Insertion sort

Insertion sort

Algorithm
Insertion sort iterates, consuming one input element each repetition, and growing a sorted output list. Each iteration, insertion sort removes one element from the input data, finds the location it belongs within the sorted list, and inserts it there. It repeats until no input elements remain.
Sorting is typically done in-place, stable and online by iterating up the array, growing the sorted list behind it. At each array-position, it checks the value there against the largest value in the sorted list (which happens to be next to it, in the previous array-position checked). If larger, it leaves the element in place and moves to the next. If smaller, it finds the correct position within the sorted list, shifts all the larger values up to make a space, and inserts into that correct position.

Pseudocode

for i ← 1 to length(A) - 1

    j ← i

    while j > 0 and A[j-1] > A[j]

        swap A[j] and A[j-1]

        j ← j - 1

    end while

end for

Java Implementation of Insertion Sort :-

Here for reducing the complexity we will use an array of reversely sorted elements.

int a[]={9,8,7,6,5,4,3,2,1,0};

int j = 0;

for(int i=1;i<a.length;i++){

              j=i;

              while(j>0 && a[j-1]>a[j]){

                     int temp = a[j];

                     a[j] = a[j-1];

                     a[j-1]=temp;

                     j = j-1;

              }

       }

Best, worst, and average cases

The best case input is an array that is already sorted. In this case insertion sort has a linear running time (i.e., O(n)).

The simplest worst case input is an array sorted in reverse order. In this case insertion sort has a quadratic running time (i.e. O(n²)).

Name	Best	Average	Worst	Memory	Stable	Method	Other notes
Insertion sort	n	n^2	n^2	1	Yes	Insertion	O(n + d), in the worst case over sequences that have d inversions.