Insertion sort

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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.

Contents

[edit] Implementations

[edit] C++


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 );
}

[edit] 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;
        }
}

[edit] C#


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=J-1;
                }
                array[j + 1] = value;
        }
}

[edit] 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. 


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;
        }
}

[edit] 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
                (Einfuegeposition > Links)) DO
                BEGIN
                        Menge[Einfuegeposition] := Menge[Einfuegeposition - 1];
                        Einfuegeposition := Einfuegeposition - 1;
                END;
                Menge[Einfuegeposition] := Zwischenspeicher;
        END;
END;


[edit] 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]

[edit] 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 ;;

[edit] 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)))))

[edit] 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)

[edit] Java


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;
        }
}

[edit] Generic


static <T extends Comparable<? super 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;
        }
}

[edit] Haskell


import Data.List (insert)

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

[edit] Perl

1: 


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);

2: 


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;
        }
}

[edit] 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;
}

[edit] 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

[edit] Python Alt

An alternate method: 


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

[edit] Ruby

def insertion_sort(array)
    array.each_with_index do |el,i|
        j = i - 1
        while j >= 0
            break if array[j] <= el
            array[j + 1] = array[j]
            j -= 1
        end
        array[j + 1] = el
    end
end

[edit] 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]

[edit] 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;

[edit] 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
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