set highestSoFar to o's lst's item l
set rv to o's lst's item (l + 1)
if (highestSoFar > rv) then
set o's lst's item l to rv
else
set highestSoFar to rv
end if
-- Work through the rest of the range, rotating values back into the sorted group as necessary.
repeat with j from (l + 2) to r
set rv to o's lst's item j
if (highestSoFar > rv) then
repeat with i from (j - 2) to l by -1
set lv to o's lst's item i
if (lv > rv) then
set o's lst's item (i + 1) to lv
else
set i to i + 1
exit repeat
end if
end repeat
set o's lst's item i to rv
else
set o's lst's item (j - 1) to highestSoFar
set highestSoFar to rv
end if
end repeat
set o's lst's item r to highestSoFar

return -- nothing.
end insertionSort
property sort : insertionSort

-- Demo:
local aList
set aList to {60, 73, 11, 66, 6, 77, 41, 97, 59, 45, 64, 15, 91, 100, 22, 89, 77, 59, 54, 61}
sort(aList, 1, -1) -- Sort items 1 thru -1 of aList.
return aList
```
Output:
```{6, 11, 15, 22, 41, 45, 54, 59, 59, 60, 61, 64, 66, 73, 77, 77, 89, 91, 97, 100}
```

## ARM Assembly

Works with: as version Raspberry Pi
```/* ARM assembly Raspberry PI  */
/*  program insertionSort.s   */
/* look Pseudocode begin this task  */

/************************************/
/* Constantes                       */
/************************************/
.equ STDOUT, 1     @ Linux output console
.equ EXIT,   1     @ Linux syscall
.equ WRITE,  4     @ Linux syscall
/*********************************/
/* Initialized data              */
/*********************************/
.data
szMessSortOk:       .asciz "Table sorted.\n"
szMessSortNok:      .asciz "Table not sorted !!!!!.\n"
sMessResult:        .ascii "Value  : "
sMessValeur:        .fill 11, 1, ' '            @ size => 11
szCarriageReturn:  .asciz "\n"

.align 4
iGraine:  .int 123456
.equ NBELEMENTS,      10
#TableNumber:      .int   1,3,6,2,5,9,10,8,4,7
TableNumber:     .int   10,9,8,7,6,5,4,3,2,1
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main
main:                                              @ entry of program

1:
mov r1,#0
mov r2,#NBELEMENTS                             @ number of élements
bl insertionSort
bl displayTable

mov r1,#NBELEMENTS                             @ number of élements
bl isSorted                                    @ control sort
cmp r0,#1                                      @ sorted ?
beq 2f
ldr r0,iAdrszMessSortNok                       @ no !! error sort
bl affichageMess
b 100f
2:                                                 @ yes
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

/******************************************************************/
/*     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:
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
/******************************************************************/
/*         insertion sort                                              */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the first element    */
/* r2 contains the number of element */
insertionSort:
push {r2,r3,r4,lr}                                     @ save registers
add r3,r1,#1                                           @ start index i
1:                                                         @ start loop
ldr r4,[r0,r3,lsl #2]                                  @ load value A[i]
sub r5,r3,#1                                           @ index j
2:
ldr r6,[r0,r5,lsl #2]                                  @ load value A[j]
cmp r6,r4                                              @ compare value
ble 3f
add r5,#1                                              @ increment index j
str r6,[r0,r5,lsl #2]                                  @ store value A[j+1]
sub r5,#2                                              @ j = j - 1
cmp r5,r1
bge 2b                                                 @ loop if j >= first item
3:
add r5,#1                                              @ increment index j
str r4,[r0,r5,lsl #2]                                  @ store value A[i] in A[j+1]
add r3,#1                                              @ increment index i
cmp r3,r2                                              @ end ?
blt 1b                                                 @ no -> loop

100:
pop {r2,r3,r4,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,iAdrsMessValeur                             @ display value
bl conversion10                                    @ call function
bl affichageMess                                   @ display message
cmp r3,#NBELEMENTS - 1
ble 1b
bl affichageMess
100:
pop {r0-r3,lr}
bx lr
/******************************************************************/
/*     display text with size calculation                         */
/******************************************************************/
/* r0 contains the address of the message */
affichageMess:
push {r0,r1,r2,r7,lr}                          @ save  registres
mov r2,#0                                      @ counter length
1:                                                 @ loop length calculation
ldrb r1,[r0,r2]                                @ read octet start position + index
cmp r1,#0                                      @ if 0 its over
addne r2,r2,#1                                 @ else add 1 in the length
bne 1b                                         @ and loop
@ so here r2 contains the length of the message
mov r1,r0                                      @ address message in r1
mov r0,#STDOUT                                 @ code to write to the standard output Linux
mov r7, #WRITE                                 @ code call system "write"
svc #0                                         @ call systeme
pop {r0,r1,r2,r7,lr}                           @ restaur des  2 registres */
bx lr                                          @ return
/******************************************************************/
/*     Converting a register to a decimal unsigned                */
/******************************************************************/
/* r0 contains value and r1 address area   */
/* r0 return size of result (no zero final in area) */
/* area size => 11 bytes          */
.equ LGZONECAL,   10
conversion10:
push {r1-r4,lr}                                 @ save registers
mov r3,r1
mov r2,#LGZONECAL

1:	                                            @ start loop
bl divisionpar10U                               @ unsigned  r0 <- dividende. quotient ->r0 reste -> r1
add r1,#48                                      @ digit
strb r1,[r3,r2]                                 @ store digit on area
cmp r0,#0                                       @ stop if quotient = 0
subne r2,#1                                     @ else previous position
bne 1b	                                    @ and loop
@ and move digit from left of area
mov r4,#0
2:
ldrb r1,[r3,r2]
strb r1,[r3,r4]
cmp r2,#LGZONECAL
ble 2b
@ and move spaces in end on area
mov r0,r4                                         @ result length
mov r1,#' '                                       @ space
3:
strb r1,[r3,r4]                                   @ store space in area
add r4,#1                                         @ next position
cmp r4,#LGZONECAL
ble 3b                                            @ loop if r4 <= area size

100:
pop {r1-r4,lr}                                    @ restaur registres
bx lr                                             @return

/***************************************************/
/*   division par 10   unsigned                    */
/***************************************************/
/* r0 dividende   */
/* r0 quotient */
/* r1 remainder  */
divisionpar10U:
push {r2,r3,r4, lr}
mov r4,r0                                          @ save value
//mov r3,#0xCCCD                                   @ r3 <- magic_number lower  raspberry 3
//movt r3,#0xCCCC                                  @ r3 <- magic_number higter raspberry 3
ldr r3,iMagicNumber                                @ r3 <- magic_number    raspberry 1 2
umull r1, r2, r3, r0                               @ r1<- Lower32Bits(r1*r0) r2<- Upper32Bits(r1*r0)
mov r0, r2, LSR #3                                 @ r2 <- r2 >> shift 3
add r2,r0,r0, lsl #2                               @ r2 <- r0 * 5
sub r1,r4,r2, lsl #1                               @ r1 <- r4 - (r2 * 2)  = r4 - (r0 * 10)
pop {r2,r3,r4,lr}
bx lr                                              @ leave function
iMagicNumber:  	.int 0xCCCCCCCD```

## Arturo

```insertionSort: function [items][
arr: new items
loop 1..(size items)-1 'i [
value: arr\[i]
j: i - 1

while [and? -> j >= 0
-> value < arr\[j]]
[
arr\[j+1]: arr\[j]
j: j - 1
]
arr\[j+1]: value
]
return arr
]

print insertionSort [3 1 2 8 5 7 9 4 6]
```
Output:
`1 2 3 4 5 6 7 8 9`

## ATS

### For arrays whose elements must not be of linear type

This implementation finds the position at which the element is to be inserted, and then uses array_subcirculate to move it into place. The prelude's implementation of array_subcirculate is a memmove(3).

```#include "share/atspre_staload.hats"

(*------------------------------------------------------------------*)
(* Interface                                                        *)

extern fn {a : t@ype}           (* The "less than" template. *)
insertion_sort\$lt : (a, a) -<> bool (* Arguments by value. *)

extern fn {a : t@ype}
insertion_sort
{n   : int}
(arr : &array (a, n) >> _,
n   : size_t n)
:<!wrt> void

(*------------------------------------------------------------------*)
(* Implementation                                                   *)

implement {a}
insertion_sort {n} (arr, n) =
let
macdef lt = insertion_sort\$lt<a>

fun
sort {i : int | 1 <= i; i <= n}
.<n - i>.
(arr : &array (a, n) >> _,
i   : size_t i)
:<!wrt> void =
if i <> n then
let
fun
find_new_position
{j : nat | j <= i}
.<j>.
(arr  : &array (a, n) >> _,
elem : a,
j    : size_t j)
:<> [j : nat | j <= i] size_t j =
if j = i2sz 0 then
j
else if ~(elem \lt arr[pred j]) then
j
else
find_new_position (arr, elem, pred j)

val j = find_new_position (arr, arr[i], i)
in
if j < i then
array_subcirculate<a> (arr, j, i);
sort (arr, succ i)
end

prval () = lemma_array_param arr
in
if n <> i2sz 0 then
sort (arr, i2sz 1)
end

(*------------------------------------------------------------------*)

implement
insertion_sort\$lt<int> (x, y) =
x < y

implement
main0 () =
let
#define SIZE 30
var i : [i : nat] int i
var arr : array (int, SIZE)
in
array_initize_elt<int> (arr, i2sz SIZE, 0);
for (i := 0; i < SIZE; i := succ i)
arr[i] := \$extfcall (int, "rand") % 10;

for (i := 0; i < SIZE; i := succ i)
print! (" ", arr[i]);
println! ();

insertion_sort<int> (arr, i2sz SIZE);

for (i := 0; i < SIZE; i := succ i)
print! (" ", arr[i]);
println! ()
end```
Output:

Sorting random numbers.

```\$ patscc -DATS_MEMALLOC_GCBDW -O3 insertion_sort_task_array_of_nonlinear.dats -lgc && ./a.out
3 6 7 5 3 5 6 2 9 1 2 7 0 9 3 6 0 6 2 6 1 8 7 9 2 0 2 3 7 5
0 0 0 1 1 2 2 2 2 2 3 3 3 3 5 5 5 6 6 6 6 6 7 7 7 7 8 9 9 9```

### For arrays whose elements may be of linear type

If the elements of the array may be of linear type, then it becomes necessary to compare the elements by reference. Furthermore it is necessary to break down the array's view, to obtain views of the elements to be compared. Here, as in the simpler implementation for non-linear elements, I use array_subcirculate to insert an element into its correct position.

(The complications are necessary to prevent us accidentally having two copies of a linear value. Having two copies would introduce such nasty possibilities as a double-free error, use of a destroyed list, etc.)

```#include "share/atspre_staload.hats"

(*------------------------------------------------------------------*)
(* Interface                                                        *)

extern fn {a : vt@ype}          (* The "less than" template. *)
insertion_sort\$lt : (&a, &a) -<> bool (* Arguments by reference. *)

extern fn {a : vt@ype}
insertion_sort
{n   : int}
(arr : &array (a, n) >> _,
n   : size_t n)
:<!wrt> void

(*------------------------------------------------------------------*)
(* Implementation                                                   *)

implement {a}
insertion_sort {n} (arr, n) =
let
macdef lt = insertion_sort\$lt<a>

fun
sort {i     : int | 1 <= i; i <= n}
.<n - i>.
(pf_arr : !array_v (a, p_arr, n) >> _ |
p_arr  : ptr p_arr,
i      : size_t i)
:<!wrt> void =
if i <> n then
let
val pi = ptr_add<a> (p_arr, i)

fun
find_new_position
{j : nat | j <= i}
.<j>.
(pf_left : !array_v (a, p_arr, j) >> _,
pf_i    : !a @ (p_arr + (i * sizeof a)) |
j       : size_t j)
:<> [j : nat | j <= i] size_t j =
if j = i2sz 0 then
j
else
let
prval @(pf_left1, pf_k) = array_v_unextend pf_left

val k = pred j
val pk = ptr_add<a> (p_arr, k)
in
if ~((!pi) \lt (!pk)) then
let
prval () = pf_left :=
array_v_extend (pf_left1, pf_k)
in
j
end
else
let
val new_pos =
find_new_position (pf_left1, pf_i | k)
prval () = pf_left :=
array_v_extend (pf_left1, pf_k)
in
new_pos
end
end

prval @(pf_left, pf_right) =
array_v_split {a} {p_arr} {n} {i} pf_arr
prval @(pf_i, pf_rest) = array_v_uncons pf_right

val j = find_new_position (pf_left, pf_i | i)

prval () = pf_arr :=
array_v_unsplit (pf_left, array_v_cons (pf_i, pf_rest))
in
if j < i then
array_subcirculate<a> (!p_arr, j, i);
sort (pf_arr | p_arr, succ i)
end

prval () = lemma_array_param arr
in
if n <> i2sz 0 then
sort (view@ arr | addr@ arr, i2sz 1)
end

(*------------------------------------------------------------------*)

(* The demonstration converts random numbers to linear strings, then
sorts the elements by their first character. Thus here is a simple
demonstration that the sort can handle elements of linear type, and
also that the sort is stable. *)

implement
main0 () =
let
implement
insertion_sort\$lt<Strptr1> (x, y) =
let
val sx = \$UNSAFE.castvwtp1{string} x
and sy = \$UNSAFE.castvwtp1{string} y
val cx = \$effmask_all \$UNSAFE.string_get_at (sx, 0)
and cy = \$effmask_all \$UNSAFE.string_get_at (sy, 0)
in
cx < cy
end

implement
array_initize\$init<Strptr1> (i, x) =
let
#define BUFSIZE 10
var buffer : array (char, BUFSIZE)

val () = array_initize_elt<char> (buffer, i2sz BUFSIZE, '\0')
val _ = \$extfcall (int, "snprintf", addr@ buffer,
i2sz BUFSIZE, "%d",
\$extfcall (int, "rand") % 100)
val () = buffer[BUFSIZE - 1] := '\0'
in
x := string0_copy (\$UNSAFE.cast{string} buffer)
end

implement
array_uninitize\$clear<Strptr1> (i, x) =
strptr_free x

#define SIZE 30
val @(pf_arr, pfgc_arr | p_arr) =
array_ptr_alloc<Strptr1> (i2sz SIZE)
macdef arr = !p_arr

var i : [i : nat] int i
in
array_initize<Strptr1> (arr, i2sz SIZE);

for (i := 0; i < SIZE; i := succ i)
let
val p = ptr_add<Strptr1> (p_arr, i)
val s = \$UNSAFE.ptr0_get<string> p
in
print! (" ", s)
end;
println! ();

insertion_sort<Strptr1> (arr, i2sz SIZE);

for (i := 0; i < SIZE; i := succ i)
let
val p = ptr_add<Strptr1> (p_arr, i)
val s = \$UNSAFE.ptr0_get<string> p
in
print! (" ", s)
end;
println! ();

array_uninitize<Strptr1> (arr, i2sz SIZE);
array_ptr_free (pf_arr, pfgc_arr | p_arr)
end```
Output:

Sorting random numbers by their first digit, to demonstrate that the sort is stable. The numbers are stored in the array as linear strings (strings that must be explicitly freed), to demonstrate that the sort works with linear types.

```\$ patscc -DATS_MEMALLOC_LIBC -O3 insertion_sort_task_array_of_linear.dats && ./a.out
83 86 77 15 93 35 86 92 49 21 62 27 90 59 63 26 40 26 72 36 11 68 67 29 82 30 62 23 67 35
15 11 21 27 26 26 29 23 35 36 30 35 49 40 59 62 63 68 67 62 67 77 72 83 86 86 82 93 92 90```

### For linear lists whose elements may be of linear type

It is useful in a language such as ATS to have a stable insertion sort that operates on singly-linked lists. Such a sort can serve as the innermost part of a list mergesort or list quicksort.

None of the activities in the following implementation requires allocating a new node. The original list is consumed. However, you can use this code to non-destructively sort a non-linear list by first creating a copy, casting the copy to a linear list, and sorting the copy, then casting the result to a non-linear list.

```#include "share/atspre_staload.hats"

(*------------------------------------------------------------------*)
(* Interface                                                        *)

extern fn {a : vt@ype}                (* The "less than" template. *)
insertion_sort\$lt : (&a, &a) -<> bool (* Arguments by reference. *)

extern fn {a : vt@ype}
insertion_sort
{n   : int}
(lst : list_vt (a, n))
:<!wrt> list_vt (a, n)

(*------------------------------------------------------------------*)
(* Implementation                                                   *)

(* This implementation is based on the insertion-sort part of the
mergesort code of the ATS prelude.

Unlike the prelude, however, I build the sorted list in reverse
order. Building the list in reverse order actually makes the
implementation more like that for an array. *)

(* Some convenient shorthands. *)
#define NIL list_vt_nil ()
#define ::  list_vt_cons

(* Inserting in reverse order minimizes the work for a list already
nearly sorted, or for stably sorting a list whose entries often
have equal keys. *)
fun {a : vt@ype}
insert_reverse
{m       : nat}
.<m>.
(pf_x  : a @ p_x,
pf_xs : list_vt (a, 0)? @ p_xs |
dst   : &list_vt (a, m) >> list_vt (a, m + 1),
(* list_vt_cons_unfold is a viewtype created by the
unfolding of a list_vt_cons (our :: operator). *)
xnode : list_vt_cons_unfold (p_xnode, p_x, p_xs),
p_x   : ptr p_x,
p_xs  : ptr p_xs)
:<!wrt> void =
(* dst is some tail of the current (reverse-order) destination list.
xnode is a viewtype for the current node in the source list.
p_x points to the node's CAR.
p_xs points to the node's CDR. *)
case+ dst of
| @ (y :: ys) =>
if insertion_sort\$lt<a> (!p_x, y) then
let                     (* Move to the next destination node. *)
val () = insert_reverse (pf_x, pf_xs | ys, xnode, p_x, p_xs)
prval () = fold@ dst
in
end
else
let                       (* Insert xnode here. *)
prval () = fold@ dst
val () = !p_xs := dst
val () = dst := xnode
prval () = fold@ dst
in
end
| ~ NIL =>
let                         (* Put xnode at the end. *)
val () = dst := xnode
val () = !p_xs := NIL
prval () = fold@ dst
in
end

implement {a}
insertion_sort {n} lst =
let
fun                         (* Create a list sorted in reverse. *)
loop {i : nat | i <= n}
.<n - i>.
(dst : &list_vt (a, i) >> list_vt (a, n),
src : list_vt (a, n - i))
:<!wrt> void =
case+ src of
| @ (x :: xs) =>
let
val tail = xs
in
insert_reverse<a> (view@ x, view@ xs |
loop (dst, tail)
end
| ~ NIL => ()             (* We are done. *)

prval () = lemma_list_vt_param lst

var dst : List_vt a = NIL
in
loop (dst, lst);

(* Reversing a linear list is an in-place operation. *)
list_vt_reverse<a> dst
end

(*------------------------------------------------------------------*)

(* The demonstration converts random numbers to linear strings, then
sorts the elements by their first character. Thus here is a simple
demonstration that the sort can handle elements of linear type, and
also that the sort is stable. *)

implement
main0 () =
let
implement
insertion_sort\$lt<Strptr1> (x, y) =
let
val sx = \$UNSAFE.castvwtp1{string} x
and sy = \$UNSAFE.castvwtp1{string} y
val cx = \$effmask_all \$UNSAFE.string_get_at (sx, 0)
and cy = \$effmask_all \$UNSAFE.string_get_at (sy, 0)
in
cx < cy
end

implement
list_vt_freelin\$clear<Strptr1> x =
strptr_free x

#define SIZE 30

fn
create_the_list ()
:<!wrt> list_vt (Strptr1, SIZE) =
let
fun
loop {i : nat | i <= SIZE}
.<SIZE - i>.
(lst : list_vt (Strptr1, i),
i   : size_t i)
:<!wrt> list_vt (Strptr1, SIZE) =
if i = i2sz SIZE then
list_vt_reverse lst
else
let
#define BUFSIZE 10
var buffer : array (char, BUFSIZE)

val () =
array_initize_elt<char> (buffer, i2sz BUFSIZE, '\0')
val _ = \$extfcall (int, "snprintf", addr@ buffer,
i2sz BUFSIZE, "%d",
\$extfcall (int, "rand") % 100)
val () = buffer[BUFSIZE - 1] := '\0'
val s = string0_copy (\$UNSAFE.cast{string} buffer)
in
loop (s :: lst, succ i)
end
in
loop (NIL, i2sz 0)
end

var p : List string

val lst = create_the_list ()

val () =
for (p := \$UNSAFE.castvwtp1{List string} lst;
isneqz p;
p := list_tail p)
print! (" ", list_head p)
val () = println! ()

val lst = insertion_sort<Strptr1> lst

val () =
for (p := \$UNSAFE.castvwtp1{List string} lst;
isneqz p;
p := list_tail p)
print! (" ", list_head p)
val () = println! ()

val () = list_vt_freelin lst
in
end```
Output:

Sorting random numbers by their first digit, to demonstrate that the sort is stable. The numbers are stored in the list as linear strings (strings that must be explicitly freed), to demonstrate that the sort works if the list elements themselves are linear.

```\$ patscc -DATS_MEMALLOC_LIBC -O3 insertion_sort_task_linear_list.dats && ./a.out
83 86 77 15 93 35 86 92 49 21 62 27 90 59 63 26 40 26 72 36 11 68 67 29 82 30 62 23 67 35
15 11 21 27 26 26 29 23 35 36 30 35 49 40 59 62 63 68 67 62 67 77 72 83 86 86 82 93 92 90```

## AutoHotkey

contributed by Laszlo on the ahk forum

```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
}
```

## AWK

Sort standard input (storing lines into an array) and output to standard output

```{
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]
}
}
```

## Bash

```#!/bin/bash

# Sorting integers with insertion sort

function  insertion_sort ()
{
# input: unsorted integer array
# output:  sorted integer array (ascending)

# local variables
local -a arr         # array
local -i i           # integers
local -i j
local -i key
local -i prev
local -i leftval
local -i N          # size of array

arr=( \$@ )    # copy args into array

N=\${#arr[*]}  # arr extent
readonly N    # make const

# insertion sort
for (( i=1; i<\$N; i++ ))  # c-style for loop
do
key=\$((arr[\$i]))      # current value
prev=\$((arr[\$i-1]))   # previous value
j=\$i                  # current index

while [ \$j -gt 0 ]  && [ \$key -lt \$prev ]  # inner loop
do
arr[\$j]=\$((arr[\$j-1])) # shift

j=\$((\$j-1))            # decrement

prev=\$((arr[\$j-1]))    # last value

done

arr[\$j]=\$((\$key))          # insert key in proper order

done

echo \${arr[*]}                   # output sorted array
}

################
function main ()
{
# main script
declare -a sorted

# use a default if no cmdline list
if [ \$# -eq 0 ]; then
arr=(10 8 20 100 -3 12 4 -5 32 0 1)
else
arr=(\$@) #cmdline list of ints
fi

echo
echo "original"
echo -e "\t \${arr[*]} \n"

sorted=(\$(insertion_sort \${arr[*]}))  # call function

echo
echo "sorted:"
echo -e "\t \${sorted[*]} \n"
}

#script starts here
# source or run
if [[ "\$0" == "bash" ]]; then # script is sourced
unset main
else
main "\$@"                 # call with cmdline args
fi

#END
```
Output:
```original
10 8 20 100 -3 12 4 -5 32 0 1

sorted:
-5 -3 0 1 4 8 10 12 20 32 100
```

## B4X

The array type can be changed to Object and it will then work with any numeric type.

```Sub InsertionSort (A() As Int)
For i = 1 To A.Length - 1
Dim value As Int = A(i)
Dim j As Int = i - 1
Do While j >= 0 And A(j) > value
A(j + 1) = A(j)
j = j - 1
Loop
A(j + 1) = value
Next
End Sub

Sub Test
Dim arr() As Int = Array As Int(34, 23, 54, 123, 543, 123)
InsertionSort(arr)
For Each i As Int In arr
Log(i)
Next
End Sub```
Output:
```23
34
54
123
123
543
```

## BASIC

Translation of: REALbasic
Works with: QBasic

This version should work on any BASIC that can accept arrays as function arguments.

```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); ";";
NEXT

SUB InsertionSort (theList() AS INTEGER)
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
```
Output:
``` 1486 ; 9488 ; 9894 ; 17479 ; 18989 ; 23119 ; 23233 ; 24927 ; 25386 ; 26689 ;
```

### GWBASIC

Works with: BASICA
Works with: QBASIC/QUICKBASIC
Works with: VBDOS

Sorts N integers in an array a() with the Insertion sort

```10 'SAVE "INSERTGW",A
20 DEFINT A-Z
30 OPTION BASE 1
40 N=20: R=100: I=0: Y=0: V=0: P=0
50 DIM A(N)
60 ' Creates the disordered array
70 CLS: PRINT "This program sorts by Insertion a list of randomly generated numbers."
80 PRINT: PRINT "Unsorted list:"
90 RANDOMIZE TIMER
100 FOR I = 1 TO N
110   A(I) = INT(RND * R) + 1
120 NEXT I
130 GOSUB 260
140 PRINT: PRINT "Sorted list."
150 ' Insertion Sort
160 FOR I=1 TO N
170   V=A(I): P=I-1: S=1
180   WHILE P>0 AND S=1
185     S=0
190     IF A(P) > V THEN A(P+1)=A(P): P=P-1: S=1
200   WEND
210   A(P+1) = V
220 NEXT I
230 GOSUB 260
240 PRINT: PRINT "End of program execution."
250 END
260 ' Print list routine
270   FOR I=1 TO N
280     PRINT A(I);
290   NEXT I
300   PRINT
310 RETURN
```
Output:
```This program sorts by Insertion a list of randomly generated numbers.

Unsorted list:
73  11  100  68  28  48  3  36  15  34  31  26  47  61  5  58  15  86  69  79

Sorted list:
3  5  11  15  15  26  28  31  34  36  47  48  58  61  68  69  73  79  86  100

End of program execution.
```

### ZX BASIC

Sorts N elements in array i() into ascending order. Invoke with GO SUB 500.

```500 FOR j=1 TO N-1
510   IF i(j)<=i(j+1) THEN NEXT j: RETURN
520   LET c=i(j+1)
530   FOR k=j TO 1 STEP -1: IF i(k)>c THEN LET i(k+1)=i(k): NEXT k
540   LET i(k+1)=c
600 NEXT j: RETURN
```

For those who prefer GO TOs over conditional NEXTs (fine in ZX BASIC but problematic for compilers and stack-dependent interpreters like NextBASIC’s integer extensions) replace NEXT J: RETURN in line 510 with GO TO 600 and use this line 530:

`530 IF k>0 THEN IF i(k)>c THEN LET i(k+1)=i(k): LET k=k-1: GO TO 530 `

### BBC BASIC

Note that the array index is assumed to start at zero.

```      DIM test(9)
test() = 4, 65, 2, -31, 0, 99, 2, 83, 782, 1
PROCinsertionsort(test(), 10)
FOR i% = 0 TO 9
PRINT test(i%) ;
NEXT
PRINT
END

DEF PROCinsertionsort(a(), n%)
LOCAL i%, j%, t
FOR i% = 1 TO n%-1
t = a(i%)
j% = i%
WHILE j%>0 AND t<a(ABS(j%-1))
a(j%) = a(j%-1)
j% -= 1
ENDWHILE
a(j%) = t
NEXT
ENDPROC
```
Output:
```       -31         0         1         2         2         4        65        83        99       782
```

### Commodore BASIC

```10 DIM A(10): N=9
11 REM GENERATE SOME RANDOM NUMBERS AND PRINT THEM
12 FOR I=0 TO N: A(I)=INT(RND(1)*10)+1: NEXT: GOSUB 50
20 FOR J=1 TO N:KEY=A(J): I=J-1: GOSUB 30: A(I+1)=KEY: NEXT: GOSUB 50: END
30 IFI=-1 THEN RETURN
31 IFA(I)>KEY THEN A(I+1)=A(I):I=I-1: GOTO 30
32 RETURN
50 PRINT: FOR I=0 TO N: PRINTA(I): NEXT: RETURN
```

### IS-BASIC

```  100 PROGRAM "InserSrt.bas"
110 RANDOMIZE
120 NUMERIC ARRAY(5 TO 21)
130 CALL INIT(ARRAY)
140 CALL WRITE(ARRAY)
150 CALL INSERTSORT(ARRAY)
160 CALL WRITE(ARRAY)
170 DEF INIT(REF A)
180   FOR I=LBOUND(A) TO UBOUND(A)
190     LET A(I)=RND(98)+1
200   NEXT
210 END DEF
220 DEF WRITE(REF A)
230   FOR I=LBOUND(A) TO UBOUND(A)
240     PRINT A(I);
250   NEXT
260   PRINT
270 END DEF
280 DEF INSERTSORT(REF A)
290   FOR J=LBOUND(A)+1 TO UBOUND(A)
300     LET I=J-1:LET SW=A(J)
310     DO WHILE I>=LBOUND(A) AND SW<A(I)
320       LET A(I+1)=A(I):LET I=I-1
330     LOOP
340     LET A(I+1)=SW
350   NEXT
360 END DEF```

## BASIC256

Translation of: FreeBASIC
```global array
dim array(15)
a = array[?,]
b = array[?]
for i = a to b-1
array[i] = int(rand * 100)
next i

print "unsort ";
for i = a to b-1
print rjust(array[i], 4);
next i

call insertionSort(array)  # ordenar el array

print chr(10); "  sort ";
for i = a to b-1
print rjust(array[i], 4);
next i
end

subroutine insertionSort(array)
lb = array[?,]

for i = lb + 1 to array[?]-1
valor = array[i]
j = i - 1
while j >= lb  and array[j] > valor
array[j +1] = array[j]
j -= 1
end while

array[j+1] = valor
next i
end subroutine
```

## BCPL

```get "libhdr"

let insertionSort(A, len) be
for i = 1 to len-1 do
\$(  let value = A!i
let j = i-1
while j >= 0 & A!j > value do
\$(  A!(j+1) := A!j
j := j-1
\$)
A!(j+1) := value
\$)

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)
insertionSort(array, length)
write("After:  ", array, length)
\$)```
Output:
```Before:    4  65   2 -31   0  99   2  83 782   1
After:   -31   0   1   2   2   4  65  83  99 782```

## C

```#include <stdio.h>

void insertion_sort(int*, const size_t);

void insertion_sort(int *a, const size_t n) {
for(size_t i = 1; i < n; ++i) {
int key = a[i];
size_t j = i;
while( (j > 0) && (key < a[j - 1]) ) {
a[j] = a[j - 1];
--j;
}
a[j] = key;
}
}

int main (int argc, char** argv) {

int a[] = {4, 65, 2, -31, 0, 99, 2, 83, 782, 1};

const size_t n = sizeof(a) / sizeof(a[0]) ;   // array extent

for (size_t i = 0; i < n; i++)
printf("%d%s", a[i], (i == (n - 1))? "\n" : " ");

insertion_sort(a, n);

for (size_t i = 0; i < n; i++)
printf("%d%s", a[i], (i == (n - 1))? "\n" : " ");

return 0;
}
```
Output:
```4 65 2 -31 0 99 2 83 782 1
-31 0 1 2 2 4 65 83 99 782
```

## C#

```namespace Sort {
using System;

static class InsertionSort<T> where T : IComparable {
public static void Sort(T[] entries) {
Sort(entries, 0, entries.Length - 1);
}

public static void Sort(T[] entries, Int32 first, Int32 last) {
for (var i = first + 1; i <= last; i++) {
var entry = entries[i];
var j = i;

while (j > first && entries[j - 1].CompareTo(entry) > 0)
entries[j] = entries[--j];

entries[j] = entry;
}
}
}
}
```

Example:

```  using Sort;
using System;

class Program {
static void Main(String[] args) {
var entries = new Int32[] { 3, 9, 4, 6, 8, 1, 7, 2, 5 };
InsertionSort<Int32>.Sort(entries);
Console.WriteLine(String.Join(" ", entries));
}
}
```

## C++

Uses C++11. Compile with

```g++ -std=c++11 insertion.cpp
```

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

```#include <algorithm>
#include <iostream>
#include <iterator>

// std::rotate is used to shift the sub-region
// if the predicate  p is true
template <typename RandomAccessIterator, typename Predicate>
void insertion_sort(RandomAccessIterator begin, RandomAccessIterator end,
Predicate p) {
for (auto i = begin; i != end; ++i) {
std::rotate(std::upper_bound(begin, i, *i, p), i, i + 1);
}
}

// calls with default Predicate std::less (sort ascending)
template <typename RandomAccessIterator>
void insertion_sort(RandomAccessIterator begin, RandomAccessIterator end) {
insertion_sort(begin, end, std::less<typename std::iterator_traits<RandomAccessIterator>::value_type>());
}

int main() {

int a[] = { 100, 2, 56, 200, -52, 3, 99, 33, 177, -199 };

insertion_sort(std::begin(a), std::end(a));

// 'iterates' numbers to std::cout
// converts ints to strings for output to screen
copy(std::begin(a), std::end(a), std::ostream_iterator<int>(std::cout, " "));

std::cout << "\n";
}
```
Output:
```-199 -52 2 3 33 56 99 100 177 200
```

## Clojure

```(defn insertion-sort [coll]
(reduce (fn [result input]
(let [[less more] (split-with #(< % input) result)]
(concat less [input] more)))
[]
coll))
```

Translated from the Haskell example:

```(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]
```

## CLU

```% Insertion-sort an array in place.
insertion_sort = proc [T: type] (a: array[T])
where T has lt: proctype (T,T) returns (bool)

bound_lo: int := array[T]\$low(a)
bound_hi: int := array[T]\$high(a)

for i: int in int\$from_to(bound_lo, bound_hi) do
value: T := a[i]
j: int := i - 1
while j >= bound_lo cand value < a[j] do
a[j+1] := a[j]
j := j-1
end
a[j+1] := value
end
end insertion_sort

% Print an array
print_arr = proc [T: type] (a: array[T], w: int, s: stream)
where T has unparse: proctype (T) returns (string)
for el: T in array[T]\$elements(a) do
stream\$putright(s, T\$unparse(el), w)
end
stream\$putc(s, '\n')
end print_arr

start_up = proc ()
ai = array[int]
po: stream := stream\$primary_output()
test: ai := ai\$[7, -5, 0, 2, 99, 16, 4, 20, 47, 19]

stream\$puts(po, "Before: ") print_arr[int](test, 3, po)
insertion_sort[int](test)
stream\$puts(po, "After:  ") print_arr[int](test, 3, po)
end start_up```
Output:
```Before:   7 -5  0  2 99 16  4 20 47 19
After:   -5  0  2  4  7 16 19 20 47 99```

## 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 1 \${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)

foreach(i RANGE 1 \${last})
endforeach(i)
endfunction(insertion_sort)
```
```insertion_sort(result 33 11 44 22 66 55)
message(STATUS "\${result}") # -- 11;22;33;44;55;66
```

## 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.

```       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.
```

And a fully runnable version, by Steve Williams

Works with: GnuCOBOL
```        >>SOURCE FORMAT FREE
*> This code is dedicated to the public domain
*> This is GNUCOBOL 2.0
identification division.
program-id. insertionsort.
environment division.
configuration section.
repository. function all intrinsic.
data division.
working-storage section.
01  filler.
03  a pic 99.
03  a-lim pic 99 value 10.
03  array occurs 10 pic 99.

01  filler.
03  s pic 99.
03  o pic 99.
03  o1 pic 99.
03  sorted-len pic 99.
03  sorted-lim pic 99 value 10.
03  sorted-array occurs 10 pic 99.

procedure division.
start-insertionsort.

*> fill the array
compute a = random(seconds-past-midnight)
perform varying a from 1 by 1 until a > a-lim
compute array(a) = random() * 100
end-perform

*> display the array
perform varying a from 1 by 1 until a > a-lim
display space array(a) with no advancing
end-perform
display  space 'initial array'

*> sort the array
move 0 to sorted-len
perform varying a from 1 by 1 until a > a-lim
*> find the insertion point
perform varying s from 1 by 1
until s > sorted-len
or array(a) <= sorted-array(s)
continue
end-perform

*>open the insertion point
perform varying o from sorted-len by -1
until o < s
compute o1 = o + 1
move sorted-array(o) to sorted-array(o1)
end-perform

*> move the array-entry to the insertion point
move array(a) to sorted-array(s)

add 1 to sorted-len
end-perform

*> display the sorted array
perform varying s from 1 by 1 until s > sorted-lim
display space sorted-array(s) with no advancing
end-perform
display space 'sorted array'

stop run
.
end program insertionsort.
```
Output:
```prompt\$ cobc -xj insertionsort.cob
89 04 86 32 65 62 83 75 24 69 initial array
04 24 32 62 65 69 75 83 86 89 sorted array```

## Common 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))
```
```(defun insertion-sort (sequence &optional (predicate #'<))
(if (cdr sequence)
(insert (car sequence)                 ;; insert the current item into
(insertion-sort (cdr sequence) ;; the already-sorted
predicate)     ;; remainder of the list
predicate)
sequence)) ; a list of one element is already sorted

(defun insert (item sequence predicate)
(cond ((null sequence) (list item))
((funcall (complement predicate)      ;; if the first element of the list
(car sequence)  ;; isn't better than the item,
item)           ;; cons the item onto
(cons item sequence))                ;; the front of the list
(t (cons (car sequence) ;; otherwise cons the first element onto the front of
(insert item   ;; the list of the item sorted with the rest of the list
(cdr sequence)
predicate)))))
```

## Craft Basic

```define size = 10, value = 0

dim list[size]

gosub fill
gosub sort
gosub show

end

sub fill

for i = 0 to size - 1

let list[i] = int(rnd * 100)

next i

return

sub sort

for i = 1 to size - 1

let value = list[i]
let j = i - 1

do

if j >= 0 and list[j] > value then

let p = j + 1
let list[p] = list[j]
let j = j - 1

endif

loop j >= 0 and list[j] > value

let p = j + 1
let list[p] = value

wait

next i

return

sub show

for i = 0 to size - 1

print i, ": ", list[i]

next i

return
```

## D

```void insertionSort(T)(T[] data) pure nothrow @safe @nogc {
foreach (immutable 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;
items.writeln;
}
```
Output:
`[2, 4, 11, 17, 19, 24, 25, 28, 44, 46]`

### Higher Level Version

Translation of: C++
```import std.stdio, std.range, std.algorithm, std.traits;

void insertionSort(R)(R arr)
if (hasLength!R && isRandomAccessRange!R && hasSlicing!R) {
foreach (immutable i; 1 .. arr.length)
bringToFront(arr[0 .. i].assumeSorted.upperBound(arr[i]), arr[i .. i + 1]);
}

void main() {
import std.random, std.container;

auto arr1 = [28, 44, 46, 24, 19, 2, 17, 11, 25, 4];
arr1.insertionSort;
assert(arr1.isSorted);
writeln("arr1 sorted: ", arr1);

auto arr2 = Array!int([28, 44, 46, 24, 19, 2, 17, 11, 25, 4]);
arr2[].insertionSort;
assert(arr2[].isSorted);
writeln("arr2 sorted: ", arr2[]);

// Random data test.
int[10] buf;
foreach (immutable _; 0 .. 100_000) {
auto arr3 = buf[0 .. uniform(0, \$)];
foreach (ref x; arr3)
x = uniform(-6, 6);
arr3.insertionSort;
assert(arr3.isSorted);
}
}
```
Output:
```arr1 sorted: [2, 4, 11, 17, 19, 24, 25, 28, 44, 46]
arr2 sorted: [2, 4, 11, 17, 19, 24, 25, 28, 44, 46]```

## Dart

Translation of: Java
```insertSort(List<int> array){
for(int i = 1; i < array.length; i++){
int value = array[i];
int j = i - 1;
while(j >= 0 && array[j] > value){
array[j + 1] = array[j];
j = j - 1;
}
array[j + 1] = value;
}
return array;
}

void main() {
List<int> a = insertSort([10, 3, 11, 15, 19, 1]);
print('\${a}');
}
```
Output:
```array unsorted: [10, 3, 11, 15, 19, 1];
a sorted: [1, 3, 10, 11, 15, 19]```

## Delphi

### Array sort

Dynamic array is a 0-based array of variable length

Static array is an arbitrary-based array of fixed length

```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;
end.
```
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

```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;
```
```// 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.

```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
}
}```

Test case:

```? 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()```

## EasyLang

```proc sort . d[] .
for i = 2 to len d[]
h = d[i]
j = i - 1
while j >= 1 and h < d[j]
d[j + 1] = d[j]
j -= 1
.
d[j + 1] = h
.
.
data[] = [ 29 4 72 44 55 26 27 77 92 5 ]
call sort data[]
print data[]
```

## 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.

```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
```

## Elena

ELENA 5.0 :

```import extensions;

extension op
{
insertionSort()
= self.clone().insertionSort(0, self.Length - 1);

insertionSort(int first, int last)
{
for(int i := first + 1, i <= last, i += 1)
{
var entry := self[i];
int j := i;

while (j > first && self[j - 1] > entry)
{
self[j] := self[j - 1];

j -= 1
};

self[j] := entry
}
}
}

public program()
{
var list := new int[]{3, 9, 4, 6, 8, 1, 7, 2, 5};

console.printLine("before:", list.asEnumerable());
console.printLine("after :", list.insertionSort().asEnumerable());
}```
Output:
```before:3,9,4,6,8,1,7,2,5
after :1,2,3,4,5,6,7,8,9
```

## Elixir

```defmodule Sort do
def insert_sort(list) when is_list(list), do: insert_sort(list, [])

def insert_sort([], sorted), do: sorted
def insert_sort([h | t], sorted), do: insert_sort(t, insert(h, sorted))

defp insert(x, []), do: [x]
defp insert(x, sorted) when x < hd(sorted), do: [x | sorted]
defp insert(x, [h | t]), do: [h | insert(x, t)]
end
```

Example:

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

## Emacs Lisp

```(defun min-or-max-of-a-list (numbers comparator)
"Return minimum or maximum of NUMBERS using COMPARATOR."
(let ((extremum (car numbers)))
(dolist (n (cdr numbers))
(when (funcall comparator n extremum)
(setq extremum n)))
extremum))

(defun remove-number-from-list (numbers n)
"Return NUMBERS without N.
If n is present twice or more, it will be removed only once."
(let (result)
(while numbers
(let ((number (pop numbers)))
(if (= number n)
(while numbers
(push (pop numbers) result))
(push number result))))
(nreverse result)))

(defun insertion-sort (numbers comparator)
"Return sorted list of NUMBERS using COMPARATOR."
(if numbers
(let ((extremum (min-or-max-of-a-list numbers comparator)))
(cons extremum
(insertion-sort (remove-number-from-list numbers extremum)
comparator)))
nil))

(insertion-sort '(1 2 3 9 8 7 25 12 3 2 1) #'>)
```
Output:
```(25 12 9 8 7 3 3 2 2 1 1)
```

## EMal

```fun insertionSort = void by List a # sort list in place
for int i = 1; i < a.length; ++i
var v = a[i]
int j
for j = i - 1; j >= 0 and a[j] > v; --j
a[j + 1] = a[j]
end
a[j + 1] = v
end
end
List lists = List[ # a list of lists
int[4, 65, 2, -31, 0, 99, 83, 782, 1],
real[5.17, 2, 5.12],
text["this", "is", "insertion", "sort"]]
for each List list in lists
writeLine("Before: " + text!list) # list as text
insertionSort(list)
writeLine("After : " + text!list)
writeLine()
end```
Output:
```Before: [4,65,2,-31,0,99,83,782,1]
After : [-31,0,1,2,4,65,83,99,782]

Before: [5.17,2.0,5.12]
After : [2.0,5.12,5.17]

Before: [this,is,insertion,sort]
After : [insertion,is,sort,this]
```

## 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)].
```

And the calls:

```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]
```

## ERRE

Note: array index is assumed to start at zero.

```PROGRAM INSERTION_SORT

DIM A[9]

PROCEDURE INSERTION_SORT(A[])
LOCAL I,J
FOR I=0 TO UBOUND(A,1) DO
V=A[I]
J=I-1
WHILE J>=0 DO
IF A[J]>V THEN
A[J+1]=A[J]
J=J-1
ELSE
EXIT
END IF
END WHILE
A[J+1]=V
END FOR
END PROCEDURE

BEGIN
A[]=(4,65,2,-31,0,99,2,83,782,1)
FOR I%=0 TO UBOUND(A,1) DO
PRINT(A[I%];)
END FOR
PRINT
INSERTION_SORT(A[])
FOR I%=0 TO UBOUND(A,1) DO
PRINT(A[I%];)
END FOR
PRINT
END PROGRAM```
Output:
``` 4  65  2 -31  0  99  2  83  782  1
-31  0  1  2  2  4  65  83  99  782
```

## 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})```
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"
}```

## F#

Procedural Version

```// This function performs an insertion sort with an array.
// The input parameter is a generic array (any type that can perform comparison).
// As is typical of functional programming style the input array is not modified;
// a copy of the input array is made and modified and returned.
let insertionSort (A: _ array) =
let B = Array.copy A
for i = 1 to B.Length - 1 do
let mutable value = B.[i]
let mutable j = i - 1
while (j >= 0 && B.[j] > value) do
B.[j+1] <- B.[j]
j <- j - 1
B.[j+1] <- value
B  // the array B is returned
```

Functional Version

```let insertionSort collection =

// Inserts an element into its correct place in a sorted collection
let rec sinsert element collection =
match element, collection with
| x, [] -> [x]
| x, y::ys when x < y -> x::y::ys
| x, y::ys -> y :: (ys |> sinsert x)

// Performs Insertion Sort
let rec isort acc collection =
match collection, acc with
| [], _ -> acc
| x::xs, ys -> xs |> isort (sinsert x ys)
collection |> isort []
```

## Factor

```USING: kernel prettyprint sorting.extras sequences ;

: insertion-sort ( seq -- sorted-seq )
<reversed> V{ } clone [ swap insort-left! ] reduce ;

{ 6 8 5 9 3 2 1 4 7 } insertion-sort .
```
Output:
```{ 1 2 3 4 5 6 7 8 9 }
```

But note that Factor already comes with an `insertion-sort` in the `sorting.insertion` vocabulary that is likely faster and more robust. See its implementation here.

## 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
```

## Fortran

Works with: Fortran version 90 and later
```subroutine sort(n, a)
implicit none
integer :: n, i, j
real :: a(n), x

do i = 2, n
x = a(i)
j = i - 1
do while (j >= 1)
if (a(j) <= x) exit
a(j + 1) = a(j)
j = j - 1
end do
a(j + 1) = x
end do
end subroutine
```

### Alternate Fortran 77 version

```      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) GO TO 20
IF (A(J).LE.X) GO TO 20
A(J + 1) = A(J)
GO TO 10
20   A(J + 1) = X
30 CONTINUE
END
```

## FreeBASIC

```' version 20-10-2016
' compile with: fbc -s console
' for boundry checks on array's compile with: fbc -s console -exx

Sub insertionSort( arr() As Long )

' sort from lower bound to the highter bound
' array's can have subscript range from -2147483648 to +2147483647

Dim As Long lb = LBound(arr)
Dim As Long i, j, value

For i = lb +1 To UBound(arr)

value = arr(i)
j = i -1
While j >= lb  And arr(j) > value
arr(j +1) = arr(j)
j = j -1
Wend

arr(j +1) = value

Next

End Sub

' ------=< MAIN >=------

Dim As Long i, array(-7 To 7)
Dim As Long a = LBound(array), b = UBound(array)

Randomize Timer
For i = a To b : array(i) = i  : Next
For i = a To b ' little shuffle
Swap array(i), array(Int(Rnd * (b - a +1)) + a)
Next

Print "unsort ";
For i = a To b : Print Using "####"; array(i); : Next : Print
insertionSort(array())  ' sort the array
Print "  sort ";
For i = a To b : Print Using "####"; array(i); : Next : Print

' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End
```
Output:
```unsort   -7  -1   4  -6   5   2   1  -2   0  -5  -4   6  -3   7   3
sort   -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7```

## 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"
```

## Go

```package main

import "fmt"

func insertionSort(a []int) {
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
}
}

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

insertionSort(list)
fmt.Println("sorted!  ", list)
}
```
Output:
```unsorted: [31 41 59 26 53 58 97 93 23 84]
sorted!   [23 26 31 41 53 58 59 84 93 97]
```

A generic version that takes any container that conforms to `sort.Interface`:

```package main

import (
"fmt"
"sort"
)

func insertionSort(a sort.Interface) {
for i := 1; i < a.Len(); i++ {
for j := i; j > 0 && a.Less(j, j-1); j-- {
a.Swap(j-1, j)
}
}
}

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

insertionSort(sort.IntSlice(list))
fmt.Println("sorted!  ", list)
}
```
Output:
```unsorted: [31 41 59 26 53 58 97 93 23 84]
sorted!   [23 26 31 41 53 58 59 84 93 97]
```

Using binary search to locate the place to insert:

```package main

import (
"fmt"
"sort"
)

func insertionSort(a []int) {
for i := 1; i < len(a); i++ {
value := a[i]
j := sort.Search(i, func(k int) bool { return a[k] > value })
copy(a[j+1:i+1], a[j:i])
a[j] = value
}
}

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

insertionSort(list)
fmt.Println("sorted!  ", list)
}
```
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:

```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
}
```

Test:

```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]))
```
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]```

```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]
```

## Haxe

```class InsertionSort {
@:generic
public static function sort<T>(arr:Array<T>) {
for (i in 1...arr.length) {
var value = arr[i];
var j = i - 1;
while (j >= 0 && Reflect.compare(arr[j], value) > 0) {
arr[j + 1] = arr[j--];
}
arr[j + 1] = value;
}
}
}

class Main {
static function main() {
var integerArray = [1, 10, 2, 5, -1, 5, -19, 4, 23, 0];
var floatArray = [1.0, -3.2, 5.2, 10.8, -5.7, 7.3,
3.5, 0.0, -4.1, -9.5];
var stringArray = ['We', 'hold', 'these', 'truths', 'to',
'be', 'self-evident', 'that', 'all',
'men', 'are', 'created', 'equal'];
Sys.println('Unsorted Integers: ' + integerArray);
InsertionSort.sort(integerArray);
Sys.println('Sorted Integers:   ' + integerArray);
Sys.println('Unsorted Floats:   ' + floatArray);
InsertionSort.sort(floatArray);
Sys.println('Sorted Floats:     ' + floatArray);
Sys.println('Unsorted Strings:  ' + stringArray);
InsertionSort.sort(stringArray);
Sys.println('Sorted Strings:    ' + stringArray);
}
}
```
Output:
```Unsorted Integers: [1,10,2,5,-1,5,-19,4,23,0]
Sorted Integers:   [-19,-1,0,1,2,4,5,5,10,23]
Unsorted Floats:   [1,-3.2,5.2,10.8,-5.7,7.3,3.5,0,-4.1,-9.5]
Sorted Floats:     [-9.5,-5.7,-4.1,-3.2,0,1,3.5,5.2,7.3,10.8]
Unsorted Strings:  [We,hold,these,truths,to,be,self-evident,that,all,men,are,created,equal]
Sorted Strings:    [We,all,are,be,created,equal,hold,men,self-evident,that,these,to,truths]
```

## 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```

## Icon and Unicon

```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
```

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:
```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)```

## 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)
```

A shorter, but slightly less efficient, version:

```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)
```

## Isabelle

```theory Insertionsort
imports Main
begin

fun insert :: "int ⇒ int list ⇒ int list" where
"insert x [] = [x]"
| "insert x (y#ys) = (if x ≤ y then (x#y#ys) else y#(insert x ys))"

text‹Example:›
lemma "insert 4 [1, 2, 3, 5, 6] = [1, 2, 3, 4, 5, 6]" by(code_simp)

fun insertionsort :: "int list ⇒ int list" where
"insertionsort [] = []"
| "insertionsort (x#xs) = insert x (insertionsort xs)"

lemma "insertionsort [4, 2, 6, 1, 8, 1] = [1, 1, 2, 4, 6, 8]" by(code_simp)

text‹
Our function behaves the same as the \<^term>‹sort› function of the standard library.
›
lemma insertionsort: "insertionsort xs = sort xs"
proof(induction xs)
case Nil
show "insertionsort [] = sort []" by simp
next
case (Cons x xs)
text‹Our \<^const>‹insert› behaves the same as the std libs \<^const>‹insort›.›
have "insert a as = insort a as" for a as by(induction as) simp+
with Cons show "insertionsort (x # xs) = sort (x # xs)" by simp
qed

text‹
Given that we behave the same as the std libs sorting algorithm,
we get the correctness properties for free.
›
corollary insertionsort_correctness:
"sorted (insertionsort xs)" and
"set (insertionsort xs) = set xs"
using insertionsort by(simp)+

text‹
The Haskell implementation from
also behaves the same. Ultimately, they all return a sorted list.
One exception to the Haskell implementation is that the type signature of
\<^const>‹foldr› in Isabelle is slightly different:
The initial value of the accumulator goes last.
›
definition rosettacode_haskell_insertionsort :: "int list ⇒ int list" where
"rosettacode_haskell_insertionsort ≡ λxs. foldr insert xs []"

lemma "rosettacode_haskell_insertionsort [4, 2, 6, 1, 8, 1] =
[1, 1, 2, 4, 6, 8]" by(code_simp)

lemma "rosettacode_haskell_insertionsort xs = insertionsort xs"
unfolding rosettacode_haskell_insertionsort_def by(induction xs) simp+

end
```

## 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:

```isort=:((>: # ]) , [ , < #])/
```

Example of use:

```   isort 32 4 1 34 95 3 2 120 _38
_38 1 2 3 4 32 34 95 120
```

## Java

```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;
}
}
```

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

Translation of: C++
```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;
}
}
```

## 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(" "));
```

## jq

Works with: jq version 1.4

The insertion sort can be expressed directly in jq as follows:

```def insertion_sort:
reduce .[] as \$x ([]; insert(\$x));```
where insert/1 inserts its argument into its input, which can, by construction, be assumed here to be sorted. This algorithm will work in jq for any JSON array.

The following solution uses an "industrial strength" implementation of bsearch (binary search) that requires the following control structure:

```# As soon as "condition" is true, then emit . and stop:
def do_until(condition; next):
def u: if condition then . else (next|u) end;
u;```

bsearch is the only non-trivial part of this solution, and so we include its complete specification:

Assuming the input array is sorted, bsearch/1 returns the index of the target if the target is in the input array; and otherwise (-1 - ix), where ix is the insertion point that would leave the array sorted.

If the input is not sorted, bsearch will terminate but with irrelevant results.
```def bsearch(target):
if length == 0 then -1
elif length == 1 then
if target == .[0] then 0 elif target < .[0] then -1 else -2 end
else . as \$in
# state variable: [start, end, answer]
# where start and end are the upper and lower offsets to use.
| [0, length-1, null]
| do_until( .[0] > .[1] ;
(if .[2] != null then (.[1] = -1) # i.e. break
else
( ( (.[1] + .[0]) / 2 ) | floor ) as \$mid
| \$in[\$mid] as \$monkey
| if \$monkey == target  then (.[2] = \$mid)     # success
elif .[0] == .[1]     then (.[1] = -1)       # failure
elif \$monkey < target then (.[0] = (\$mid + 1))
else (.[1] = (\$mid - 1))
end
end ))
| if .[2] == null then # compute the insertion point
if \$in[ .[0] ] < target then (-2 -.[0])
else (-1 -.[0])
end
else .[2]
end
end;

# insert x assuming input is sorted
def insert(x):
if length == 0 then [x]
else
bsearch(x) as \$i
| ( if \$i < 0 then -(1+\$i) else \$i end ) as \$i
| .[0:\$i] + [x] + .[\$i:]
end ;

def insertion_sort:
reduce .[] as \$x ([]; insert(\$x));```
Example:
`[1, 2, 1, 1.1, -1.1, null, [null], {"null":null}] | insertion_sort`
Output:
```[null,-1.1,1,1,1.1,2,[null],{"null":null}]
```

## Julia

```# v0.6

function insertionsort!(A::Array{T}) where T <: Number
for i in 1:length(A)-1
value = A[i+1]
j = i
while j > 0 && A[j] > value
A[j+1] = A[j]
j -= 1
end
A[j+1] = value
end
return A
end

x = randn(5)
@show x insertionsort!(x)
```
Output:
```x = [-1.24011, -1.23848, 0.176698, -1.01986, 0.830544]
insertionsort!(x) = [-1.24011, -1.23848, -1.01986, 0.176698, 0.830544]```

## Kotlin

```fun insertionSort(array: IntArray) {
for (index in 1 until array.size) {
val value = array[index]
var subIndex = index - 1
while (subIndex >= 0 && array[subIndex] > value) {
array[subIndex + 1] = array[subIndex]
subIndex--
}
array[subIndex + 1] = value
}
}

fun main(args: Array<String>) {
val numbers = intArrayOf(5, 2, 3, 17, 12, 1, 8, 3, 4, 9, 7)

fun printArray(message: String, array: IntArray) = with(array) {
print("\$message [")
forEachIndexed { index, number ->
print(if (index == lastIndex) number else "\$number, ")
}
println("]")
}

printArray("Unsorted:", numbers)
insertionSort(numbers)
printArray("Sorted:", numbers)
}
```
Output:
```Unsorted: [5, 2, 3, 17, 12, 1, 8, 3, 4, 9, 7]
Sorted:   [1, 2, 3, 3, 4, 5, 7, 8, 9, 12, 17]```

## Ksh

```#!/bin/ksh

# An insertion sort in ksh

#	# Variables:
#
typeset -a arr=( 4 65 2 -31 0 99 2 83 782 1 )

#	# Functions:
#

#	# Function _insertionSort(array) - Insersion sort of array of integers
#
function _insertionSort {
typeset _arr ; nameref _arr="\$1"
typeset _i _j _val ; integer _i _j _val

for (( _i=1; _i<\${#_arr[*]}; _i++ )); do
_val=\${_arr[_i]}
(( _j = _i - 1 ))
while (( _j>=0 && _arr[_j]>_val )); do
_arr[_j+1]=\${_arr[_j]}
(( _j-- ))
done
_arr[_j+1]=\${_val}
done
}

######
# main #
######

_insertionSort arr

printf "%s" "( "
for (( i=0; i<\${#arr[*]}; i++ )); do
printf "%d " \${arr[i]}
done
printf "%s\n" " )"
```
Output:

( -31 0 1 2 2 4 65 83 99 782 )

## Lambdatalk

```{def sort

{def sort.i
{lambda {:x :a}
{if {A.empty? :a}
then {A.new :x}
else {if {<= :x {A.first :a}}
then {A.addfirst! :x :a}
else {A.addfirst! {A.first :a} {sort.i :x {A.rest :a}}} }}}}

{def sort.r
{lambda {:a1 :a2}
{if {A.empty? :a1}
then :a2
else {sort.r {A.rest :a1} {sort.i {A.first :a1} :a2}} }}}

{lambda {:a}
{sort.r :a {A.new}} }}
-> sort

{def A {A.new 4 65 2 -31 0 99 83 782 1}}
-> A

{sort {A}}
-> [-31,0,1,2,4,65,83,99,782]
```

## Liberty BASIC

```   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```

## Lua

Binary variation of Insertion sort (Has better complexity)

```do
local function lower_bound(container, container_begin, container_end, value, comparator)
local count = container_end - container_begin + 1

while count > 0 do
local half = bit.rshift(count, 1) -- or math.floor(count / 2)
local middle = container_begin + half

if comparator(container[middle], value) then
container_begin = middle + 1
count = count - half - 1
else
count = half
end
end

return container_begin
end

local function binary_insertion_sort_impl(container, comparator)
for i = 2, #container do
local j = i - 1
local selected = container[i]
local loc = lower_bound(container, 1, j, selected, comparator)

while j >= loc do
container[j + 1] = container[j]
j = j - 1
end

container[j + 1] = selected
end
end

local function binary_insertion_sort_comparator(a, b)
return a < b
end

function table.bininsertionsort(container, comparator)
if not comparator then
comparator = binary_insertion_sort_comparator
end

binary_insertion_sort_impl(container, comparator)
end
end
```
```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}))
```

## Maple

```arr := Array([17,3,72,0,36,2,3,8,40,0]):
len := numelems(arr):
for i from 2 to len do
val := arr[i]:
j := i-1:
while(j > 0 and arr[j] > val) do
arr[j+1] := arr[j]:
j--:
end do:
arr[j+1] := val:
end do:
arr;```
Output:
`[0,0,2,3,3,8,17,36,40,72]`

## Mathematica/Wolfram Language

```insertionSort[a_List] := Module[{A = a},
For[i = 2, i <= Length[A], i++,
value = A[[i]];    j = i - 1;
While[j >= 1 && A[[j]] > value, A[[j + 1]] = A[[j]]; j--;];
A[[j + 1]] = value;];
A
]
```
Output:
```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.

```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
```

Sample Usage:

```>> insertionSort([4 3 1 5 6 2])

ans =

1     2     3     4     5     6
```

## Maxima

```insertion_sort(u) := block(
[n: length(u), x, j],
for i from 2 thru n do (
x: u[i],
j: i - 1,
while j >= 1 and u[j] > x do (
u[j + 1]: u[j],
j: j - 1
),
u[j + 1]: x
)
)\$
```

## MAXScript

```fn inSort arr =
(
arr = deepcopy arr
for i = 1 to arr.count do
(
j = i
while j > 1 and arr[j-1] > arr[j] do
(
swap arr[j] arr[j-1]
j -= 1
)
)
return arr
)```

Output:

```b = for i in 1 to 20 collect random 1 40
#(2, 28, 35, 31, 27, 24, 2, 22, 15, 34, 9, 10, 22, 40, 26, 5, 23, 6, 18, 33)
a = insort b
#(2, 2, 5, 6, 9, 10, 15, 18, 22, 22, 23, 24, 26, 27, 28, 31, 33, 34, 35, 40)```

## Miranda

```main :: [sys_message]
main = [Stdout ("Before: " ++ show testlist ++ "\n"),
Stdout ("After:  " ++ show (insertionsort testlist) ++ "\n")]
where testlist = [4,65,2,-31,0,99,2,83,782,1]

insertionsort :: [*]->[*]
insertionsort = foldr insert []

insert :: *->[*]->[*]
insert x []     = [x]
insert x (y:ys) = x:y:ys,        if x<y
= y:insert x ys, otherwise```
Output:
```Before: [4,65,2,-31,0,99,2,83,782,1]
After:  [-31,0,1,2,2,4,65,83,99,782]```

## ML

### mLite

Translation of: OCaml
```fun insertion_sort L =
let
fun insert
(x,[]) = [x]
|	(x, y :: ys) =
if x <= y then
x :: y :: ys
else
y :: insert (x, ys)
in
foldr (insert,[]) L
end;

println ` insertion_sort [6,8,5,9,3,2,1,4,7];
```

Output

```[1, 2, 3, 4, 5, 6, 7, 8, 9]
```

### Standard ML

```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];
```

## Modula-3

```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.
```

## N/t/roff

Works with: GNU Troff version 1.22.2

### Sliding method

```.de end
..
.de array
.	nr \\\$1.c 0 1
.	de \\\$1.push end
.		nr \\\$1..\\\\n+[\\\$1.c] \\\\\$1
.	end
.	de \\\$1.pushln end
.		if \\\\n(.\$>0 .\\\$1.push \\\\\$1
.		if \\\\n(.\$>1 \{ \
.			shift
.			\\\$1.pushln \\\\\$@
.		\}
.	end
.	de \\\$1.dump end
.		nr i 0 1
.		ds out "
.		while \\\\n+i<=\\\\n[\\\$1.c] .as out "\\\\n[\\\$1..\\\\ni]
.		tm \\\\*[out]
.		rm out
.		rr i
.	end
.	de \\\$1.slideright end
.		nr i \\\\\$1
.		nr i+1 \\\\ni+1
.		nr \\\$1..\\\\n[i+1] \\\\n[\\\$1..\\\\ni]
.		rr i
.		rr i+1
.	end
..
.de insertionsort
.	nr keyidx 1 1
.	while \\n+[keyidx]<=\\n[\\\$1.c] \{ \
.		nr key \\n[\\\$1..\\n[keyidx]]
.		nr compidx \\n[keyidx] 1
.		while \\n-[compidx]>=0 \{ \
.			if \\n[compidx]=0 \{ \
.				nr \\\$1..1 \\n[key]
.				break
.			\}
.			ie \\n[\\\$1..\\n[compidx]]>\\n[key] \{ \
.				\\\$1.slideright \\n[compidx]
.			\}
.			el \{ \
.				nr compidx+1 \\n[compidx]+1
.				nr \\\$1..\\n[compidx+1] \\n[key]
.				break
.			\}
.		\}
.	\}
..
.array a
.a.pushln 13 64 22 87 54 87 23 92 11 64 5 9 3 3 0
.insertionsort a
.a.dump```

### Swapping method

```.de end
..
.de array
.	nr \\\$1.c 0 1
.	de \\\$1.push end
.		nr \\\$1..\\\\n+[\\\$1.c] \\\\\$1
.	end
.	de \\\$1.pushln end
.		if \\\\n(.\$>0 .\\\$1.push \\\\\$1
.		if \\\\n(.\$>1 \{ \
.			shift
.			\\\$1.pushln \\\\\$@
.		\}
.	end
.	de \\\$1.dump end
.		nr i 0 1
.		ds out "
.		while \\\\n+i<=\\\\n[\\\$1.c] .as out "\\\\n[\\\$1..\\\\ni]
.		tm \\\\*[out]
.		rm out
.		rr i
.	end
.	de \\\$1.swap end
.		if (\\\\\$1<=\\\\n[\\\$1.c])&(\\\\\$1<=\\\\n[\\\$1.c]) \{ \
.			nr tmp \\\\n[\\\$1..\\\\\$2]
.			nr \\\$1..\\\\\$2 \\\\n[\\\$1..\\\\\$1]
.			nr \\\$1..\\\\\$1 \\\\n[tmp]
.			rr tmp
.		\}
.	end
..
.de insertionsort
.	nr keyidx 1 1
.	while \\n+[keyidx]<=\\n[\\\$1.c] \{ \
.		nr compidx \\n[keyidx]+1 1
.		nr compidx-1 \\n[keyidx] 1
.		while (\\n-[compidx]>0)&(\\n[\\\$1..\\n-[compidx-1]]>\\n[\\\$1..\\n[compidx]]) \{ \
.			\\\$1.swap \\n[compidx] \\n[compidx-1]
.		\}
.	\}
..
.array a
.a.pushln 13 64 22 87 54 87 23 92 11 64 5 9 3 3 0
.insertionsort a
.a.dump```

## Nanoquery

Translation of: Python
```def insertion_sort(L)
for i in range(1, len(L) - 1)
j = i - 1
key = L[i]
while (L[j] > key) and (j >= 0)
L[j + 1] = L[j]
j -= 1
end
L[j+1] = key
end

return L
end```

## Nemerle

From the psuedocode.

```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  ");
}
}
```

## 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)
```
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

```proc insertSort[T](a: var openarray[T]) =
for i in 1 .. a.high:
let value = a[i]
var j = i
while j > 0 and value < a[j-1]:
a[j] = a[j-1]
dec j
a[j] = value

var a = @[4, 65, 2, -31, 0, 99, 2, 83, 782]
insertSort a
echo a
```
Output:
`@[-31, 0, 2, 2, 4, 65, 83, 99, 782]`

## Oberon-2

Translation of: Modula-3
```MODULE InsertionSort;

IMPORT Out;

VAR
A1:ARRAY 10 OF INTEGER;

PROCEDURE Init;
BEGIN
A1[0] := 4; A1[1] := 65; A1[2] := 2; A1[3] := -31;
A1[4] := 0; A1[5] := 99; A1[6] := 2; A1[7] := 83;
A1[8] := 782; A1[9] := 1;
END Init;

PROCEDURE InsertionSort(VAR A:ARRAY OF INTEGER);
VAR
i,j:LONGINT;
value:INTEGER;
BEGIN
FOR i := 1 TO LEN(A)-1 DO
value := A[i];
j := i-1;
WHILE((j >= 0) & (A[j] > value)) DO A[j+1] := A[j]; DEC(j) END;
A[j+1] := value
END;
END InsertionSort;

PROCEDURE PrintArray(VAR A:ARRAY OF INTEGER);
VAR i:LONGINT;
BEGIN
FOR i := 0 TO LEN(A)-1 DO Out.Int(A[i],0); Out.Char(' ') END;
Out.Ln
END PrintArray;

BEGIN
Init;
PrintArray(A1);
InsertionSort(A1);
PrintArray(A1);
END InsertionSort.
```
Output:
```4 65 2 -31 0 99 2 83 782 1
-31 0 1 2 2 4 65 83 99 782
```

## 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;
};
}
}
}```

## OCaml

```let rec insert lst x =
match lst with
| y :: ys when x > y -> y :: insert ys x
| _ -> x :: lst

let insertion_sort = List.fold_left insert []

let () = [6; 8; 5; 9; 3; 2; 1; 4; 7]
|> insertion_sort |> List.iter (Printf.printf " %u") |> print_newline
```
Output:
` 1 2 3 4 5 6 7 8 9`

## Oforth

Returns a new sorted list.

```: insertionSort(a)
| l i j v |
a asListBuffer ->l
2 l size for: i [
l at(i) ->v
i 1- ->j
while(j) [
l at(j) dup v <= ifTrue: [ drop break ]
j 1+ swap l put
j 1- ->j
]
l put(j 1 +, v)
]
l ;```
Output:
```>[ 4, 65, 2, -31, 0, 99, 2, 83, 782, 1 ] insertionSort .
[-31, 0, 1, 2, 2, 4, 65, 83, 99, 782] ok
>
```

## ooRexx

Translation of: REXX
```/* REXX program sorts a stemmed array (has characters)                */
/* using the insertion sort algorithm                                 */
Call gen                          /* fill the array with test data  */
Call show 'before sort'           /* display the elements           */
Say copies('-',79)                /* display a separator line       */
Call insertionSort x.0            /* invoke the insertion sort.     */
Call show ' after sort'           /* display the elements after sort*/
Exit
/*--------------------------------------------------------------------*/
gen: Procedure Expose x.
x.1="---Monday's Child Is Fair of Face  (by Mother Goose)---"
x.2="======================================================="
x.3="Monday's child is fair of face;"
x.4="Tuesday's child is full of grace;"
x.5="Wednesday's child is full of woe;"
x.6="Thursday's child has far to go;"
x.7="Friday's child is loving and giving;"
x.8="Saturday's child works hard for a living;"
x.9="But the child that is born on the Sabbath day"
x.10="Is blithe and bonny, good and gay."
x.0=10                            /* number of elements             */
Return
/*--------------------------------------------------------------------*/
insertionsort: Procedure Expose x.
Parse Arg n
Do i=2 To n
y=x.i
Do j=i-1 By -1 To 1 While x.j>y
z=j+1
x.z=x.j
/* Say 'set x.'z 'to x.'j '('||x.j||')' */
End
z=j+1
x.z=y
/* Say 'set x.'z 'to' y                   */
End
Return
/*--------------------------------------------------------------------*/
show:
Do j=1 To x.0
Say 'Element' right(j,length(x.0)) arg(1)":" x.j
End
Return
```
Output:
```Element  1 before sort: ---Monday's Child Is Fair of Face  (by Mother Goose)---
Element  2 before sort: =======================================================
Element  3 before sort: Monday's child is fair of face;
Element  4 before sort: Tuesday's child is full of grace;
Element  5 before sort: Wednesday's child is full of woe;
Element  6 before sort: Thursday's child has far to go;
Element  7 before sort: Friday's child is loving and giving;
Element  8 before sort: Saturday's child works hard for a living;
Element  9 before sort: But the child that is born on the Sabbath day
Element 10 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: =======================================================
Element  3  after sort: But the child that is born on the Sabbath day
Element  4  after sort: Friday's child is loving and giving;
Element  5  after sort: Is blithe and bonny, good and gay.
Element  6  after sort: Monday's child is fair of face;
Element  7  after sort: Saturday's child works hard for a living;
Element  8  after sort: Thursday's child has far to go;
Element  9  after sort: Tuesday's child is full of grace;
Element 10  after sort: Wednesday's child is full of woe;```

## Oz

Direct translation of pseudocode. In-place sorting of mutable arrays.

```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}}```

## PARI/GP

```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
};```

## Pascal

Works with: FPC
```program SortDemo;

{\$mode objfpc}{\$h+}{\$b-}

procedure InsertionSort(var A: array of Integer);
var
I, J, Tmp: Integer;
begin
for I := 1 to High(a) do
if A[I] < A[I - 1] then begin
J := I;
Tmp := A[I];
repeat
A[J] := A[J - 1];
Dec(J);
until (J = 0) or (Tmp >= A[J - 1]);
A[J] := Tmp;
end;
end;

procedure PrintArray(const A: array of Integer);
var
I: Integer;
begin
Write('[');
for I := 0 to High(A) - 1 do
Write(A[I], ', ');
WriteLn(A[High(A)], ']');
end;

var
a: array[-7..6] of Integer = (-34, -20, 30, 13, 36, -10, 5, -25, 9, 19, 35, -50, 29, 11);

begin
InsertionSort(a);
PrintArray(a);
end.
```
Output:
```[-50, -34, -25, -20, -10, 5, 9, 11, 13, 19, 29, 30, 35, 36]
```

## 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";
```
Output:
```-31 0 1 2 4 65 83 99 782
```

## Phix

Copy of 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 s[j]>temp do
s[j+1] = s[j]
j -= 1
end while
s[j+1] = temp
end for
return s
end function

constant s = {4, 15, "delta", 2, -31, 0, "alpha", 19, "gamma", 2, 13, "beta", 782, 1}

puts(1,"Before: ")    ?s
puts(1,"After: ")     ?insertion_sort(s)
```
Output:
```Before: {4,15,"delta",2,-31,0,"alpha",19,"gamma",2,13,"beta",782,1}
After: {-31,0,1,2,2,4,13,15,19,782,"alpha","beta","delta","gamma"}
```

## 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);
```
`1,2,3,4,6,7,8,9`

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

## PL/I

```insert_sort: proc(array);
dcl array(*)      fixed bin(31);
dcl (i,j,tmp,h,l) fixed bin(31);

l = lbound(array, 1);
h = hbound(array, 1);

do i = l + 1 to h;
tmp = array(i);

do j = i - 1 by -1 while(j > l - 1 & array(j) > tmp);
array(j + 1) = array(j);
end;

array(j + 1) = tmp;
end;
end insert_sort;```

## PL/M

```100H:

/* INSERTION SORT ON 16-BIT INTEGERS */
INSERTION\$SORT: PROCEDURE (AP, LEN);
DECLARE (AP, LEN, I, J, V, A BASED AP) ADDRESS;
DO I = 1 TO LEN-1;
V = A(I);
J = I;
DO WHILE J > 0 AND A(J-1) > V;
A(J) = A(J-1);
J = J-1;
END;
A(J) = V;
END;
END INSERTION\$SORT;

/* CP/M CALLS AND FUNCTION TO PRINT INTEGERS */
BDOS: PROCEDURE (FN, ARG);
DECLARE FN BYTE, ARG ADDRESS;
GO TO 5;
END BDOS;

PRINT\$NUMBER: PROCEDURE (N);
DECLARE S (7) BYTE INITIAL ('..... \$');
DECLARE (N, P) ADDRESS, C BASED P BYTE;
P = .S(5);
DIGIT:
P = P-1;
C = N MOD 10 + '0';
N = N / 10;
IF N > 0 THEN GO TO DIGIT;
CALL BDOS(9, P);
END PRINT\$NUMBER;

/* SORT AN ARRAY */
DECLARE NUMBERS (11) ADDRESS INITIAL (4, 65, 2, 31, 0, 99, 2, 8, 3, 782, 1);
CALL INSERTION\$SORT(.NUMBERS, LENGTH(NUMBERS));

/* PRINT THE SORTED ARRAY */
DECLARE N BYTE;
DO N = 0 TO LAST(NUMBERS);
CALL PRINT\$NUMBER(NUMBERS(N));
END;

CALL BDOS(0,0);
EOF```
Output:
`0 1 2 2 3 4 8 31 65 99 782`

## PowerShell

Very similar to the PHP code.

```function insertionSort(\$arr){
for(\$i=0;\$i -lt \$arr.length;\$i++){
\$val = \$arr[\$i]
\$j = \$i-1
while(\$j -ge 0 -and \$arr[\$j] -gt \$val){
\$arr[\$j+1] = \$arr[\$j]
\$j--
}
\$arr[\$j+1] = \$val
}
}

\$arr = @(4,2,1,6,9,3,8,7)
insertionSort(\$arr)
\$arr -join ","
```
Output:
`1,2,3,4,6,7,8,9`

## 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).
```
```% 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.

```% 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).
```

Example use:

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

## 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
```

## Python

```def insertion_sort(L):
for i in xrange(1, len(L)):
j = i-1
key = L[i]
while j >= 0 and L[j] > key:
L[j+1] = L[j]
j -= 1
L[j+1] = key
```

Using pythonic iterators:

```def insertion_sort(L):
for i, value in enumerate(L):
for j in range(i - 1, -1, -1):
if L[j] > value:
L[j + 1] = L[j]
L[j] = value
```

### Insertion sort with binary search

```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:]
```

This is also built-in to the standard library:

```import bisect
def insertion_sort_bin(seq):
for i in range(1, len(seq)):
bisect.insort(seq, seq.pop(i), 0, i)
```

## Qi

Based on the scheme version.

```(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])```

## Quackery

```[ [] swap witheach
[ swap 2dup findwith
[ over > ] [ ]
nip stuff ] ]        is insertionsort ( [ --> [ )```

## R

Direct translation of pseudocode.

```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
```

R has native vectorized operations which allow the following, more efficient implementation.

```insertion_sort <- function(x) {
for (j in 2:length(x)) {
key <- x[j]
bp <- which.max(x[1:j] > key)
# 'bp' stands for breakpoint
if (bp == 1) {
if (key < ar[1]){
x <- c(key, ar[-j])
}
}
else {
x <- x[-j]
x <- c(ar[1:bp - 1], key, x[bp : (s-1)])
}
return(x)
}
}
```

## Racket

This implementation makes use of the pattern matching facilities in the Racket distribution.

```#lang racket

(define (sort < l)
(define (insert x ys)
(match ys
[(list) (list x)]
[(cons y rst) (cond [(< x y) (cons x ys)]
[else (cons y (insert x rst))])]))
(foldl insert '() l))
```

## Raku

(formerly Perl 6)

```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;
```
Output:
```input  = 22 7 2 -5 8 4
output = -5 2 4 7 8 22
```

## Rascal

```import List;

public list[int] insertionSort(a){
for(i <- [0..size(a)-1]){
v = a[i];
j = i-1;
while(j >= 0 && a[j] > v){
a[j+1] = a[j];
j -= 1;
}
a[j+1] = v;
}
return a;
}```
Output:
```rascal>rascal>insertionSort([4, 65, 2, -31, 0, 99, 83, 782, 1])
list[int]: [-31,0,1,2,4,65,83,99,782]```

## REALbasic

```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
```

## REBOL

```; This program works with REBOL version R2 and R3, to make it work with Red
; change the word func to function
insertion-sort: func [
a [block!]
/local i [integer!] j [integer!] n [integer!]
value [integer! string! date!]
][
i: 2
n: length? a

while [i <= n][
value: a/:i
j: i
while [ all [ 	1 < j
value < a/(j - 1) ]][

a/:j: a/(j - 1)
j: j - 1
]
a/:j: value
i: i + 1
]
a
]

probe insertion-sort [4 2 1 6 9 3 8 7]

probe insertion-sort [ "---Monday's Child Is Fair of Face (by Mother Goose)---"
"Monday's child is fair of face;"
"Tuesday's child is full of grace;"
"Wednesday's child is full of woe;"
"Thursday's child has far to go;"
"Friday's child is loving and giving;"
"Saturday's child works hard for a living;"
"But the child that is born on the Sabbath day"
"Is blithe and bonny, good and gay."]

; just by adding the date! type to the local variable value the same function can sort dates.
probe insertion-sort [12-Jan-2015 11-Jan-2015 11-Jan-2016 12-Jan-2014]
```
Output:
```[1 2 3 4 6 7 8 9]
[{---Monday's Child Is Fair of Face (by Mother Goose)---}
"But the child that is born on the Sabbath day"
"Friday's child is loving and giving;"
"Is blithe and bonny, good and gay."
"Monday's child is fair of face;"
"Saturday's child works hard for a living;"
"Thursday's child has far to go;"
"Tuesday's child is full of grace;"
"Wednesday's child is full of woe;"
]
[12-Jan-2014 11-Jan-2015 12-Jan-2015 11-Jan-2016]
```

## REXX

```/*REXX program sorts a stemmed array (has characters) using the insertion sort algorithm*/
call gen                                         /*generate the array's (data) elements.*/
call show           'before sort'                /*display the  before  array elements. */
say copies('▒', 85)                         /*display a separator line  (a fence). */
call insertionSort  #                            /*invoke the  insertion  sort.         */
call show           ' after sort'                /*display the   after  array elements. */
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
gen: @.=;                 @.1  = "---Monday's Child Is Fair of Face  (by Mother Goose)---"
@.2  = "======================================================="
@.3  = "Monday's child is fair of face;"
@.4  = "Tuesday's child is full of grace;"
@.5  = "Wednesday's child is full of woe;"
@.6  = "Thursday's child has far to go;"
@.7  = "Friday's child is loving and giving;"
@.8  = "Saturday's child works hard for a living;"
@.9  = "But the child that is born on the Sabbath day"
@.10 = "Is blithe and bonny, good and gay."
do #=1  while @.#\==''; end;  #= #-1 /*determine how many entries in @ array*/
return                                      /* [↑]  adjust # for the DO loop index.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
insertionSort:  procedure expose @.;      parse arg #
do i=2  to #;   \$= @.i;       do j=i-1  by -1  to 1  while @.j>\$
_= j + 1;        @._= @.j
end   /*j*/
_= j + 1;       @._= \$
end   /*i*/
return
/*──────────────────────────────────────────────────────────────────────────────────────*/
show:  do j=1  for #;  say '   element'  right(j,length(#))  arg(1)": "  @.j; end;  return
```
output   when using the default internal data:
```   element  1 before sort:  ---Monday's Child Is Fair of Face  (by Mother Goose)---
element  2 before sort:  =======================================================
element  3 before sort:  Monday's child is fair of face;
element  4 before sort:  Tuesday's child is full of grace;
element  5 before sort:  Wednesday's child is full of woe;
element  6 before sort:  Thursday's child has far to go;
element  7 before sort:  Friday's child is loving and giving;
element  8 before sort:  Saturday's child works hard for a living;
element  9 before sort:  But the child that is born on the Sabbath day
element 10 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:  =======================================================
element  3  after sort:  But the child that is born on the Sabbath day
element  4  after sort:  Friday's child is loving and giving;
element  5  after sort:  Is blithe and bonny, good and gay.
element  6  after sort:  Monday's child is fair of face;
element  7  after sort:  Saturday's child works hard for a living;
element  8  after sort:  Thursday's child has far to go;
element  9  after sort:  Tuesday's child is full of grace;
element 10  after sort:  Wednesday's child is full of woe;
```

## Ring

```alist = [7,6,5,9,8,4,3,1,2,0]
see insertionsort(alist)

func insertionsort blist
for i = 1 to len(blist)
value = blist[i]
j = i - 1
while j >= 1 and blist[j] > value
blist[j+1] = blist[j]
j = j - 1
end
blist[j+1] = value
next
return blist```

## RPL

In RPL, the condition `while j > 0 and A[j] > value do` needs to be fully assessed before performing the loop: an error would then occur when j will equal zero. This is why the loop condition has been encapsulated in a `IFERR..THEN..END` structure, which removes the need to test the value of j.

Works with: Halcyon Calc version 4.2.7
RPL code Comment
``` ≪ 'A' STO
2 A SIZE FOR ii
A ii GET
ii 1 -
WHILE
IFERR DUP2 A SWAP GET < THEN 3 DROPN 0 END REPEAT
'A' OVER GETI PUT
1 -
END
'A' SWAP 1 + ROT PUT
NEXT
A 'A' PURGE
≫ 'ISORT' STO
```
```( [array] -- [array] )
for i from 2 to length[A] do // RPL arrays starts at 1
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
Display result and delete global variable

```
Input:
```[ 1 4 -1 0 3 7 4 8 20 -6 ] ISORT
```
Output:
```1: [ -6 -1 0 1 3 4 4 7 8 20 ]
```

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

Alternative version which doesn't swap elements but rather removes and inserts the value at the correct place:

```class Array
def insertionsort!
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]
p ary.insertionsort!
# => [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
```

## Run BASIC

```dim insSort(100)
sortEnd = 0
global inSort
global sortEnd

' -- insert some random numbers --

for i = 1 to 20
a = int(1000 * rnd(1))
x = insertSort(a)
next i

' --- Print the Sorted Data -----

print "End Sort:";sortEnd                ' number sorted
for i = 1 to sortEnd
print i;" ";insSort(i)                  ' location and sorted data
next i
wait

function insertSort(x)                   ' Insert Sort Function
i = 1
while x > insSort(i) and i <= sortEnd
i = i + 1
wend
for j = sortEnd to i step -1
insSort(j + 1) = insSort(j)
next j
insSort(i) = x
sortEnd    = sortEnd + 1
end function```
```End Sort:20
1 124
2 248
3 263
4 279
5 390
6 431
7 458
8 480
9 543
10 556
11 567
12 619
13 625
........```

## Rust

```fn insertion_sort<T: std::cmp::Ord>(arr: &mut [T]) {
for i in 1..arr.len() {
let mut j = i;
while j > 0 && arr[j] < arr[j-1] {
arr.swap(j, j-1);
j = j-1;
}
}
}
```

## SASL

Copied from SASL manual, Appendix II, answer (2)(a)

```DEF
sort () = ()
sort (a : x) = insert a (sort x)
insert a () = a,
insert a (b : x) = a < b -> a : b : x
b : insert a x
?```

## Scala

```def insertSort[X](list: List[X])(implicit ord: Ordering[X]) = {
def insert(list: List[X], value: X) = list.span(x => ord.lt(x, value)) match {
case (lower, upper) => lower ::: value :: upper
}
list.foldLeft(List.empty[X])(insert)
}
```

## 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))
```

## 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;```

Original source: [1]

## Sidef

```class Array {
method insertion_sort {
{ |i|
var j = i-1
var k = self[i]
while ((j >= 0) && (k < self[j])) {
self[j+1] = self[j]
j--
}
self[j+1] = k
} << 1..self.end
return self
}
}

var a = 10.of { 100.irand }
say a.insertion_sort
```

## SNOBOL4

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

* sort array
i = 1
loop1	value = A<i>
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>; i = ?lt(i,aSize) i + 1	:s(while)
end
```

## Stata

```mata
void insertion_sort(real vector a) {
real scalar i, j, n, x

n = length(a)
for (i=2; i<=n; i++) {
x = a[i]
for (j=i-1; j>=1; j--) {
if (a[j] <= x) break
a[j+1] = a[j]
}
a[j+1] = x
}
}
end
```

## Swift

Using generics.

```func insertionSort<T:Comparable>(inout list:[T]) {
for i in 1..<list.count {
var j = i

while j > 0 && list[j - 1] > list[j] {
swap(&list[j], &list[j - 1])
j--
}
}
}
```

## 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
```

## 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
```

## uBasic/4tH

```PRINT "Insertion sort:"
n = FUNC (_InitArray)
PROC _ShowArray (n)
PROC _Insertionsort (n)
PROC _ShowArray (n)
PRINT

END

_Insertionsort PARAM (1)               ' Insertion sort
LOCAL (3)

FOR b@ = 1 TO a@-1
c@ = @(b@)
d@ = b@
DO WHILE (d@>0) * (c@ < @(ABS(d@-1)))
@(d@) = @(d@-1)
d@ = d@ - 1
LOOP
@(d@) = c@
NEXT
RETURN

_Swap PARAM(2)                         ' Swap two array elements
PUSH @(a@)
@(a@) = @(b@)
@(b@) = POP()
RETURN

_InitArray                             ' Init example array
PUSH 4, 65, 2, -31, 0, 99, 2, 83, 782, 1

FOR i = 0 TO 9
@(i) = POP()
NEXT

RETURN (i)

_ShowArray PARAM (1)                   ' Show array subroutine
FOR i = 0 TO a@-1
PRINT @(i),
NEXT

PRINT
RETURN
```

## UnixPipes

```selectionsort() {
test -n "\$a" && ( selectionsort | sort -nm <(echo \$a) -)
}
```
```cat to.sort | selectionsort
```

## Ursala

```#import nat

insort = ~&i&& @hNCtX ~&r->lx ^\~&rt nleq-~rlrSPrhlPrSCPTlrShlPNCTPQ@rhPlD```

test program:

```#cast %nL

example = insort <45,82,69,82,104,58,88,112,89,74>```
Output:
```<45,58,69,74,82,82,88,89,104,112>
```

## Vala

Translation of: Nim
```void insertion_sort(int[] array) {
var count = 0;
for (int i = 1; i < array.length; i++) {
var val = array[i];
var j = i;
while (j > 0 && val < array[j - 1]) {
array[j] = array[j - 1];
j--;
}
array[j] = val;
}
}

void main() {
int[] array = {4, 65, 2, -31, 0, 99, 2, 83, 782};
insertion_sort(array);
foreach (int i in array)
print("%d ", i);
}
```
Output:
```-31 0 2 2 4 65 83 99 782
```

## VBA

Translation of: Phix
```Option Base 1
Private Function insertion_sort(s As Variant) As Variant
Dim temp As Variant
Dim j As Integer
For i = 2 To UBound(s)
temp = s(i)
j = i - 1
Do While s(j) > temp
s(j + 1) = s(j)
j = j - 1
If j = 0 Then Exit Do
Loop
s(j + 1) = temp
Next i
insertion_sort = s
End Function

Public Sub main()
s = [{4, 15, "delta", 2, -31, 0, "alpha", 19, "gamma", 2, 13, "beta", 782, 1}]
Debug.Print "Before: ", Join(s, ", ")
Debug.Print "After: ", Join(insertion_sort(s), "' ")
End Sub
```
Output:
```Before:       4, 15, delta, 2, -31, 0, alpha, 19, gamma, 2, 13, beta, 782, 1
After:        -31' 0' 1' 2' 2' 4' 13' 15' 19' 782' alpha' beta' delta' gamma```

## VBScript

Translation of: REALbasic
```Randomize
Dim n(9) 'nine is the upperbound.
'since VBS arrays are 0-based, it will have 10 elements.
For L = 0 to 9
n(L) = Int(Rnd * 32768)
Next

WScript.StdOut.Write "ORIGINAL : "
For L = 0 to 9
WScript.StdOut.Write n(L) & ";"
Next

InsertionSort n

WScript.StdOut.Write vbCrLf & "  SORTED : "
For L = 0 to 9
WScript.StdOut.Write n(L) & ";"
Next

'the function
Sub InsertionSort(theList)
For insertionElementIndex = 1 To UBound(theList)
insertionElement = theList(insertionElementIndex)
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
```
Output:
```ORIGINAL : 26699;2643;10249;31612;21346;19702;29799;31115;20413;5197;
SORTED : 2643;5197;10249;19702;20413;21346;26699;29799;31115;31612;```

## V (Vlang)

```fn insertion(mut arr []int) {
for i in 1 .. arr.len {
value := arr[i]
mut j := i - 1
for j >= 0 && arr[j] > value {
arr[j + 1] = arr[j]
j--
}
arr[j + 1] = value
}
}

fn main() {
mut arr := [4, 65, 2, -31, 0, 99, 2, 83, 782, 1]
println('Input: ' + arr.str())
insertion(mut arr)
println('Output: ' + arr.str())
}```
Output:
```Input: [4, 65, 2, -31, 0, 99, 2, 83, 782, 1]
Output: [-31, 0, 1, 2, 2, 4, 65, 83, 99, 782]```

## Wren

```var insertionSort = Fn.new { |a|
for (i in 1..a.count-1) {
var v = a[i]
var j = i - 1
while (j >= 0 && a[j] > v) {
a[j+1] = a[j]
j = j - 1
}
a[j+1] = v
}
}

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)")
insertionSort.call(a)
System.print("After : %(a)")
System.print()
}
```
Output:
```Before: [4, 65, 2, -31, 0, 99, 2, 83, 782, 1]
After : [-31, 0, 1, 2, 2, 4, 65, 83, 99, 782]

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

Alternatively we can just call a library method.

Library: Wren-sort
```import "/sort" for Sort

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

## XPL0

```code ChOut=8, IntOut=11;

proc InsertionSort(A, L);       \Sort array A of length L
int  A, L;
int  I, J, V;
[for I:= 1 to L-1 do
[V:= A(I);
J:= I-1;
while J>=0 and A(J)>V do
[A(J+1):= A(J);
J:= J-1;
];
A(J+1):= V;
];
];

int A, I;
[A:= [3, 1, 4, 1, -5, 9, 2, 6, 5, 4];
InsertionSort(A, 10);
for I:= 0 to 10-1 do [IntOut(0, A(I));  ChOut(0, ^ )];
]```
Output:
```-5 1 1 2 3 4 4 5 6 9
```

## Yabasic

Translation of: FreeBASIC
```sub InsertionSort (matriz())
for i = 1 to arraysize(matriz(),1)
valor = matriz(i)
j = i - 1
while (j >= 0) and (valor < matriz(j))
matriz(j + 1) = matriz(j)
j = j - 1
wend
matriz(j + 1) = valor
next i
end sub

//--------------------------
dim array(10)
print "Antes de ordenar:"
for i = 1 to 10
array(i) = int(ran(32768))
print array(i), " ";
next i
print
print "\nDespues de ordenar:"

InsertionSort(array())

for i = 1 to 10
print array(i), " ";
next i
print
end```

## Yorick

Based on pseudocode, except using 1-based arrays.

```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;
}
}```

## zkl

```fcn insertionSort(list){
sink:=List();
foreach x in (list){
if(False==(n:=sink.filter1n('>(x)))) sink.append(x); // x>all items in sink
else sink.insert(n,x);
}
sink.close();
}```
```insertionSort(T(4,65,2,-31,0,99,2,83,782,1)).println();
insertionSort("big fjords vex quick waltz nymph".split()).println();```
Output:
```L(-31,0,1,2,2,4,65,83,99,782)
L("big","fjords","nymph","quick","vex","waltz")
```