You are encouraged to
solve this taskaccording to the task description, using any language you may know.
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:
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.
11lF 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)
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]360 Assembly
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
-31 0 1 2 2 4 45 58 65 69 74 82 82 83 88 89 99 104 112 782Assembler 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
Same as previous
AArch64 Assembly.section .text
.globl insertion_sort
// C equivalent at bottom
/* void insertion_sort(int *arr, size_t len);
* X0: pointer to &a[0]
* X1: index of one past the last element of arr
* Preconditions:
* - Arg 1 (X0) is not a null pointer
* - Arg 2 (X1) is not zero
*/
#define ARR_BEGIN x0
#define ARR_END x2
#define I x3
#define J x4
#define OUTER_TMP w6
#define INNER_TMP w5
insertion_sort:
add ARR_END, ARR_BEGIN, x1, LSL #2
add I, ARR_BEGIN, #4
b 2f
// goto test;
// do {
0:
ldr OUTER_TMP, [I] // OUTER_TMP = *I;
// int INNER_TMP, *J;
// for (J = I; J != &arr[0] && (INNER_TMP = J[-1]) > OUTER_TMP; J--)
// *J = INNER_TMP;
mov J, I
b 3f
1:
// Loop body
str INNER_TMP, [J], #-4
3:
// Loop test
cmp J, ARR_BEGIN
b.eq 1f
ldr INNER_TMP, [J, #-4]
cmp INNER_TMP, OUTER_TMP
b.gt 1b
1:
str OUTER_TMP, [J] // *J = OUTER_TMP
add I, I, #4
// test:; } while (I < &arr[len]);
2:
cmp I, ARR_END
b.lo 0b
ret
/*
// First I wrote this C code, then I hand-compiled it to the above assembly.
void insertion_sort(int arr[], size_t len) {
int x, *pi, *pj;
for (pi = &a[1]; pi != &arr[len]; pi++) {
x = *pi;
for (pj = pi; pj != &a[0] && pj[-1] > x; pj--)
*pj = pj[-1];
*pj = x;
}
}
*/
/* 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
#TableNumber: .quad 1,3,6,2,5,9,10,8,4,7
TableNumber: .quad 10,9,8,7,6,-5,4,3,2,1
.equ NBELEMENTS, (. - TableNumber) / 8
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
sZoneConv: .skip 24
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: // entry of program
ldr x0,qAdrTableNumber // address number table
mov x1,0 // first element
mov x2,NBELEMENTS // number of élements
bl insertionSort
ldr x0,qAdrTableNumber // address number table
bl displayTable
ldr x0,qAdrTableNumber // address number table
mov x1,NBELEMENTS // number of élements
bl isSorted // control sort
cmp x0,1 // sorted ?
beq 1f
ldr x0,qAdrszMessSortNok // no !! error sort
bl affichageMess
b 100f
1: // yes
ldr x0,qAdrszMessSortOk
bl affichageMess
100: // standard end of the program
mov x0,0 // return code
mov x8,EXIT // request to exit program
svc 0 // perform the system call
qAdrsZoneConv: .quad sZoneConv
qAdrszCarriageReturn: .quad szCarriageReturn
qAdrsMessResult: .quad sMessResult
qAdrTableNumber: .quad TableNumber
qAdrszMessSortOk: .quad szMessSortOk
qAdrszMessSortNok: .quad szMessSortNok
/******************************************************************/
/* control sorted table */
/******************************************************************/
/* x0 contains the address of table */
/* x1 contains the number of elements > 0 */
/* x0 return 0 if not sorted 1 if sorted */
isSorted:
stp x2,lr,[sp,-16]! // save registers
stp x3,x4,[sp,-16]! // save registers
mov x2,0
ldr x4,[x0,x2,lsl 3]
1:
add x2,x2,1
cmp x2,x1
bge 99f
ldr x3,[x0,x2, lsl 3]
cmp x3,x4
blt 98f
mov x4,x3
b 1b
98:
mov x0,0 // not sorted
b 100f
99:
mov x0,1 // sorted
100:
ldp x3,x4,[sp],16 // restaur 2 registers
ldp x2,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* 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
ret // return to address lr x30
/******************************************************************/
/* Display table elements */
/******************************************************************/
/* x0 contains the address of table */
displayTable:
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
mov x2,x0 // table address
mov x3,0
1: // loop display table
ldr x0,[x2,x3,lsl 3]
ldr x1,qAdrsZoneConv
bl conversion10S // décimal conversion
ldr x0,qAdrsMessResult
ldr x1,qAdrsZoneConv
bl strInsertAtCharInc // insert result at @ character
bl affichageMess // display message
add x3,x3,1
cmp x3,NBELEMENTS - 1
ble 1b
ldr x0,qAdrszCarriageReturn
bl affichageMess
mov x0,x2
100:
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/********************************************************/
/* File Include fonctions */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"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
Screenshot from Atari 8-bit computer
Array before sort: [1 4 -1 0 3 7 4 8 20 -6] Array after sort: [-6 -1 0 1 3 4 4 7 8 20] Array before sort: [10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10] Array after sort: [-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10] Array before sort: [101 102 103 104 105 106 107 108] Array after sort: [101 102 103 104 105 106 107 108] Array before sort: [1 -1 1 -1 1 -1 1 -1 1 -1 1 -1] Array after sort: [-1 -1 -1 -1 -1 -1 1 1 1 1 1 1]ActionScript
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;
}
Ada
type Data_Array is array(Natural range <>) of Integer;
procedure Insertion_Sort(Item : in out Data_Array) is
First : Natural := Item'First;
Last : Natural := Item'Last;
Value : Integer;
J : Integer;
begin
for I in (First + 1)..Last loop
Value := Item(I);
J := I - 1;
while J in Item'range and then Item(J) > Value loop
Item(J + 1) := Item(J);
J := J - 1;
end loop;
Item(J + 1) := Value;
end loop;
end Insertion_Sort;
ALGOL 68
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))
abcdefghiijklmnopqrstuvwxyz big fjords vex quick waltz nymphALGOL 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.
-56 -1 0 0 2 3 9 34AppleScript
-- 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
{6, 11, 15, 22, 41, 45, 54, 59, 59, 60, 61, 64, 66, 73, 77, 77, 89, 91, 97, 100}
ARM Assembly
/* 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:
ldr r0,iAdrTableNumber @ address number table
mov r1,#0
mov r2,#NBELEMENTS @ number of élements
bl insertionSort
ldr r0,iAdrTableNumber @ address number table
bl displayTable
ldr r0,iAdrTableNumber @ address number table
mov r1,#NBELEMENTS @ number of élements
bl isSorted @ control sort
cmp r0,#1 @ sorted ?
beq 2f
ldr r0,iAdrszMessSortNok @ no !! error sort
bl affichageMess
b 100f
2: @ yes
ldr r0,iAdrszMessSortOk
bl affichageMess
100: @ standard end of the program
mov r0, #0 @ return code
mov r7, #EXIT @ request to exit program
svc #0 @ perform the system call
iAdrsMessValeur: .int sMessValeur
iAdrszCarriageReturn: .int szCarriageReturn
iAdrsMessResult: .int sMessResult
iAdrTableNumber: .int TableNumber
iAdrszMessSortOk: .int szMessSortOk
iAdrszMessSortNok: .int szMessSortNok
/******************************************************************/
/* control sorted table */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the number of elements > 0 */
/* r0 return 0 if not sorted 1 if sorted */
isSorted:
push {r2-r4,lr} @ save registers
mov r2,#0
ldr r4,[r0,r2,lsl #2]
1:
add r2,#1
cmp r2,r1
movge r0,#1
bge 100f
ldr r3,[r0,r2, lsl #2]
cmp r3,r4
movlt r0,#0
blt 100f
mov r4,r3
b 1b
100:
pop {r2-r4,lr}
bx lr @ return
/******************************************************************/
/* 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
ldr r0,iAdrsMessResult
bl affichageMess @ display message
add r3,#1
cmp r3,#NBELEMENTS - 1
ble 1b
ldr r0,iAdrszCarriageReturn
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]
add r2,#1
add r4,#1
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 0xCCCCCCCDArturo
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]
1 2 3 4 5 6 7 8 9ATS 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
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 9For 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}
{p_arr : addr}
.<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
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 90For 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$lt : (&a, &a) -<> bool (* Arguments by reference. *)
extern fn {a : vt@ype}
insertion_sort
{n : int}
(lst : list_vt (a, n))
:<!wrt> list_vt (a, n)
(*------------------------------------------------------------------*)
(* Implementation *)
(* This implementation is based on the insertion-sort part of the
mergesort code of the ATS prelude.
Unlike the prelude, however, I build the sorted list in reverse
order. Building the list in reverse order actually makes the
implementation more like that for an array. *)
(* Some convenient shorthands. *)
#define NIL list_vt_nil ()
#define :: list_vt_cons
(* Inserting in reverse order minimizes the work for a list already
nearly sorted, or for stably sorting a list whose entries often
have equal keys. *)
fun {a : vt@ype}
insert_reverse
{m : nat}
{p_xnode : addr}
{p_x : addr}
{p_xs : addr}
.<m>.
(pf_x : a @ p_x,
pf_xs : list_vt (a, 0)? @ p_xs |
dst : &list_vt (a, m) >> list_vt (a, m + 1),
(* list_vt_cons_unfold is a viewtype created by the
unfolding of a list_vt_cons (our :: operator). *)
xnode : list_vt_cons_unfold (p_xnode, p_x, p_xs),
p_x : ptr p_x,
p_xs : ptr p_xs)
:<!wrt> void =
(* dst is some tail of the current (reverse-order) destination list.
xnode is a viewtype for the current node in the source list.
p_x points to the node's CAR.
p_xs points to the node's CDR. *)
case+ dst of
| @ (y :: ys) =>
if insertion_sort$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 |
dst, src, addr@ x, addr@ 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
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 90AutoHotkey
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
original 10 8 20 100 -3 12 4 -5 32 0 1 sorted: -5 -3 0 1 4 8 10 12 20 32 100B4X
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
23 34 54 123 123 543BASIC
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
1486 ; 9488 ; 9894 ; 17479 ; 18989 ; 23119 ; 23233 ; 24927 ; 25386 ; 26689 ;GW-BASIC
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
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 530BBC 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
-31 0 1 2 2 4 65 83 99 782Commodore 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: RETURNIS-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 DEFBASIC256
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 subroutineBCPL
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)
$)
Before: 4 65 2 -31 0 99 2 83 782 1 After: -31 0 1 2 2 4 65 83 99 782Binary Lambda Calculus
As documented at https://github.com/tromp/AIT/blob/master/lists/sort.lam, the 55 byte BLC program
15 46 84 06 05 46 81 60 15 fb ec 2f 80 01 5b f9 7f 0b 7e f7 2f ec 2d fb 80 56 05 fd 85 bb 76 11 5d 50 5c 00 8b f3 ff 04 af fe 60 de 57 ff 30 5d 81 ff c2 dd 9a 28 20
sorts a list of bitstrings, such as integers of a fixed bit-width, lexicographically.
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;
}
4 65 2 -31 0 99 2 83 782 1 -31 0 1 2 2 4 65 83 99 782C#
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";
}
-199 -52 2 3 33 56 99 100 177 200Clojure
(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
Before: 7 -5 0 2 99 16 4 20 47 19 After: -5 0 2 4 7 16 19 20 47 99CMake
# 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)
set(answer)
foreach(i RANGE 1 ${last})
list(APPEND answer ${ARGV${i}})
endforeach(i)
set("${var}" "${answer}" PARENT_SCOPE)
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
>>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.
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 arrayCommon 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)))))
(defgeneric nsrt (sequence predicate))
(defmethod nsrt ((sequence sequence) predicate)
(loop :for i :from 1 :below (length sequence)
:do (loop :for j :from i :downto 1
:do (let ((current (elt sequence j))
(previous (elt sequence (1- j))))
(when (funcall predicate current previous)
(rotatef (elt sequence j)
(elt sequence (1- j))))))
:finally (return sequence)))
;; (nsrt "adfcghjiklmnoprbtuvqewysxz" #'char<)
;; => "abcdefghijklmnopqrstuvwxyz"
;;
;; (nsrt '(who the hecc do you think i am?)
;; (lambda (x y)
;; (string< (nsrt (format nil "~a" x) #'char<)
;; (nsrt (format nil "~a" y) #'char<))))
;; => (AM? HECC DO THE THINK WHO I YOU)
;;
;; (nsrt (loop :for i :from 1 :to 1000 :collect (random i))
;; #'<)
;; => [not printed but works, try it!]
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 returnD
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;
}
[2, 4, 11, 17, 19, 24, 25, 28, 44, 46]Higher Level Version
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, $)];
foreach (ref x; arr3)
x = uniform(-6, 6);
arr3.insertionSort;
assert(arr3.isSorted);
}
}
arr1 sorted: [2, 4, 11, 17, 19, 24, 25, 28, 44, 46] arr2 sorted: [2, 4, 11, 17, 19, 24, 25, 28, 44, 46]Dart
insertSort(List<int> array){
for(int i = 1; i < array.length; i++){
int value = array[i];
int j = i - 1;
while(j >= 0 && array[j] > value){
array[j + 1] = array[j];
j = j - 1;
}
array[j + 1] = value;
}
return array;
}
void main() {
List<int> a = insertSort([10, 3, 11, 15, 19, 1]);
print('${a}');
}
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;
Readln;
end.
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 86String 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 ]
sort data[]
print data[]
[ 4 5 26 27 29 44 55 72 77 92 ]Eiffel
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 6.x :
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());
}
before:3,9,4,6,8,1,7,2,5 after :1,2,3,4,5,6,7,8,9Elixir
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) #'>)
(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
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
4 65 2 -31 0 99 2 83 782 1 -31 0 1 2 2 4 65 83 99 782Euphoria
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})
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 .
{ 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.
: 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
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
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 7FutureBasic
Insertion Sort in FutureBasic
//
// Insertion Sort
// Using FutureBasic 7.0.34, July 2025 R.W
//
_maxDim = 99 // size of array
dim theArray(_maxDim) as Int
dim x as Int
// sorts array "theArray"
// in ascending order
void local function insertionSort(arr(_maxDim) as Int, siz as Int)
dim as Int j,k,s
for x = 0 to siz
j = x - 1
s = 1
k = arr(x)
while (j => 0) && (s == 1)
arr(j + 1) = arr(j)
s = 0
if arr(j) > k
arr(j + 1) = arr(j)
j--
s = 1
end if
wend
arr(j + 1) = k
next x
end fn
//
//
// main
//
window 1,@"Insertion Sort"
// load array with random 0-99
for x = 0 to 99
theArray(x) = rnd(100)-1
next x
print "Unsorted:"
for x = 1 to 100
print theArray(x-1);
if x MOD 20 then print "-"; else print
next x
print
fn insertionSort(@theArray(0),99)
print "Sorted:"
for x = 1 to 100
print theArray(x-1);
if x MOD 20 then print "-"; else print
next x
handleevents
Unsorted: 73-63-73-58-77-23-55-36-4-49-14-14-48-23-90-60-50-47-36-25 28-57-62-62-16-25-39-10-51-30-14-90-1-2-60-17-77-67-0-80 63-6-33-36-78-3-65-16-79-40-69-86-78-24-71-7-33-80-7-64 52-49-32-30-20-80-70-74-42-33-17-15-83-91-38-2-1-30-15-66 96-87-62-84-80-34-98-97-20-91-47-23-95-80-85-29-89-97-57-66 Sorted: 0-1-1-2-2-3-4-6-7-7-10-14-14-14-15-15-16-16-17-17 20-20-23-23-23-24-25-25-28-29-30-30-30-32-33-33-33-34-36-36 36-38-39-40-42-47-47-48-49-49-50-51-52-55-57-57-58-60-60-62 62-62-63-63-64-65-66-66-67-69-70-71-73-73-74-77-77-78-78-79 80-80-80-80-80-83-84-85-86-87-89-90-90-91-91-95-96-97-97-98GAP
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)
}
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)
}
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)
}
unsorted: [31 41 59 26 53 58 97 93 23 84] sorted! [23 26 31 41 53 58 59 84 93 97]Golfscript
{{.@.@<@@\)>}\+~\++}:at;
{:A ,,
{.A=:V;(
{.-1>1$A=V>&}{
A 1$)A 3$=at:A;(
}while
)A\V at:A;
}/
}:sort;
"[7, 6, 5, 9, 8, 4, 3, 1, 2, 0]" ','-~ sort
A `
[0 1 2 3 4 5 6 7 8 9]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]))
..................................................................................................................................................................[4, 12, 14, 23, 24, 24, 31, 35, 38, 46, 51, 57, 57, 58, 76, 78, 89, 92, 95, 97, 99] ...............................................................................................................................................................[0, 1, 4, 5, 7, 8, 12, 14, 18, 20, 31, 33, 44, 62, 70, 73, 75, 76, 78, 81, 82, 84, 88]Haskell
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);
}
}
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
ENDDOIcon 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.
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
🌐‹https://rosettacode.org/wiki/Sorting_algorithms/Insertion_sort#Haskell›
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 120Java
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)
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
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
[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)
x = [-1.24011, -1.23848, 0.176698, -1.01986, 0.830544] insertionsort!(x) = [-1.24011, -1.23848, -1.01986, 0.176698, 0.830544]Kotlin Standard solution, using int array
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)
}
Unsorted: [5, 2, 3, 17, 12, 1, 8, 3, 4, 9, 7] Sorted: [1, 2, 3, 3, 4, 5, 7, 8, 9, 12, 17]Alternative solution, optimized using binary search
Similar concept to C++ solution. This solution uses a hand-written algorithm to find the upper bound as there is no Kotlin/Java equivalent to C++'s `std::upper_bound`. Thus this function performs a stable sort (unlike the Java solution which uses `binarySearch`). It uses `copyInto` which is a faster way of shifting the elements of an array before inserting an element, compared to assigning individual array elements in a loop.
fun <T : Comparable<T>> Array<T>.insertionSort() {
for (i in 1..lastIndex) {
val currentElement = this[i]
var low = 0
var high = i - 1
while (low <= high) {
val mid = low + (high - low) / 2
if (this[mid] <= currentElement)
low = mid + 1
else
high = mid - 1
}
copyInto(this, low + 1, low, i)
this[low] = currentElement
}
}
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" " )"
( -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
returnLua
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;
[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
]
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
Before: [4,65,2,-31,0,99,2,83,782,1] After: [-31,0,1,2,2,4,65,83,99,782]ML mLite
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 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
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 endNemerle
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)
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 WashingtonNim
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
@[-31, 0, 2, 2, 4, 65, 83, 99, 782]Oberon-2
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.
4 65 2 -31 0 99 2 83 782 1 -31 0 1 2 2 4 65 83 99 782Objeck
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
1 2 3 4 5 6 7 8 9Oforth
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 ;
>[ 4, 65, 2, -31, 0, 99, 2, 83, 782, 1 ] insertionSort . [-31, 0, 1, 2, 2, 4, 65, 83, 99, 782] ok >ooRexx
/* 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
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
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.
[-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] = $k;
}
return @list;
}
my @a = insertion_sort(4, 65, 2, -31, 0, 99, 83, 782, 1);
print "@a\n";
-31 0 1 2 4 65 83 99 782Phix
Copy of Euphoria
function insertion_sort(sequence s)
object temp
integer j
for i=2 to length(s) do
temp = s[i]
j = i-1
while j>=1 and s[j]>temp do
s[j+1] = s[j]
j -= 1
end while
s[j+1] = temp
end for
return s
end function
constant s = {4, 15, "delta", 2, -31, 0, "alpha", 19, "gamma", 2, 13, "beta", 782, 1}
puts(1,"Before: ") ?s
puts(1,"After: ") ?insertion_sort(s)
Before: {4,15,"delta",2,-31,0,"alpha",19,"gamma",2,13,"beta",782,1}
After: {-31,0,1,2,2,4,13,15,19,782,"alpha","beta","delta","gamma"}
PHP
function insertionSort(&$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(',',$arr);
1,2,3,4,6,7,8,9PicoLisp
(de insertionSort (Lst)
(for (I (cdr Lst) I (cdr I))
(for (J Lst (n== J I) (cdr J))
(T (> (car J) (car I))
(rot J (offset I J)) ) ) )
Lst )
: (insertionSort (5 3 1 7 4 1 1 20)) -> (1 1 1 3 4 5 7 20)PL/I
insert_sort: proc(array);
dcl array(*) fixed bin(31);
dcl (i,j,tmp,h,l) fixed bin(31);
l = lbound(array, 1);
h = hbound(array, 1);
do i = l + 1 to h;
tmp = array(i);
do j = i - 1 by -1 while(j > l - 1 & array(j) > tmp);
array(j + 1) = array(j);
end;
array(j + 1) = tmp;
end;
end insert_sort;PL/M
100H:
/* INSERTION SORT ON 16-BIT INTEGERS */
INSERTION$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
0 1 2 2 3 4 8 31 65 99 782PowerShell
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 ","
1,2,3,4,6,7,8,9Prolog
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] ? % yesFunctional 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;
input = 22 7 2 -5 8 4 output = -5 2 4 7 8 22Rascal
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;
}
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 SubRebol
; 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]
[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]
Refal
$ENTRY Go {
, 7 6 5 9 8 4 3 1 2 0: e.Arr
= <Prout e.Arr>
<Prout <Sort e.Arr>>;
};
Sort {
(e.S) = e.S;
(e.S) s.I e.X = <Sort (<Insert s.I e.S>) e.X>;
e.X = <Sort () e.X>;
};
Insert {
s.N = s.N;
s.N s.M e.X, <Compare s.N s.M>: {
'+' = s.M <Insert s.N e.X>;
s.C = s.N s.M e.X;
};
};
7 6 5 9 8 4 3 1 2 0 0 1 2 3 4 5 6 7 8 9REXX
/*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
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 blistRPL
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.
≪ '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
[ 1 4 -1 0 3 7 4 8 20 -6 ] ISORT
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
?S-BASIC
$constant NUM_ITEMS = 10
dim integer items(NUM_ITEMS)
var i, j, t = integer
rem - create a randomly-ordered list of numbers
for i = 1 to NUM_ITEMS
items(i) = int(rnd(1) * 100) + 1
next i
rem - show unsorted list
print "Unsorted list: ";
for i = 1 to NUM_ITEMS
print items(i);
next i
print
rem - sort the list
for i = 1 to NUM_ITEMS
j = i
while j > 1 and items(j-1) > items(j) do
begin
t = items(j)
items(j) = items(j-1)
items(j-1) = t
j = j - 1
end
next i
rem - show the sorted list
print "Sorted list : ";
for i = 1 to NUM_ITEMS
print items(i);
next i
end
Unsorted list: 4 10 31 96 1 1 3 8 24 73 Sorted list : 1 1 3 4 8 10 24 31 73 96Scala
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]
Sidefclass 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_sortSNOBOL4
* 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) endStata
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
}
}
endSwift
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 $m
}
puts [insertionsort {8 6 4 2 1 3 5 7 9}] ;# => 1 2 3 4 5 6 7 8 9TI-83 BASIC
Input into L1, run prgmSORTINS, output in L2.
:"INSERTION" :L1→L2 :0→A :Lbl L :A+1→A :A→B :While B>0 :If L2(B)≤L2(B+1) :Goto B :L2(B)→C :L2(B+1)→L2(B) :C→L2(B+1) :B-1→B :End :Lbl B :If A<(dim(L2)-1) :Goto L :DelVar A :DelVar B :DelVar C :ReturnuBasic/4tH
PRINT "Insertion sort:"
n = FUNC (_InitArray)
PROC _ShowArray (n)
PROC _Insertionsort (n)
PROC _ShowArray (n)
PRINT
END
_Insertionsort PARAM (1) ' Insertion sort
LOCAL (3)
FOR b@ = 1 TO a@-1
c@ = @(b@)
d@ = b@
DO WHILE (d@>0) * (c@ < @(ABS(d@-1)))
@(d@) = @(d@-1)
d@ = d@ - 1
LOOP
@(d@) = c@
NEXT
RETURN
_Swap PARAM(2) ' Swap two array elements
PUSH @(a@)
@(a@) = @(b@)
@(b@) = POP()
RETURN
_InitArray ' Init example array
PUSH 4, 65, 2, -31, 0, 99, 2, 83, 782, 1
FOR i = 0 TO 9
@(i) = POP()
NEXT
RETURN (i)
_ShowArray PARAM (1) ' Show array subroutine
FOR i = 0 TO a@-1
PRINT @(i),
NEXT
PRINT
RETURNUnixPipes
selectionsort() {
read a
test -n "$a" && ( selectionsort | sort -nm <(echo $a) -)
}
cat to.sort | selectionsortUrsala
#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>
<45,58,69,74,82,82,88,89,104,112>Vala
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);
}
-31 0 2 2 4 65 83 99 782VBA
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
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' gammaVBScript
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
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())
}
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 array = [ [4, 65, 2, -31, 0, 99, 2, 83, 782, 1], [7, 5, 2, 6, 1, 4, 2, 6, 3] ]
for (a in array) {
System.print("Before: %(a)")
insertionSort.call(a)
System.print("After : %(a)")
System.print()
}
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.
import "./sort" for Sort
var array = [ [4, 65, 2, -31, 0, 99, 2, 83, 782, 1], [7, 5, 2, 6, 1, 4, 2, 6, 3] ]
for (a in array) {
System.print("Before: %(a)")
Sort.insertion(a)
System.print("After : %(a)")
System.print()
}
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, ^ )];
]
-5 1 1 2 3 4 4 5 6 9Yabasic
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
endYorick
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();
L(-31,0,1,2,2,4,65,83,99,782)
L("big","fjords","nymph","quick","vex","waltz")
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