Insertion Sort algorithm “Java”

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Insertion Sort algorithm “Java”

sort unordered list of elements

this an example 

void insertionSort(int[] ar)_x000D_
{_x000D_
   for (int i=1; i ‹ ar.length; i++)_x000D_
   {_x000D_
      int index = ar[i]; int j = i;_x000D_
      while (j > 0 && ar[j-1] > index)_x000D_
      {_x000D_
           ar[j] = ar[j-1];_x000D_
           j--;_x000D_
      }_x000D_
      ar[j] = index;_x000D_
} }_x000D_


Example. We color a sorted part in green, and an unsorted part in black. Here is an insertion sort step by step. We take an element from unsorted part and compare it with elements in sorted part, moving form right to left.

29, 20, 73, 34, 64

29, 20, 73, 34, 64

20, 29, 73, 34, 64

20, 29, 73, 34, 64

20, 29, 34, 73, 64

20, 29, 34, 64, 73

Let us compute the worst-time complexity of the insertion sort. In sorting the most expensive part is a comparison of two elements. Surely that is a dominant factor in the running time. We will calculate the number of comparisons of an array of N elements:

we need 0 comparisons to insert the first element

we need 1 comparison to insert the second element

we need 2 comparisons to insert the third element

…

we need (N-1) comparisons (at most) to insert the last element

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