# Insertion sort

 Related content:

Insertion sort is similar to bubble sort, but is more efficient as it reduces element comparisons somewhat with each pass. An element is compared to all the prior elements until a lesser element is found. In other words, if an element contains a value less than all the previous elements, it compares the element to all the previous elements before going on to the next comparison. Although this algorithm is more efficient than the Bubble sort, it is still inefficient compared to many other sort algorithms since it, and bubble sort, move elements only one position at a time. However, insertion sort is a good choice for small lists (about 30 elements or fewer), and for nearly-sorted lists.

## Implementations

### C++

<highlightsyntax language="cpp"> template< typename Iterator > void insertion_sort( Iterator First, Iterator Last ) {

Iterator min = First;
for( Iterator i = First + 1; i < Last; ++i )
if ( *i < *min )
min = i;
std::iter_swap( First, min );
while( ++First < Last )
for( Iterator j = First; *j < *(j - 1); --j )
std::iter_swap( (j - 1), j );

} </highlightsyntax>

### C

<highlightsyntax language="c"> void insertSort(int a[], size_t length) {

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

} </highlightsyntax>

### C#

<highlightsyntax language="csharp"> static void InsertSort(IComparable[] array) {

int i, j;
for (i = 1; i < array.Length; i++)
{
IComparable value = array[i];
j = i - 1;
while ((j >= 0) && (array[j].CompareTo(value) > 0))
{
array[j + 1] = array[j];
j--;
}
array[j + 1] = value;
}

} </highlightsyntax>

### C# 2.0

This example sorts a list of objects of any type T that implements IComparable. It demonstrates C# 2.0 generics and in particular the "where" clause.

<highlightsyntax language="csharp"> static void InsertSort<T>(IList<T> list) where T : IComparable<T> {

int i, j;
for (i = 1; i < list.Count; i++)
{
T value = list[i];
j = i - 1;
while ((j >= 0) && (list[j].CompareTo(value) > 0))
{
list[j + 1] = list[j];
j--;
}
list[j + 1] = value;
}

} </highlightsyntax>

### Pascal

<highlightsyntax language="pascal"> PROCEDURE InsertionSort(var Menge: MengeIntegerTyp; Links, Rechts: INTEGER;) VAR

Index, Einfuegeposition, Zwischenspeicher: INTEGER;

BEGIN

FOR Index := Links + 1 TO Rechts DO
BEGIN
Zwischenspeicher := Menge[Index];
Einfuegeposition := Index;
WHILE ((Menge[Einfugeposition - 1] > Zwischenspeicher) AND
BEGIN
Menge[Einfuegeposition] := Menge[Einfuegeposition - 1];
Einfuegeposition := Einfuegeposition - 1;
END;
Menge[Einfuegeposition] := Zwischenspeicher;
END;

END; </highlightsyntax>

### OCaml

This implementation uses physical equality to avoid copying sublists that are already sorted:

# let rec sort = function
| [] -> []
| h1::t as list -> match sort t with
| h2::t when h1>h2 -> h2::sort(h1::t)
| t' -> if t==t' then list else h1::t';;
val sort : 'a list -> 'a list = <fun>

For example:

# sort [1;9;2;8;3;7;4;6;5];;
- : int list = [1; 2; 3; 4; 5; 6; 7; 8; 9]

### CAML

let rec insertion_Sort l =
match l with
| [] -> []
| (h::n) -> insert h (insertion_Sort n)
and insert t l =
match l with
| [] -> [t]
| (h::n) -> if t > h then h::(insert t n)
else t::h::n ;;

### Common Lisp

(defun insert (target list)
(if (null list)
(cons target '())
(if (<= target (first list))
(cons target list)
(cons (first list) (insert target (rest list))))))

(defun insertSort (myList)
(if (null mylist)
'()
(insert (first myList) (insertSort (rest myList)))))

### F#

let rec insert x l =  match l with
| []    -> [x]
| y::ys -> if x <= y then x::y::ys
else y::insert x ys
and insertsort l = match l with
| []    -> []
| x::xs -> insert x (insertsort xs)

### Java

<highlightsyntax language="language"> static void insertionSort (int[] A) {

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

} </highlightsyntax>

#### Generic

<highlightsyntax language="language"> static <T extends Comparable<T>> void insertionSort (T[] A) {

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

} </highlightsyntax>

<highlightsyntax language="haskell"> insert :: Ord a => a -> [a] -> [a] insert item [] = [item] insert item (h:t) | item <= h = item:h:t

| otherwise = h:(insert item t)

insertsort :: Ord a => [a] -> [a] insertsort = foldr insert [] </highlightsyntax>

### Perl

1: <highlightsyntax language="perl"> sub insertionSort {

my @unsorted = @{\$_[0]};
my @sorted   = @{\$_[1]};
INSERTION:
for my \$current ( @unsorted ) {
for my \$pos ( 0 .. \$#sorted ) {
if ( \$sorted[\$pos] >= \$current ) {
splice @sorted, \$pos, 0, \$current; # Insert \$current
next INSERTION;
}
}
push @sorted, \$current; # No larger value has been found in @sorted
}
return @sorted;

}

my @unsorted = qw(1 82 73 745839 928 7346 8 6 4 8 0 6 34 102); my @sorted = qw(1 5);

@sorted = insertionSort(\@unsorted, \@sorted); </highlightsyntax>

2: <highlightsyntax language="perl"> sub insert_sort {

for(my \$i = 0; \$i <= \$#_; \$i++) {
my (\$j, \$val) = (\$i - 1, \$_[\$i]);
\$_[\$j-- + 1] = \$_[\$j] while (\$j >= 0 && \$_[\$j] > \$val);
\$_[\$j+1] = \$val;
}

} </highlightsyntax>

### PHP

<highlightsyntax language="php">

for(\$j=1; \$j < count(\$array); \$j++){
\$temp = \$array[\$j];
\$i = \$j;
while((\$i >= 0) && (\$array[\$i-1] > \$temp)){
\$array[\$i] = \$array[\$i-1];
\$i--;
}
\$array[\$i] = \$temp;
}

//Non-decreasing order for (\$j=1; \$j < count(\$array); \$j++) { \$key = \$array[\$j]; \$i = \$j - 1;

while(\$i >= 0 and \$array[\$i] > \$key) { \$array[\$i + 1] = \$array[\$i]; \$i = \$i - 1; }

\$array[\$i + 1] = \$key; }

//Non-increasing order for (\$j=1; \$j < count(\$array); \$j++) { \$key = \$array[\$j]; \$i = \$j - 1;

while(\$i >= 0 and \$array[\$i] < \$key) { \$array[\$i + 1] = \$array[\$i]; \$i = \$i - 1; }

\$array[\$i + 1] = \$key; } </highlightsyntax>

### Python

<highlightsyntax language="python"> def insertsort(array):

for removed_index in range(1, len(array)):
removed_value = array[removed_index]
insert_index = removed_index
while insert_index > 0 and array[insert_index - 1] > removed_value:
array[insert_index] = array[insert_index - 1]
insert_index -= 1
array[insert_index] = removed_value

</highlightsyntax>

#### Python Alt

An alternate method: <highlightsyntax language="python"> def insertsort(array):

for lastsortedelement in range(len(array)-1):
checked = lastsortedelement
while array[checked] > array[lastsortedelement + 1] and checked >= 0:
checked -= 1
#Insert the number into the correct position
array[checked+1], array[checked+2 : lastsortedelement+2] = array[lastsortedelement+1], array[checked+1 : lastsortedelement+1]
return array

</highlightsyntax>

### Seed7

const proc: insertionSort (inout array integer: arr) is func
local
var integer: i is 0;
var integer: j is 0;
var integer: help is 0;
begin
for i range 2 to length(arr) do
j := i;
help := arr[i];
while j > 1 and arr[j-1] > help do
a[j] := a[j-1];
decr(j);
end while;
a[j] := help;
end for;
end func;

Original source: [1]

### Standard ML

fun insertsort [] = []
| insertsort (x::xs) =
let fun insert (x:real, []) = [x]
| insert (x:real, y::ys) =
if x<=y then x::y::ys
else y::insert(x, ys)
in insert(x, insertsort xs)
end;

### Turing

var nombres, limit : int
get nombres
get limit
var sure : boolean := false
var g, smaller : int := 0
var k : int := limit + 1
var last : int := limit
var first : int := 1
var last2 : int := nombres
var br : int := limit - 1
var rann, sort : array 1 .. nombres of int
for i : 1 .. nombres
rann (i) := Rand.Int (0, limit)
sort (i) := k
end for
if rann (1) <= limit then
last := rann (1)
sort (1) := rann (1)
end if
for h : 2 .. upper (rann)
if rann (h) < last then
for decreasing f : nombres - 1 .. 1
sort (f + 1) := sort (f)
end for
sort (1) := rann (h)
last := rann (h)
else
for i : 1 .. upper (rann)
if rann (h) < sort (i) then
for decreasing f : nombres - 1 .. i
sort (f + 1) := sort (f)
end for
sort (i) := rann (h)
exit
end if
end for
end if
end for
for b : 1 .. upper (sort)
put " ", sort (b) ..
end for