Insertion Sort in Depth

Insertion sort 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 inserted in this sorted sub-list, has to find its appropriate place and then it is to be inserted there. Hence the name insertion sort.

We have already discussed some basics of insertion sort in the previous chapter Insertion Sort. In this chapter, we will discuss insertion sort in more detail.

Insertion Sort Code

#include<stdio.h>
#include <stdbool.h>
#define MAX 7

int intArray[MAX] = {4,6,3,2,1,9,7};

void printline(int count) {
   int i;
	
   for(i = 0;i < count-1;i++) {
      printf("=");
   }
	
   printf("=\n");
}

void display() {
   int i;
   printf("[");
	
   // navigate through all items 
   for(i = 0;i < MAX;i++) {
      printf("%d ",intArray[i]);
   }
	
   printf("]\n");
}

void insertionSort() {

   int valueToInsert;
   int holePosition;
   int i;
  
   // loop through all numbers 
   for(i = 1; i < MAX; i++) { 
	
      // select a value to be inserted. 
      valueToInsert = intArray[i];
		
      // select the hole position where number is to be inserted 
      holePosition = i;
		
      // check if previous no. is larger than value to be inserted 
      while (holePosition > 0 && intArray[holePosition-1] > valueToInsert) {
         intArray[holePosition] = intArray[holePosition-1];
         holePosition--;
         printf(" item moved : %d\n" , intArray[holePosition]);
      }

      if(holePosition != i) {
         printf(" item inserted : %d, at position : %d\n" , valueToInsert,holePosition);
         // insert the number at hole position 
         intArray[holePosition] = valueToInsert;
      }

      printf("Iteration %d#:",i);
      display();
		
   }  
}

int main() 
{
   printf("Input Array: ");
   display();
   printline(50);
   insertionSort();
   printf("Output Array: ");
   display();
   printline(50);
   
   return 0;
}

Output

Input Array: [4 6 3 2 1 9 7 ]
==================================================
Iteration 1#:[4 6 3 2 1 9 7 ]
 item moved : 6
 item moved : 4
 item inserted : 3, at position : 0
Iteration 2#:[3 4 6 2 1 9 7 ]
 item moved : 6
 item moved : 4
 item moved : 3
 item inserted : 2, at position : 0
Iteration 3#:[2 3 4 6 1 9 7 ]
 item moved : 6
 item moved : 4
 item moved : 3
 item moved : 2
 item inserted : 1, at position : 0
Iteration 4#:[1 2 3 4 6 9 7 ]
Iteration 5#:[1 2 3 4 6 9 7 ]
 item moved : 9
 item inserted : 7, at position : 5
Iteration 6#:[1 2 3 4 6 7 9 ]
Output Array: [1 2 3 4 6 7 9 ]

Insertion sort is a very simple method to sort numbers in an ascending or descending order. This method follows the incremental method. It can be compared with the technique how cards are sorted at the time of playing a game.

The numbers, which are needed to be sorted, are known as keys. Here is the algorithm of the insertion sort method.

Insertion Sort Algorithm

Input − An array of data, and the total number in the array
Output --The sorted Array

Begin
   for i := 1 to size-1 do
      key := array[i]
      j := i
      while j > 0 AND array[j-1] > key do
         array[j] := array[j-1];
         j := j – 1
      done
      array[j] := key
   done
End

This sorting technique is similar with the card sorting technique, in other words, we sort cards using insertion sort mechanism. For this technique, we pick up one element from the data set and shift the data elements to make a place to insert back the picked up an element into the data set.

Complexity Analysis of Insertion Sort

Run time of this algorithm is very much dependent on the given input.

If the given numbers are sorted, this algorithm runs in O(n) time. If the given numbers are in reverse order, the algorithm runs in O(n²) time.

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 Ο(n2), where n is the number of items.

As we mentioned above that insertion sort is an efficient sorting algorithm, as it does not run on preset conditions using for loops, but instead it uses one while loop, which avoids extra steps once the array gets sorted.

Even though insertion sort is efficient, still, if we provide an already sorted array to the insertion sort algorithm, it will still execute the outer for loop, thereby requiring n steps to sort an already sorted array of n elements, which makes its best case time complexity a linear function of n.