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{{task|Sorting Algorithms}} {{Sorting Algorithm}} {{wikipedia|Insertion sort}} {{omit from|GUISS}}
An [[O]](''n''<sup>2</sup>) 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]](''n''<sup>2</sup>) algorithm, its simplicity, low overhead, good locality of reference and efficiency make it a good choice in two cases:
(i) small ''n'',
(ii) as the final finishing-off algorithm for [[O]](''n'' log''n'') algorithms such as [[Merge sort|mergesort]] and [[quicksort]].
The algorithm is as follows (from [[wp:Insertion_sort#Algorithm|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.
360 Assembly
{{trans|PL/I}} These programs use two ASSIST macros (XDECO, XPRNT) to keep the code as short as possible.
Basic
* Insertion sort 16/06/2016
INSSORT CSECT
USING INSSORT,R13 base register
B 72(R15) skip savearea
DC 17F'0' savearea
STM R14,R12,12(R13) prolog
ST R13,4(R15) "
ST R15,8(R13) "
LR R13,R15 "
LA R6,2 i=2
LA R9,A+L'A @a(2)
LOOPI C R6,N do i=2 to n
BH ELOOPI leave i
L R2,0(R9) a(i)
ST R2,V v=a(i)
LR R7,R6 j=i
BCTR R7,0 j=i-1
LR R8,R9 @a(i)
S R8,=A(L'A) @a(j)
LOOPJ LTR R7,R7 do j=i-1 to 1 by -1 while j>0
BNH ELOOPJ leave j
L R2,0(R8) a(j)
C R2,V a(j)>v
BNH ELOOPJ leave j
MVC L'A(L'A,R8),0(R8) a(j+1)=a(j)
BCTR R7,0 j=j-1
S R8,=A(L'A) @a(j)
B LOOPJ next j
ELOOPJ MVC L'A(L'A,R8),V a(j+1)=v;
LA R6,1(R6) i=i+1
LA R9,L'A(R9) @a(i)
B LOOPI next i
ELOOPI LA R9,PG pgi=0
LA R6,1 i=1
LA R8,A @a(1)
LOOPXI C R6,N do i=1 to n
BH ELOOPXI leave i
L R1,0(R8) a(i)
XDECO R1,XDEC edit a(i)
MVC 0(4,R9),XDEC+8 output a(i)
LA R9,4(R9) pgi=pgi+1
LA R6,1(R6) i=i+1
LA R8,L'A(R8) @a(i)
B LOOPXI next i
ELOOPXI XPRNT PG,L'PG print buffer
L R13,4(0,R13) epilog
LM R14,R12,12(R13) "
XR R15,R15 "
BR R14 exit
A DC F'4',F'65',F'2',F'-31',F'0',F'99',F'2',F'83',F'782',F'1'
DC F'45',F'82',F'69',F'82',F'104',F'58',F'88',F'112',F'89',F'74'
V DS F variable
N DC A((V-A)/L'A) n=hbound(a)
PG DC CL80' ' buffer
XDEC DS CL12 for xdeco
YREGS symbolics for registers
END INSSORT
{{out}}
-31 0 1 2 2 4 45 58 65 69 74 82 82 83 88 89 99 104 112 782
Assembler Structured Macros
No harmful gotos [:)Dijkstra], no labels. It's cleaner, but is it clearer?
* Insertion sort 16/06/2016
INSSORTS CSECT
USING INSSORTS,R13 base register
B 72(R15) skip savearea
DC 17F'0' savearea
STM R14,R12,12(R13) prolog
ST R13,4(R15) "
ST R15,8(R13) "
LR R13,R15 "
LA R6,2 i=2
LA R9,A+L'A @a(2)
DO WHILE=(C,R6,LE,N) do while i<=n
L R2,0(R9) a(i)
ST R2,V v=a(i)
LR R7,R6 j=i
BCTR R7,0 j=i-1
LR R8,R9 @a(i)
S R8,=A(L'A) @a(j)
L R2,0(R8) a(j)
DO WHILE=(C,R7,GT,0,AND,C,R2,GT,V) do while j>0 & a(j)>v
MVC L'A(L'A,R8),0(R8) a(j+1)=a(j)
BCTR R7,0 j=j-1
S R8,=A(L'A) @a(j)
L R2,0(R8) a(j)
ENDDO , next j
MVC L'A(L'A,R8),V a(j+1)=v;
LA R6,1(R6) i=i+1
LA R9,L'A(R9) @a(i)
ENDDO , next i
LA R9,PG pgi=0
LA R6,1 i=1
LA R8,A @a(1)
DO WHILE=(C,R6,LE,N) do while i<=n
L R1,0(R8) a(i)
XDECO R1,XDEC edit a(i)
MVC 0(4,R9),XDEC+8 output a(i)
LA R9,4(R9) pgi=pgi+1
LA R6,1(R6) i=i+1
LA R8,L'A(R8) @a(i)
ENDDO , next i
XPRNT PG,L'PG print buffer
L R13,4(0,R13) epilog
LM R14,R12,12(R13) "
XR R15,R15 "
BR R14 exit
A DC F'4',F'65',F'2',F'-31',F'0',F'99',F'2',F'83',F'782',F'1'
DC F'45',F'82',F'69',F'82',F'104',F'58',F'88',F'112',F'89',F'74'
V DS F variable
N DC A((V-A)/L'A) n=hbound(a)
PG DC CL80' ' buffer
XDEC DS CL12 for xdeco
YREGS symbolics for registers
END INSSORTS
{{out}} Same as previous
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)))))
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
{{trans|Ada}}
{{works with|ALGOL 68|Revision 1 - no extensions to language used}}
{{works with|ALGOL 68G|Any - tested with release [http://sourceforge.net/projects/algol68/files/algol68g/algol68g-1.18.0/algol68g-1.18.0-9h.tiny.el5.centos.fc11.i386.rpm/download 1.18.0-9h.tiny]}}
{{works with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release [http://sourceforge.net/projects/algol68/files/algol68toc/algol68toc-1.8.8d/algol68toc-1.8-8d.fc9.i386.rpm/download 1.8-8d]}}
MODE DATA = REF CHAR;
PROC in place insertion sort = (REF[]DATA item)VOID:
BEGIN
INT first := LWB item;
INT last := UPB item;
INT j;
DATA value;
FOR i FROM first + 1 TO last DO
value := item[i];
j := i - 1;
# WHILE j >= LWB item AND j <= UPB item ANDF item[j] > value DO // example of ANDF extension #
WHILE ( j >= LWB item AND j <= UPB item | item[j]>value | FALSE ) DO # no extension! #
item[j + 1] := item[j];
j -:= 1
OD;
item[j + 1] := value
OD
END # in place insertion sort #;
[32]CHAR data := "big fjords vex quick waltz nymph";
[UPB data]DATA ref data; FOR i TO UPB data DO ref data[i] := data[i] OD;
in place insertion sort(ref data);
FOR i TO UPB ref data DO print(ref data[i]) OD; print(new line);
print((data))
{{out}}
abcdefghiijklmnopqrstuvwxyz
big fjords vex quick waltz nymph
ALGOL W
External in-place insertion sort routine for integers. From the pseudo code but with variable bounds.
% insertion sorts in-place the array A. As Algol W procedures can't find the bounds %
% of an array parameter, the lower and upper bounds must be specified in lb and ub %
procedure insertionSortI ( integer array A ( * ); integer value lb, ub ) ;
for i := lb + 1 until ub do begin
integer v, j;
v := A( i );
j := i - 1;
while j >= lb and A( j ) > v do begin
A( j + 1 ) := A( j );
j := j - 1
end while_j_ge_0_and_Aj_gt_v ;
A( j + 1 ) := v
end insertionSortI ;
Test the insertionSortI procedure.
begin
% external in-place insertion sort procedure %
procedure insertionSortI ( integer array A( * ); integer value lb, ub ) ;
algol "ISORTI" ;
integer array d ( 1 :: 8 );
integer p;
p := 1;
for i := 34, 2, -1, 0, 0, 9, -56, 3 do begin
d( p ) := i;
p := p + 1
end for_i ;
insertionSortI( d, 1, 8 );
write( i_w := 1, d( 1 ) );
for i := 2 until 8 do writeon( i_w := 1, d( i ) )
end.
{{out}}
-56 -1 0 0 2 3 9 34
ARM Assembly
{{works with|as|Raspberry Pi}}
/* ARM assembly Raspberry PI */
/* program insertionSort.s */
/* look Pseudocode begin this task */
/************************************/
/* Constantes */
/************************************/
.equ STDOUT, 1 @ Linux output console
.equ EXIT, 1 @ Linux syscall
.equ WRITE, 4 @ Linux syscall
/*********************************/
/* Initialized data */
/*********************************/
.data
szMessSortOk: .asciz "Table sorted.\n"
szMessSortNok: .asciz "Table not sorted !!!!!.\n"
sMessResult: .ascii "Value : "
sMessValeur: .fill 11, 1, ' ' @ size => 11
szCarriageReturn: .asciz "\n"
.align 4
iGraine: .int 123456
.equ NBELEMENTS, 10
#TableNumber: .int 1,3,6,2,5,9,10,8,4,7
TableNumber: .int 10,9,8,7,6,5,4,3,2,1
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: @ entry of program
1:
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 0xCCCCCCCD
AutoHotkey
contributed by Laszlo on the ahk [http://www.autohotkey.com/forum/post-276481.html#276481 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]
}
}
BASIC
{{trans|REALbasic}} {{works with|QBasic}}
This version should work on any BASIC that can accept arrays as function arguments.
DECLARE SUB InsertionSort (theList() AS INTEGER)
DIM n(10) AS INTEGER, L AS INTEGER, o AS STRING
FOR L = 0 TO 10
n(L) = INT(RND * 32768)
NEXT
InsertionSort n()
FOR L = 1 TO 10
PRINT n(L); ";";
NEXT
SUB InsertionSort (theList() AS INTEGER)
DIM insertionElementIndex AS INTEGER
FOR insertionElementIndex = 1 TO UBOUND(theList)
DIM insertionElement AS INTEGER
insertionElement = theList(insertionElementIndex)
DIM j AS INTEGER
j = insertionElementIndex - 1
DO WHILE (j >= 0)
'necessary for BASICs without short-circuit evaluation
IF (insertionElement < theList(j)) THEN
theList(j + 1) = theList(j)
j = j - 1
ELSE
EXIT DO
END IF
LOOP
theList(j + 1) = insertionElement
NEXT
END SUB
{{out}}
1486 ; 9488 ; 9894 ; 17479 ; 18989 ; 23119 ; 23233 ; 24927 ; 25386 ; 26689 ;
=
BBC BASIC
= Note that the array index is assumed to start at zero.
DIM test(9)
test() = 4, 65, 2, -31, 0, 99, 2, 83, 782, 1
PROCinsertionsort(test(), 10)
FOR i% = 0 TO 9
PRINT test(i%) ;
NEXT
PRINT
END
DEF PROCinsertionsort(a(), n%)
LOCAL i%, j%, t
FOR i% = 1 TO n%-1
t = a(i%)
j% = i%
WHILE j%>0 AND t<a(ABS(j%-1))
a(j%) = a(j%-1)
j% -= 1
ENDWHILE
a(j%) = t
NEXT
ENDPROC
{{out}}
-31 0 1 2 2 4 65 83 99 782
=
Commodore BASIC
=
10 DIM A(10): N=9
11 REM GENERATE SOME RANDOM NUMBERS AND PRINT THEM
12 FOR I=0 TO N: A(I)=INT(RND(1)*10)+1: NEXT: GOSUB 50
20 FOR J=1 TO N:KEY=A(J): I=J-1: GOSUB 30: A(I+1)=KEY: NEXT: GOSUB 50: END
30 IFI=-1 THEN RETURN
31 IFA(I)>KEY THEN A(I+1)=A(I):I=I-1: GOTO 30
32 RETURN
50 PRINT: FOR I=0 TO N: PRINTA(I): NEXT: RETURN
==={{header|IS-BASIC}}===
## C
```c
#include <stdio.h>
void insertion_sort(int *a, int n) {
for(size_t i = 1; i < n; ++i) {
int tmp = a[i];
size_t j = i;
while(j > 0 && tmp < a[j - 1]) {
a[j] = a[j - 1];
--j;
}
a[j] = tmp;
}
}
int main () {
int a[] = {4, 65, 2, -31, 0, 99, 2, 83, 782, 1};
int n = sizeof a / sizeof a[0];
int i;
for (i = 0; i < n; i++)
printf("%d%s", a[i], i == n - 1 ? "\n" : " ");
insertion_sort(a, n);
for (i = 0; i < n; i++)
printf("%d%s", a[i], i == n - 1 ? "\n" : " ");
return 0;
}
{{out}}
4 65 2 -31 0 99 2 83 782 1
-31 0 1 2 2 4 65 83 99 782
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>
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);
}
}
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));
copy(std::begin(a), std::end(a), std::ostream_iterator<int>(std::cout, " "));
std::cout << "\n";
}
{{out}}
-199 -52 2 3 33 56 99 100 177 200
C#
namespace Sort {
using System;
static class InsertionSort<T> where T : IComparable {
public static void Sort(T[] entries) {
Sort(entries, 0, entries.Length - 1);
}
public static void Sort(T[] entries, Int32 first, Int32 last) {
for (var i = first + 1; i <= last; i++) {
var entry = entries[i];
var j = i;
while (j > first && entries[j - 1].CompareTo(entry) > 0)
entries[j] = entries[--j];
entries[j] = entry;
}
}
}
}
'''Example''':
using Sort;
using System;
class Program {
static void Main(String[] args) {
var entries = new Int32[] { 3, 9, 4, 6, 8, 1, 7, 2, 5 };
InsertionSort<Int32>.Sort(entries);
Console.WriteLine(String.Join(" ", entries));
}
}
Clojure
(defn insertion-sort [coll]
(reduce (fn [result input]
(let [[less more] (split-with #(< % input) result)]
(concat less [input] more)))
[]
coll))
Translated from the Haskell example:
(defn in-sort! [data]
(letfn [(insert ([raw x](insert [] raw x))
([sorted [y & raw] x]
(if (nil? y) (conj sorted x)
(if (<= x y ) (concat sorted [x,y] raw)
(recur (conj sorted y) raw x )))))]
(reduce insert [] data)))
;Usage:(in-sort! [6,8,5,9,3,2,1,4,7])
;Returns: [1 2 3 4 5 6 7 8 9]
CMake
# insertion_sort(var [value1 value2...]) sorts a list of integers.
function(insertion_sort var)
math(EXPR last "${ARGC} - 1") # Sort ARGV[1..last].
foreach(i RANGE 1 ${last})
# Extend the sorted area to ARGV[1..i].
set(b ${i})
set(v ${ARGV${b}})
# Insert v == ARGV[b] in sorted order. While b > 1, check if b is
# too high, then decrement b. After loop, set ARGV[b] = v.
while(b GREATER 1)
math(EXPR a "${b} - 1")
set(u ${ARGV${a}})
# Now u == ARGV[a]. Pretend v == ARGV[b]. Compare.
if(u GREATER ${v})
# ARGV[a] and ARGV[b] are in wrong order. Fix by moving ARGV[a]
# to ARGV[b], making room for later insertion of v.
set(ARGV${b} ${u})
else()
break()
endif()
math(EXPR b "${b} - 1")
endwhile()
set(ARGV${b} ${v})
endforeach(i)
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 {{works with|GnuCOBOL}}
>>SOURCE FORMAT FREE
*> This code is dedicated to the public domain
*> This is GNUCOBOL 2.0
identification division.
program-id. insertionsort.
environment division.
configuration section.
repository. function all intrinsic.
data division.
working-storage section.
01 filler.
03 a pic 99.
03 a-lim pic 99 value 10.
03 array occurs 10 pic 99.
01 filler.
03 s pic 99.
03 o pic 99.
03 o1 pic 99.
03 sorted-len pic 99.
03 sorted-lim pic 99 value 10.
03 sorted-array occurs 10 pic 99.
procedure division.
start-insertionsort.
*> fill the array
compute a = random(seconds-past-midnight)
perform varying a from 1 by 1 until a > a-lim
compute array(a) = random() * 100
end-perform
*> display the array
perform varying a from 1 by 1 until a > a-lim
display space array(a) with no advancing
end-perform
display space 'initial array'
*> sort the array
move 0 to sorted-len
perform varying a from 1 by 1 until a > a-lim
*> find the insertion point
perform varying s from 1 by 1
until s > sorted-len
or array(a) <= sorted-array(s)
continue
end-perform
*>open the insertion point
perform varying o from sorted-len by -1
until o < s
compute o1 = o + 1
move sorted-array(o) to sorted-array(o1)
end-perform
*> move the array-entry to the insertion point
move array(a) to sorted-array(s)
add 1 to sorted-len
end-perform
*> display the sorted array
perform varying s from 1 by 1 until s > sorted-lim
display space sorted-array(s) with no advancing
end-perform
display space 'sorted array'
stop run
.
end program insertionsort.
{{out}}
prompt$ cobc -xj insertionsort.cob
89 04 86 32 65 62 83 75 24 69 initial array
04 24 32 62 65 69 75 83 86 89 sorted array
Common Lisp
(defun span (predicate list)
(let ((tail (member-if-not predicate list)))
(values (ldiff list tail) tail)))
(defun less-than (x)
(lambda (y) (< y x)))
(defun insert (list elt)
(multiple-value-bind (left right) (span (less-than elt) list)
(append left (list elt) right)))
(defun insertion-sort (list)
(reduce #'insert list :initial-value nil))
(defun insertion-sort (sequence &optional (predicate #'<))
(if (cdr sequence)
(insert (car sequence) ;; insert the current item into
(insertion-sort (cdr sequence) ;; the already-sorted
predicate) ;; remainder of the list
predicate)
sequence)) ; a list of one element is already sorted
(defun insert (item sequence predicate)
(cond ((null sequence) (list item))
((funcall (complement predicate) ;; if the first element of the list
(car sequence) ;; isn't better than the item,
item) ;; cons the item onto
(cons item sequence)) ;; the front of the list
(t (cons (car sequence) ;; otherwise cons the first element onto the front of
(insert item ;; the list of the item sorted with the rest of the list
(cdr sequence)
predicate)))))
D
void insertionSort(T)(T[] data) pure nothrow @safe @nogc {
foreach (immutable i, value; data[1 .. $]) {
auto j = i + 1;
for ( ; j > 0 && value < data[j - 1]; j--)
data[j] = data[j - 1];
data[j] = value;
}
}
void main() {
import std.stdio;
auto items = [28, 44, 46, 24, 19, 2, 17, 11, 25, 4];
items.insertionSort;
items.writeln;
}
{{out}}
[2, 4, 11, 17, 19, 24, 25, 28, 44, 46]
Higher Level Version
{{trans|C++}}
import std.stdio, std.range, std.algorithm, std.traits;
void insertionSort(R)(R arr)
if (hasLength!R && isRandomAccessRange!R && hasSlicing!R) {
foreach (immutable i; 1 .. arr.length)
bringToFront(arr[0 .. i].assumeSorted.upperBound(arr[i]), arr[i .. i + 1]);
}
void main() {
import std.random, std.container;
auto arr1 = [28, 44, 46, 24, 19, 2, 17, 11, 25, 4];
arr1.insertionSort;
assert(arr1.isSorted);
writeln("arr1 sorted: ", arr1);
auto arr2 = Array!int([28, 44, 46, 24, 19, 2, 17, 11, 25, 4]);
arr2[].insertionSort;
assert(arr2[].isSorted);
writeln("arr2 sorted: ", arr2[]);
// Random data test.
int[10] buf;
foreach (immutable _; 0 .. 100_000) {
auto arr3 = buf[0 .. uniform(0, $)];
foreach (ref x; arr3)
x = uniform(-6, 6);
arr3.insertionSort;
assert(arr3.isSorted);
}
}
{{out}}
arr1 sorted: [2, 4, 11, 17, 19, 24, 25, 28, 44, 46]
arr2 sorted: [2, 4, 11, 17, 19, 24, 25, 28, 44, 46]
Delphi
Array sort
Dynamic array is a 0-based array of variable length
Static array is an arbitrary-based array of fixed length
program TestInsertionSort;
{$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.
{{out}}
0 3 86 20 27 67 31 16 37 42 8 47 7 84 5 29
0 3 5 7 8 16 20 27 29 31 37 42 47 67 84 86
String sort
// string is 1-based variable-length array of Char
procedure InsertionSort(var S: string);
var
I, J, L: Integer;
Ch: Char;
begin
L:= Length(S);
for I:= 2 to L do begin
Ch:= S[I];
J:= I - 1;
while (J > 0) and (S[J] > Ch) do begin
S[J + 1]:= S[J];
Dec(J);
end;
S[J + 1]:= Ch;
end;
end;
// in : S = 'the quick brown fox jumps over the lazy dog'
// out: S = ' abcdeeefghhijklmnoooopqrrsttuuvwxyz'
E
{{lines too long|E}} 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
## Eiffel
{{works with|EiffelStudio|6.6 (with provisional loop syntax)}}
This solution is shown in the routine <code lang="eiffel">sort</code> of the class <code lang="eiffel">MY_SORTED_SET</code>.
For a more complete explanation of the Eiffel sort examples, see the [[Sorting algorithms/Bubble sort#Eiffel|Bubble sort]].
```eiffel
class
MY_SORTED_SET [G -> COMPARABLE]
inherit
TWO_WAY_SORTED_SET [G]
redefine
sort
end
create
make
feature
sort
-- Insertion sort
local
l_j: INTEGER
l_value: like item
do
across 2 |..| count as ii loop
from
l_j := ii.item - 1
l_value := Current.i_th (ii.item)
until
l_j < 1 or Current.i_th (l_j) <= l_value
loop
Current.i_th (l_j + 1) := Current.i_th (l_j)
l_j := l_j - 1
end
Current.i_th (l_j + 1) := l_value
end
end
end
Elena
ELENA 4.1 :
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());
}
{{out}}
before:3,9,4,6,8,1,7,2,5
after :1,2,3,4,5,6,7,8,9
Elixir
defmodule Sort do
def insert_sort(list) when is_list(list), do: insert_sort(list, [])
def insert_sort([], sorted), do: sorted
def insert_sort([h | t], sorted), do: insert_sort(t, insert(h, sorted))
defp insert(x, []), do: [x]
defp insert(x, sorted) when x < hd(sorted), do: [x | sorted]
defp insert(x, [h | t]), do: [h | insert(x, t)]
end
Example:
iex(10)> Sort.insert_sort([5,3,9,4,1,6,8,2,7])
[1, 2, 3, 4, 5, 6, 7, 8, 9]
Emacs Lisp
(defun min-or-max-of-2-numbers (n1 n2 rel)
"n1 and n2 are two numbers, rel can be '< or '> according to
what sort of sorting is wanted, this function returns the greater
or smaller number n1 or n2"
(cond
((eval (list rel n1 n2)) n1)
(t n2)))
(defun min-or-max-of-a-list (lon rel)
"lon is a list of numbers, rel is '< or '>, this fonction
returns the higher or lower number of the list"
(if (cdr lon)
(min-or-max-of-2-numbers (car lon)
(min-or-max-of-a-list (cdr lon) rel)
rel)
(car lon)))
(defun remove-number-from-list (n lon)
"lon is a list of numbers, n is a number belonging to the list,
this function returns the same list but the number n. If n is
present twice or more, it will be removed only once"
(if lon
(cond
((= (car lon) n) (cdr lon))
(t (cons (car lon) (remove-number-from-list n (cdr lon)))))
nil))
(defun sort-insertion (lon rel)
"lon is a list of numbers, rel can be '< or '>, this function
returns a list containing the same elements but which is sorted
according to rel"
(if lon
(cons (min-or-max-of-a-list lon rel)
(sort-insertion
(remove-number-from-list
(min-or-max-of-a-list lon rel)
lon)
rel))
nil))
;;; let's try it :
(sort-insertion (list 1 2 3 9 8 7 25 12 3 2 1) '>)
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:
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
{{out}}
4 65 2 -31 0 99 2 83 782 1
-31 0 1 2 2 4 65 83 99 782
Euphoria
function insertion_sort(sequence s)
object temp
integer j
for i = 2 to length(s) do
temp = s[i]
j = i-1
while j >= 1 and compare(s[j],temp) > 0 do
s[j+1] = s[j]
j -= 1
end while
s[j+1] = temp
end for
return s
end function
include misc.e
constant s = {4, 15, "delta", 2, -31, 0, "alfa", 19, "gamma", 2, 13, "beta", 782, 1}
puts(1,"Before: ")
pretty_print(1,s,{2})
puts(1,"\nAfter: ")
pretty_print(1,insertion_sort(s),{2})
{{out}}
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"
}
=={{header|F Sharp|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 []
Forth
: insert ( start end -- start )
dup @ >r ( r: v ) \ v = a[i]
begin
2dup < \ j>0
while
r@ over cell- @ < \ a[j-1] > v
while
cell- \ j--
dup @ over cell+ ! \ a[j] = a[j-1]
repeat then
r> swap ! ; \ a[j] = v
: sort ( array len -- )
1 ?do dup i cells + insert loop drop ;
create test 7 , 3 , 0 , 2 , 9 , 1 , 6 , 8 , 4 , 5 ,
test 10 sort
test 10 cells dump
Fortran
{{works with|Fortran|90 and later}}
subroutine sort(n, a)
implicit none
integer :: n, i, j
real :: a(n), x
do i = 2, n
x = a(i)
j = i - 1
do while (j >= 1)
if (a(j) <= x) exit
a(j + 1) = a(j)
j = j - 1
end do
a(j + 1) = x
end do
end subroutine
Alternate Fortran 77 version
This also could have a problem with the compound test always being fully evaluated, so...
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
Can't IF (J.EQ.0 .OR. A(J).LE.X) GO TO 20 in case both sides are ALWAYS evaluated.
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
{{out}}
unsort -7 -1 4 -6 5 2 1 -2 0 -5 -4 6 -3 7 3
sort -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
GAP
InsertionSort := function(L)
local n, i, j, x;
n := Length(L);
for i in [ 2 .. n ] do
x := L[i];
j := i - 1;
while j >= 1 and L[j] > x do
L[j + 1] := L[j];
j := j - 1;
od;
L[j + 1] := x;
od;
end;
s := "BFKRIMPOQACNESWUTXDGLVZHYJ";
InsertionSort(s);
s;
# "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
Go
package main
import "fmt"
func insertionSort(a []int) {
for i := 1; i < len(a); i++ {
value := a[i]
j := i - 1
for j >= 0 && a[j] > value {
a[j+1] = a[j]
j = j - 1
}
a[j+1] = value
}
}
func main() {
list := []int{31, 41, 59, 26, 53, 58, 97, 93, 23, 84}
fmt.Println("unsorted:", list)
insertionSort(list)
fmt.Println("sorted! ", list)
}
{{out}}
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)
}
{{out}}
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)
}
{{out}}
unsorted: [31 41 59 26 53 58 97 93 23 84]
sorted! [23 26 31 41 53 58 59 84 93 97]
Groovy
Solution:
def insertionSort = { list ->
def size = list.size()
(1..<size).each { i ->
def value = list[i]
def j = i - 1
for (; j >= 0 && list[j] > value; j--) {
print "."; list[j+1] = list[j]
}
print "."; list[j+1] = value
}
list
}
Test:
println (insertionSort([23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78,4]))
println (insertionSort([88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70,12,7,1]))
{{out}}
..................................................................................................................................................................[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]
HicEst
DO i = 2, LEN(A)
value = A(i)
j = i - 1
1 IF( j > 0 ) THEN
IF( A(j) > value ) THEN
A(j+1) = A(j)
j = j - 1
GOTO 1 ! no WHILE in HicEst
ENDIF
ENDIF
A(j+1) = value
ENDDO
=={{header|Icon}} and {{header|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 [[Sorting_algorithms/Bubble_sort#Icon| 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.
{{out|abbreviated}}
Sorting Demo using procedure insertionsort
on list : [ 3 14 1 5 9 2 6 3 ]
with op = &null: [ 1 2 3 3 5 6 9 14 ] (0 ms)
...
on string : "qwerty"
with op = &null: "eqrtwy" (0 ms)
Io
List do(
insertionSortInPlace := method(
for(j, 1, size - 1,
key := at(j)
i := j - 1
while(i >= 0 and at(i) > key,
atPut(i + 1, at(i))
i = i - 1
)
atPut(i + 1, key)
)
)
)
lst := list(7, 6, 5, 9, 8, 4, 3, 1, 2, 0)
lst insertionSortInPlace println # ==> list(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
A shorter, but slightly less efficient, version:
List do(
insertionSortInPlace := method(
# In fact, we could've done slice(1, size - 1) foreach(...)
# but creating a new list in memory can only make it worse.
foreach(idx, key,
newidx := slice(0, idx) map(x, x > key) indexOf(true)
if(newidx, insertAt(removeAt(idx), newidx))
)
self)
)
lst := list(7, 6, 5, 9, 8, 4, 3, 1, 2, 0)
lst insertionSortInPlace println # ==> list(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
J
{{eff note|J|/:~}} Solution inspired by the Common LISP solution:
isort=:((>: # ]) , [ , < #])/
Example of use:
isort 32 4 1 34 95 3 2 120 _38
_38 1 2 3 4 32 34 95 120
Java
public static void insertSort(int[] A){
for(int i = 1; i < A.length; i++){
int value = A[i];
int j = i - 1;
while(j >= 0 && A[j] > value){
A[j + 1] = A[j];
j = j - 1;
}
A[j + 1] = value;
}
}
Using some built-in algorithms (warning: not stable, due to the lack of an "upper bound" binary search function) {{trans|C++}}
void insertionSort(List<E> a) {
for (int i = 1; i < a.size(); i++) {
int j = Math.abs(Collections.binarySearch(a.subList(0, i), a.get(i)) + 1);
Collections.rotate(a.subList(j, i+1), j - i);
}
}
public static <E extends Comparable<? super E>> void insertionSort(E[] a) {
for (int i = 1; i < a.length; i++) {
E x = a[i];
int j = Math.abs(Arrays.binarySearch(a, 0, i, x) + 1);
System.arraycopy(a, j, a, j+1, i-j);
a[j] = x;
}
}
JavaScript
function insertionSort (a) {
for (var i = 0; i < a.length; i++) {
var k = a[i];
for (var j = i; j > 0 && k < a[j - 1]; j--)
a[j] = a[j - 1];
a[j] = k;
}
return a;
}
var a = [4, 65, 2, -31, 0, 99, 83, 782, 1];
insertionSort(a);
document.write(a.join(" "));
jq
{{works with|jq|1.4}} The insertion sort can be expressed directly in jq as follows:
def insertion_sort:
reduce .[] as $x ([]; insert($x));
where insert/1 inserts its argument into its input, which can, by construction, be assumed here to be sorted. This algorithm will work in jq for any JSON array.
The following solution uses an "industrial strength" implementation of bsearch (binary search) that requires the following control structure:
# As soon as "condition" is true, then emit . and stop:
def do_until(condition; next):
def u: if condition then . else (next|u) end;
u;
bsearch is the only non-trivial part of this solution, and so we include its complete specification:
Assuming the input array is sorted, bsearch/1 returns the index of the target if the target is in the input array; and otherwise (-1 - ix), where ix is the insertion point that would leave the array sorted.
If the input is not sorted, bsearch will terminate but with irrelevant results.
def bsearch(target):
if length == 0 then -1
elif length == 1 then
if target == .[0] then 0 elif target < .[0] then -1 else -2 end
else . as $in
# state variable: [start, end, answer]
# where start and end are the upper and lower offsets to use.
| [0, length-1, null]
| do_until( .[0] > .[1] ;
(if .[2] != null then (.[1] = -1) # i.e. break
else
( ( (.[1] + .[0]) / 2 ) | floor ) as $mid
| $in[$mid] as $monkey
| if $monkey == target then (.[2] = $mid) # success
elif .[0] == .[1] then (.[1] = -1) # failure
elif $monkey < target then (.[0] = ($mid + 1))
else (.[1] = ($mid - 1))
end
end ))
| if .[2] == null then # compute the insertion point
if $in[ .[0] ] < target then (-2 -.[0])
else (-1 -.[0])
end
else .[2]
end
end;
# insert x assuming input is sorted
def insert(x):
if length == 0 then [x]
else
bsearch(x) as $i
| ( if $i < 0 then -(1+$i) else $i end ) as $i
| .[0:$i] + [x] + .[$i:]
end ;
def insertion_sort:
reduce .[] as $x ([]; insert($x));
Example:
[1, 2, 1, 1.1, -1.1, null, [null], {"null":null}] | insertion_sort
{{Out}} [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)
{{out}}
x = [-1.24011, -1.23848, 0.176698, -1.01986, 0.830544]
insertionsort!(x) = [-1.24011, -1.23848, -1.01986, 0.176698, 0.830544]
Kotlin
fun insertionSort(array: IntArray) {
for (index in 1 until array.size) {
val value = array[index]
var subIndex = index - 1
while (subIndex >= 0 && array[subIndex] > value) {
array[subIndex + 1] = array[subIndex]
subIndex--
}
array[subIndex + 1] = value
}
}
fun main(args: Array<String>) {
val numbers = intArrayOf(5, 2, 3, 17, 12, 1, 8, 3, 4, 9, 7)
fun printArray(message: String, array: IntArray) = with(array) {
print("$message [")
forEachIndexed { index, number ->
print(if (index == lastIndex) number else "$number, ")
}
println("]")
}
printArray("Unsorted:", numbers)
insertionSort(numbers)
printArray("Sorted:", numbers)
}
{{out}}
Unsorted: [5, 2, 3, 17, 12, 1, 8, 3, 4, 9, 7]
Sorted: [1, 2, 3, 3, 4, 5, 7, 8, 9, 12, 17]
Liberty BASIC
itemCount = 20
dim A(itemCount)
for i = 1 to itemCount
A(i) = int(rnd(1) * 100)
next i
print "Before Sort"
gosub [printArray]
'--- Insertion sort algorithm
for i = 2 to itemCount
value = A(i)
j = i-1
while j >= 0 and A(j) > value
A(j+1) = A(j)
j = j-1
wend
A(j+1) = value
next
'--- end of (Insertion sort algorithm)
print "After Sort"
gosub [printArray]
end
[printArray]
for i = 1 to itemCount
print using("###", A(i));
next i
print
return
Lua
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;
{{Out|Output}}
[0,0,2,3,3,8,17,36,40,72]
Mathematica
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}
=={{header|MATLAB}} / {{header|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)
ML
=
mLite
= {{trans|OCaml}}
fun insertion_sort L =
let
fun insert
(x,[]) = [x]
| (x, y :: ys) =
if x <= y then
x :: y :: ys
else
y :: insert (x, ys)
in
foldr (insert,[]) L
end;
println ` insertion_sort [6,8,5,9,3,2,1,4,7];
Output
[1, 2, 3, 4, 5, 6, 7, 8, 9]
=
Standard ML
=
fun insertion_sort cmp = let
fun insert (x, []) = [x]
| insert (x, y::ys) =
case cmp (x, y) of GREATER => y :: insert (x, ys)
| _ => x :: y :: ys
in
foldl insert []
end;
insertion_sort Int.compare [6,8,5,9,3,2,1,4,7];
=={{header|Modula-3}}== {{trans|Ada}}
MODULE InsertSort;
PROCEDURE IntSort(VAR item: ARRAY OF INTEGER) =
VAR j, value: INTEGER;
BEGIN
FOR i := FIRST(item) + 1 TO LAST(item) DO
value := item[i];
j := i - 1;
WHILE j >= FIRST(item) AND item[j] > value DO
item[j + 1] := item[j];
DEC(j);
END;
item[j + 1] := value;
END;
END IntSort;
END InsertSort.
N/t/roff
{{works with|GNU Troff|1.22.2}}
Sliding method
.de end
..
.de array
. nr \\$1.c 0 1
. de \\$1.push end
. nr \\$1..\\\\n+[\\$1.c] \\\\$1
. end
. de \\$1.pushln end
. if \\\\n(.$>0 .\\$1.push \\\\$1
. if \\\\n(.$>1 \{ \
. shift
. \\$1.pushln \\\\$@
. \}
. end
. de \\$1.dump end
. nr i 0 1
. ds out "
. while \\\\n+i<=\\\\n[\\$1.c] .as out "\\\\n[\\$1..\\\\ni]
. tm \\\\*[out]
. rm out
. rr i
. end
. de \\$1.slideright end
. nr i \\\\$1
. nr i+1 \\\\ni+1
. nr \\$1..\\\\n[i+1] \\\\n[\\$1..\\\\ni]
. rr i
. rr i+1
. end
..
.de insertionsort
. nr keyidx 1 1
. while \\n+[keyidx]<=\\n[\\$1.c] \{ \
. nr key \\n[\\$1..\\n[keyidx]]
. nr compidx \\n[keyidx] 1
. while \\n-[compidx]>=0 \{ \
. if \\n[compidx]=0 \{ \
. nr \\$1..1 \\n[key]
. break
. \}
. ie \\n[\\$1..\\n[compidx]]>\\n[key] \{ \
. \\$1.slideright \\n[compidx]
. \}
. el \{ \
. nr compidx+1 \\n[compidx]+1
. nr \\$1..\\n[compidx+1] \\n[key]
. break
. \}
. \}
. \}
..
.array a
.a.pushln 13 64 22 87 54 87 23 92 11 64 5 9 3 3 0
.insertionsort a
.a.dump
Swapping method
.de end
..
.de array
. nr \\$1.c 0 1
. de \\$1.push end
. nr \\$1..\\\\n+[\\$1.c] \\\\$1
. end
. de \\$1.pushln end
. if \\\\n(.$>0 .\\$1.push \\\\$1
. if \\\\n(.$>1 \{ \
. shift
. \\$1.pushln \\\\$@
. \}
. end
. de \\$1.dump end
. nr i 0 1
. ds out "
. while \\\\n+i<=\\\\n[\\$1.c] .as out "\\\\n[\\$1..\\\\ni]
. tm \\\\*[out]
. rm out
. rr i
. end
. de \\$1.swap end
. if (\\\\$1<=\\\\n[\\$1.c])&(\\\\$1<=\\\\n[\\$1.c]) \{ \
. nr tmp \\\\n[\\$1..\\\\$2]
. nr \\$1..\\\\$2 \\\\n[\\$1..\\\\$1]
. nr \\$1..\\\\$1 \\\\n[tmp]
. rr tmp
. \}
. end
..
.de insertionsort
. nr keyidx 1 1
. while \\n+[keyidx]<=\\n[\\$1.c] \{ \
. nr compidx \\n[keyidx]+1 1
. nr compidx-1 \\n[keyidx] 1
. while (\\n-[compidx]>0)&(\\n[\\$1..\\n-[compidx-1]]>\\n[\\$1..\\n[compidx]]) \{ \
. \\$1.swap \\n[compidx] \\n[compidx-1]
. \}
. \}
..
.array a
.a.pushln 13 64 22 87 54 87 23 92 11 64 5 9 3 3 0
.insertionsort a
.a.dump
Nemerle
From the psuedocode.
using System.Console;
using Nemerle.English;
module InsertSort
{
public static Sort(this a : array[int]) : void
{
mutable value = 0; mutable j = 0;
foreach (i in [1 .. (a.Length - 1)])
{
value = a[i]; j = i - 1;
while (j >= 0 and a[j] > value)
{
a[j + 1] = a[j];
j = j - 1;
}
a[j + 1] = value;
}
}
Main() : void
{
def arr = array[1, 4, 8, 3, 8, 3, 5, 2, 6];
arr.Sort();
foreach (i in arr) Write($"$i ");
}
}
NetRexx
/* NetRexx */
options replace format comments java crossref savelog symbols binary
import java.util.List
placesList = [String -
"UK London", "US New York", "US Boston", "US Washington" -
, "UK Washington", "US Birmingham", "UK Birmingham", "UK Boston" -
]
lists = [ -
placesList -
, insertionSort(String[] Arrays.copyOf(placesList, placesList.length)) -
]
loop ln = 0 to lists.length - 1
cl = lists[ln]
loop ct = 0 to cl.length - 1
say cl[ct]
end ct
say
end ln
return
method insertionSort(A = String[]) public constant binary returns String[]
rl = String[A.length]
al = List insertionSort(Arrays.asList(A))
al.toArray(rl)
return rl
method insertionSort(A = List) public constant binary returns ArrayList
loop i_ = 1 to A.size - 1
value = A.get(i_)
j_ = i_ - 1
loop label j_ while j_ >= 0
if (Comparable A.get(j_)).compareTo(Comparable value) <= 0 then leave j_
A.set(j_ + 1, A.get(j_))
j_ = j_ - 1
end j_
A.set(j_ + 1, value)
end i_
return ArrayList(A)
{{out}}
UK London
US New York
US Boston
US Washington
UK Washington
US Birmingham
UK Birmingham
UK Boston
UK Birmingham
UK Boston
UK London
UK Washington
US Birmingham
US Boston
US New York
US Washington
Nim
proc insertSort[T](a: var openarray[T]) =
for i in 1 .. <a.len:
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
{{out}}
@[-31, 0, 2, 2, 4, 65, 83, 99, 782]
Objeck
bundle Default {
class Insert {
function : Main(args : String[]) ~ Nil {
values := [9, 7, 10, 2, 9, 7, 4, 3, 10, 2, 7, 10];
InsertionSort(values);
each(i : values) {
values[i]->PrintLine();
};
}
function : InsertionSort (a : Int[]) ~ Nil {
each(i : a) {
value := a[i];
j := i - 1;
while(j >= 0 & a[j] > value) {
a[j + 1] := a[j];
j -= 1;
};
a[j + 1] := value;
};
}
}
}
OCaml
let rec insert lst x =
match lst with
[] -> [x]
| y :: ys when x <= y -> x :: y :: ys
| y :: ys -> y :: insert ys x
;;
let insertion_sort = List.fold_left insert [];;
insertion_sort [6;8;5;9;3;2;1;4;7];;
Oforth
Returns a new sorted list.
: insertionSort(a)
| l i j v |
a asListBuffer ->l
2 l size for: i [
l at(i) ->v
i 1- ->j
while(j) [
l at(j) dup v <= ifTrue: [ drop break ]
j 1+ swap l put
j 1- ->j
]
l put(j 1 +, v)
]
l ;
{{out}}
>[ 4, 65, 2, -31, 0, 99, 2, 83, 782, 1 ] insertionSort .
[-31, 0, 1, 2, 2, 4, 65, 83, 99, 782] ok
>
ooRexx
{{trans|REXX}}
/* REXX program sorts a stemmed array (has characters) */
/* using the insertion sort algorithm */
Call gen /* fill the array with test data */
Call show 'before sort' /* display the elements */
Say copies('-',79) /* display a separator line */
Call insertionSort x.0 /* invoke the insertion sort. */
Call show ' after sort' /* display the elements after sort*/
Exit
/*--------------------------------------------------------------------*/
gen: Procedure Expose x.
x.1="---Monday's Child Is Fair of Face (by Mother Goose)---"
x.2="
### =================================================
"
x.3="Monday's child is fair of face;"
x.4="Tuesday's child is full of grace;"
x.5="Wednesday's child is full of woe;"
x.6="Thursday's child has far to go;"
x.7="Friday's child is loving and giving;"
x.8="Saturday's child works hard for a living;"
x.9="But the child that is born on the Sabbath day"
x.10="Is blithe and bonny, good and gay."
x.0=10 /* number of elements */
Return
/*--------------------------------------------------------------------*/
insertionsort: Procedure Expose x.
Parse Arg n
Do i=2 To n
y=x.i
Do j=i-1 By -1 To 1 While x.j>y
z=j+1
x.z=x.j
/* Say 'set x.'z 'to x.'j '('||x.j||')' */
End
z=j+1
x.z=y
/* Say 'set x.'z 'to' y */
End
Return
/*--------------------------------------------------------------------*/
show:
Do j=1 To x.0
Say 'Element' right(j,length(x.0)) arg(1)":" x.j
End
Return
{{out}}
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}}
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])
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
See [[Sorting_algorithms/Insertion_sort#Delphi | Delphi]]
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";
{{out}} -31 0 1 2 4 65 83 99 782
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] = $value;
}
return @a;
}
my @data = 22, 7, 2, -5, 8, 4;
say 'input = ' ~ @data;
say 'output = ' ~ @data.&insertion_sort;
{{out}}
input = 22 7 2 -5 8 4
output = -5 2 4 7 8 22
Phix
Copy of [[Sorting_algorithms/Insertion_sort#Euphoria|Euphoria]]
function insertion_sort(sequence s)
object temp
integer j
for i=2 to length(s) do
temp = s[i]
j = i-1
while j>=1 and s[j]>temp do
s[j+1] = s[j]
j -= 1
end while
s[j+1] = temp
end for
return s
end function
constant s = {4, 15, "delta", 2, -31, 0, "alpha", 19, "gamma", 2, 13, "beta", 782, 1}
puts(1,"Before: ") ?s
puts(1,"After: ") ?insertion_sort(s)
{{out}}
Before: {4,15,"delta",2,-31,0,"alpha",19,"gamma",2,13,"beta",782,1}
After: {-31,0,1,2,2,4,13,15,19,782,"alpha","beta","delta","gamma"}
PHP
function insertionSort(&$arr){
for($i=0;$i<count($arr);$i++){
$val = $arr[$i];
$j = $i-1;
while($j>=0 && $arr[$j] > $val){
$arr[$j+1] = $arr[$j];
$j--;
}
$arr[$j+1] = $val;
}
}
$arr = array(4,2,1,6,9,3,8,7);
insertionSort($arr);
echo implode(',',$arr);
1,2,3,4,6,7,8,9
PicoLisp
(de insertionSort (Lst)
(for (I (cdr Lst) I (cdr I))
(for (J Lst (n== J I) (cdr J))
(T (> (car J) (car I))
(rot J (offset I J)) ) ) )
Lst )
{{out}}
: (insertionSort (5 3 1 7 4 1 1 20))
-> (1 1 1 3 4 5 7 20)
PL/I
INSSORT: PROC(A);
DCL A(*) FIXED BIN(31);
DCL (I,J,V,N,M) FIXED BIN(31);
N = HBOUND(A,1); M = LBOUND(A,1);
DO I=M+1 TO N;
V=A(I);
DO J=I-1 BY -1 WHILE (J>M-1 & A(J)>V);
A(J+1)=A(J);
END;
A(J+1)=V;
END;
RETURN;
END INSSORT;
PowerShell
Very similar to the PHP code.
function insertionSort($arr){
for($i=0;$i -lt $arr.length;$i++){
$val = $arr[$i]
$j = $i-1
while($j -ge 0 -and $arr[$j] -gt $val){
$arr[$j+1] = $arr[$j]
$j--
}
$arr[$j+1] = $val
}
}
$arr = @(4,2,1,6,9,3,8,7)
insertionSort($arr)
$arr -join ","
{{Out}}
1,2,3,4,6,7,8,9
Prolog
insert_sort(L1,L2) :-
insert_sort_intern(L1,[],L2).
insert_sort_intern([],L,L).
insert_sort_intern([H|T],L1,L) :-
insert(L1,H,L2),
insert_sort_intern(T,L2,L).
insert([],X,[X]).
insert([H|T],X,[X,H|T]) :-
X =< H,
!.
insert([H|T],X,[H|T2]) :-
insert(T,X,T2).
% Example use: % ?- insert_sort([2,23,42,3,10,1,34,5],L). % L = [1,2,3,5,10,23,34,42] ? % yes
Functional approach
Works with SWI-Prolog.
Insertion sort inserts elements of a list in a sorted list. So we can use foldl to sort a list.
% insertion sort
isort(L, LS) :-
foldl(insert, [], L, LS).
% foldl(Pred, Init, List, R).
foldl(_Pred, Val, [], Val).
foldl(Pred, Val, [H | T], Res) :-
call(Pred, Val, H, Val1),
foldl(Pred, Val1, T, Res).
% insertion in a sorted list
insert([], N, [N]).
insert([H | T], N, [N, H|T]) :-
N =< H, !.
insert([H | T], N, [H|L1]) :-
insert(T, N, L1).
Example use:
?- isort([2,23,42,3,10,1,34,5],L).
L = [1,2,3,5,10,23,34,42]
PureBasic
Procedure insertionSort(Array a(1))
Protected low, high
Protected firstIndex, lastIndex = ArraySize(a())
If lastIndex > firstIndex + 1
low = firstIndex + 1
While low <= lastIndex
high = low
While high > firstIndex
If a(high) < a(high - 1)
Swap a(high), a(high - 1)
Else
Break
EndIf
high - 1
Wend
low + 1
Wend
EndIf
EndProcedure
Python
def insertion_sort(L):
for i in xrange(1, len(L)):
j = i-1
key = L[i]
while (L[j] > key) and (j >= 0):
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)
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))
Rascal
import List;
public list[int] insertionSort(a){
for(i <- [0..size(a)-1]){
v = a[i];
j = i-1;
while(j >= 0 && a[j] > v){
a[j+1] = a[j];
j -= 1;
}
a[j+1] = v;
}
return a;
}
{{out}}
insertionSort([4, 65, 2, -31, 0, 99, 83, 782, 1])
list[int]: [-31,0,1,2,4,65,83,99,782]
REALbasic
Sub InsertionSort(theList() as Integer)
for insertionElementIndex as Integer = 1 to UBound(theList)
dim insertionElement as Integer = theList(insertionElementIndex)
dim j as Integer = insertionElementIndex - 1
while (j >= 0) and (insertionElement < theList(j))
theList(j + 1) = theList(j)
j = j - 1
wend
theList(j + 1) = insertionElement
next
End Sub
REBOL
; This program works with REBOL version R2 and R3, to make it work with Red
; change the word func to function
insertion-sort: func [
a [block!]
/local i [integer!] j [integer!] n [integer!]
value [integer! string! date!]
][
i: 2
n: length? a
while [i <= n][
value: a/:i
j: i
while [ all [ 1 < j
value < a/(j - 1) ]][
a/:j: a/(j - 1)
j: j - 1
]
a/:j: value
i: i + 1
]
a
]
probe insertion-sort [4 2 1 6 9 3 8 7]
probe insertion-sort [ "---Monday's Child Is Fair of Face (by Mother Goose)---"
"Monday's child is fair of face;"
"Tuesday's child is full of grace;"
"Wednesday's child is full of woe;"
"Thursday's child has far to go;"
"Friday's child is loving and giving;"
"Saturday's child works hard for a living;"
"But the child that is born on the Sabbath day"
"Is blithe and bonny, good and gay."]
; just by adding the date! type to the local variable value the same function can sort dates.
probe insertion-sort [12-Jan-2015 11-Jan-2015 11-Jan-2016 12-Jan-2014]
{{out}}
[1 2 3 4 6 7 8 9]
[{---Monday's Child Is Fair of Face (by Mother Goose)---}
"But the child that is born on the Sabbath day"
"Friday's child is loving and giving;"
"Is blithe and bonny, good and gay."
"Monday's child is fair of face;"
"Saturday's child works hard for a living;"
"Thursday's child has far to go;"
"Tuesday's child is full of grace;"
"Wednesday's child is full of woe;"
]
[12-Jan-2014 11-Jan-2015 12-Jan-2015 11-Jan-2016]
REXX
/*REXX program sorts a stemmed array (has characters) using the insertion sort algorithm*/
call gen /*generate the array's (data) elements.*/
call show 'before sort' /*display the before array elements. */
say copies('▒', 85) /*display a separator line (a fence). */
call insertionSort # /*invoke the insertion sort. */
call show ' after sort' /*display the after array elements. */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
gen: @.=; @.1 = "---Monday's Child Is Fair of Face (by Mother Goose)---"
@.2 = "
### =================================================
"
@.3 = "Monday's child is fair of face;"
@.4 = "Tuesday's child is full of grace;"
@.5 = "Wednesday's child is full of woe;"
@.6 = "Thursday's child has far to go;"
@.7 = "Friday's child is loving and giving;"
@.8 = "Saturday's child works hard for a living;"
@.9 = "But the child that is born on the Sabbath day"
@.10 = "Is blithe and bonny, good and gay."
do #=1 while @.#\==''; end; #=#-1 /*determine how many entries in @ array*/
return
/*──────────────────────────────────────────────────────────────────────────────────────*/
insertionSort: procedure expose @.; parse arg #
do i=2 to #; $=@.i; do j=i-1 by -1 to 1 while @.j>$
_=j+1; @._=@.j
end /*j*/
_=j+1; @._=$
end /*i*/
return
/*──────────────────────────────────────────────────────────────────────────────────────*/
show: do j=1 for #; say ' element' right(j,length(#)) arg(1)": " @.j; end; return
'''output''' when using the internal data:
element 1 before sort: ---Monday's Child Is Fair of Face (by Mother Goose)---
element 2 before sort:
### =================================================
element 3 before sort: Monday's child is fair of face;
element 4 before sort: Tuesday's child is full of grace;
element 5 before sort: Wednesday's child is full of woe;
element 6 before sort: Thursday's child has far to go;
element 7 before sort: Friday's child is loving and giving;
element 8 before sort: Saturday's child works hard for a living;
element 9 before sort: But the child that is born on the Sabbath day
element 10 before sort: Is blithe and bonny, good and gay.
▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
element 1 after sort: ---Monday's Child Is Fair of Face (by Mother Goose)---
element 2 after sort:
### =================================================
element 3 after sort: But the child that is born on the Sabbath day
element 4 after sort: Friday's child is loving and giving;
element 5 after sort: Is blithe and bonny, good and gay.
element 6 after sort: Monday's child is fair of face;
element 7 after sort: Saturday's child works hard for a living;
element 8 after sort: Thursday's child has far to go;
element 9 after sort: Tuesday's child is full of grace;
element 10 after sort: Wednesday's child is full of woe;
Ring
alist = [7,6,5,9,8,4,3,1,2,0]
see insertionsort(alist)
func insertionsort blist
for i = 1 to len(blist)
value = blist[i]
j = i - 1
while j >= 1 and blist[j] > value
blist[j+1] = blist[j]
j = j - 1
end
blist[j+1] = value
next
return blist
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;
}
}
}
Scala
version 1
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)
}
version 2
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
?
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: [http://seed7.sourceforge.net/algorith/sorting.htm#insertionSort]
Sidef
class Array {
method insertion_sort {
{ |i|
var j = i-1
var k = self[i]
while ((j >= 0) && (k < self[j])) {
self[j+1] = self[j]
j--
}
self[j+1] = k
} << 1..self.end
return self
}
}
var a = 10.of { 100.irand }
say a.insertion_sort
SNOBOL4
* read data into an array
A = table()
i = 0
readln A<i = i + 1> = trim(input) :s(readln)
aSize = i - 1
* sort array
i = 1
loop1 value = A<i>
j = i - 1
loop2 gt(j,0) gt(A<j>,value) :f(done2)
A<j + 1> = A<j>
j = j - 1 :(loop2)
done2 A<j + 1> = value
i = ?lt(i,aSize) i + 1 :s(loop1)
i = 1
* output sorted data
while output = A<i>; i = ?lt(i,aSize) i + 1 :s(while)
end
Stata
mata
void insertion_sort(real vector a) {
real scalar i, j, n, x
n = length(a)
for (i=2; i<=n; i++) {
x = a[i]
for (j=i-1; j>=1; j--) {
if (a[j] <= x) break
a[j+1] = a[j]
}
a[j+1] = x
}
}
end
Swift
Using generics.
(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--
}
}
}
=={{header|TI-83 BASIC}}== Store input in L1, run prgmSORTINS, get output in L2. :L1→L2 :0→A :Lbl L :A+1→A :A→B :While B>0 :If L2(B)<L2(B+1) :Goto B :L2(B)→C :L2(B+1)→L2(B) :C→L2(B+1) :B-1→B :End :Lbl B :If A<(dim(L2)-1) :Goto L :DelVar A :DelVar B :DelVar C :Stop
Tcl
package require Tcl 8.5
proc insertionsort {m} {
for {set i 1} {$i < [llength $m]} {incr i} {
set val [lindex $m $i]
set j [expr {$i - 1}]
while {$j >= 0 && [lindex $m $j] > $val} {
lset m [expr {$j + 1}] [lindex $m $j]
incr j -1
}
lset m [expr {$j + 1}] $val
}
return $m
}
puts [insertionsort {8 6 4 2 1 3 5 7 9}] ;# => 1 2 3 4 5 6 7 8 9
=={{header|TI-83 BASIC}}== Input into L1, run prgmSORTINS, output in L2. :"INSERTION" :L1→L2 :0→A :Lbl L :A+1→A :A→B :While B>0 :If L2(B)≤L2(B+1) :Goto B :L2(B)→C :L2(B+1)→L2(B) :C→L2(B+1) :B-1→B :End :Lbl B :If A<(dim(L2)-1) :Goto L :DelVar A :DelVar B :DelVar C :Return
uBasic/4tH
END
_Insertionsort PARAM (1) ' Insertion sort LOCAL (3)
FOR b@ = 1 TO a@-1 c@ = @(b@) d@ = b@ DO WHILE (d@>0) * (c@ < @(ABS(d@-1))) @(d@) = @(d@-1) d@ = d@ - 1 LOOP @(d@) = c@ NEXT RETURN
_Swap PARAM(2) ' Swap two array elements PUSH @(a@) @(a@) = @(b@) @(b@) = POP() RETURN
_InitArray ' Init example array PUSH 4, 65, 2, -31, 0, 99, 2, 83, 782, 1
FOR i = 0 TO 9 @(i) = POP() NEXT
RETURN (i)
_ShowArray PARAM (1) ' Show array subroutine FOR i = 0 TO a@-1 PRINT @(i), NEXT
PRINT RETURN
## UnixPipes
```bash
selectionsort() {
read a
test -n "$a" && ( selectionsort | sort -nm <(echo $a) -)
}
cat to.sort | selectionsort
Ursala
#import nat
insort = ~&i&& @hNCtX ~&r->lx ^\~&rt nleq-~rlrSPrhlPrSCPTlrShlPNCTPQ@rhPlD
test program:
#cast %nL
example = insort <45,82,69,82,104,58,88,112,89,74>
{{out}}
<45,58,69,74,82,82,88,89,104,112>
VBA
{{trans|Phix}}
Option Base 1
Private Function insertion_sort(s As Variant) As Variant
Dim temp As Variant
Dim j As Integer
For i = 2 To UBound(s)
temp = s(i)
j = i - 1
Do While s(j) > temp
s(j + 1) = s(j)
j = j - 1
If j = 0 Then Exit Do
Loop
s(j + 1) = temp
Next i
insertion_sort = s
End Function
Public Sub main()
s = [{4, 15, "delta", 2, -31, 0, "alpha", 19, "gamma", 2, 13, "beta", 782, 1}]
Debug.Print "Before: ", Join(s, ", ")
Debug.Print "After: ", Join(insertion_sort(s), "' ")
End Sub
{{out}}
Before: 4, 15, delta, 2, -31, 0, alpha, 19, gamma, 2, 13, beta, 782, 1
After: -31' 0' 1' 2' 2' 4' 13' 15' 19' 782' alpha' beta' delta' gamma
VBScript
{{trans|REALbasic}}
Randomize
Dim n(9) 'nine is the upperbound.
'since VBS arrays are 0-based, it will have 10 elements.
For L = 0 to 9
n(L) = Int(Rnd * 32768)
Next
WScript.StdOut.Write "ORIGINAL : "
For L = 0 to 9
WScript.StdOut.Write n(L) & ";"
Next
InsertionSort n
WScript.StdOut.Write vbCrLf & " SORTED : "
For L = 0 to 9
WScript.StdOut.Write n(L) & ";"
Next
'the function
Sub InsertionSort(theList)
For insertionElementIndex = 1 To UBound(theList)
insertionElement = theList(insertionElementIndex)
j = insertionElementIndex - 1
Do While j >= 0
'necessary for BASICs without short-circuit evaluation
If insertionElement < theList(j) Then
theList(j + 1) = theList(j)
j = j - 1
Else
Exit Do
End If
Loop
theList(j + 1) = insertionElement
Next
End Sub
{{Out}}
ORIGINAL : 26699;2643;10249;31612;21346;19702;29799;31115;20413;5197;
SORTED : 2643;5197;10249;19702;20413;21346;26699;29799;31115;31612;
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, ^ )];
]
{{out}}
-5 1 1 2 3 4 4 5 6 9
Yorick
Based on pseudocode, except using 1-based arrays.
func insertionSort(&A) {
for(i = 2; i <= numberof(A); i++) {
value = A(i);
j = i - 1;
while(j >= 1 && A(j) > value) {
A(j+1) = A(j);
j--;
}
A(j+1) = value;
}
}
zkl
fcn insertionSort(list){
sink:=List();
foreach x in (list){
if(False==(n:=sink.filter1n('>(x)))) sink.append(x); // x>all items in sink
else sink.insert(n,x);
}
sink.close();
}
insertionSort(T(4,65,2,-31,0,99,2,83,782,1)).println();
insertionSort("big fjords vex quick waltz nymph".split()).println();
{{out}}
L(-31,0,1,2,2,4,65,83,99,782)
L("big","fjords","nymph","quick","vex","waltz")