Insertion Sort - Data Structures and Algorithms

This is an in-place comparison-based sorting algorithm. Here, a sub-list is maintained which is always sorted. For example, the lower part of an array is maintained to be sorted. An element which is to be 'insert'ed in this sorted sub-list, has to find its appropriate place and then it has to be inserted there. Hence the name, insertion sort.

The array is searched sequentially and unsorted items are moved and inserted into the sorted sub-list (in the same array). This algorithm is not suitable for large data sets as its average and worst case complexity are of ?(n2), where n is the number of items.

1. How Insertion Sort Works

We take an unsorted array for our example.


Unsorted Array


Insertion sort compares the first two elements.


Insertion Sort


It finds that both 14 and 33 are already in ascending order. For now, 14 is in sorted sub-list.


Insertion Sort


Insertion sort moves ahead and compares 33 with 27.


Insertion Sort


And finds that 33 is not in the correct position.


Insertion Sort


It swaps 33 with 27. It also checks with all the elements of sorted sub-list. Here we see that the sorted sub-list has only one element 14, and 27 is greater than 14. Hence, the sorted sub-list remains sorted after swapping.


Insertion Sort


By now we have 14 and 27 in the sorted sub-list. Next, it compares 33 with 10.


Insertion Sort


These values are not in a sorted order.


Insertion Sort


So we swap them.


Insertion Sort


However, swapping makes 27 and 10 unsorted.


Insertion Sort


Hence, we swap them too.


Insertion Sort


Again we find 14 and 10 in an unsorted order.


Insertion Sort


We swap them again. By the end of third iteration, we have a sorted sub-list of 4 items.


Insertion Sort


This process goes on until all the unsorted values are covered in a sorted sub-list. Now we shall see some programming aspects of insertion sort.

2. Algorithm

Now we have a bigger picture of how this sorting technique works, so we can derive simple steps by which we can achieve insertion sort.


Step 1 − If it is the first element, it is already sorted. return 1;

Step 2 − Pick next element

Step 3 − Compare with all elements in the sorted sub-list

Step 4 − Shift all the elements in the sorted sub-list that is greater than the

         value to be sorted

Step 5 − Insert the value

Step 6 − Repeat until list is sorted


3. Pseudocode


procedure insertionSort( A : array of items )

   int holePosition

   int valueToInsert


   for i = 1 to length(A) inclusive do:


      /* select value to be inserted */

      valueToInsert = A[i]

      holePosition = i


      /*locate hole position for the element to be inserted */


      while holePosition > 0 and A[holePosition-1] > valueToInsert do:

         A[holePosition] = A[holePosition-1]

         holePosition = holePosition -1

      end while


      /* insert the number at hole position */

      A[holePosition] = valueToInsert


   end for


end procedure