GATE-2003 Insertion Sort Solved Example | GATECSE | Data Structure

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Insertion sort is a simple sorting algorithm that works similar to the way you sort playing cards in your hands. The array is virtually split into a sorted and an unsorted part. Values from the unsorted part are picked and placed at the correct position in the sorted part.
Algorithm
To sort an array of size n in ascending order:
1: Iterate from arr[1] to arr[n] over the array.
2: Compare the current element (key) to its predecessor.
3: If the key element is smaller than its predecessor, compare it to the elements before. Move the greater elements one position up to make space for the swapped element.

Time Complexity: O(n*2)

Auxiliary Space: O(1)

Boundary Cases: Insertion sort takes maximum time to sort if elements are sorted in reverse order. And it takes minimum time (Order of n) when elements are already sorted.

Sorting In Place: Yes

Stable: Yes

What is Binary Insertion Sort?
We can use binary search to reduce the number of comparisons in normal insertion sort. Binary Insertion Sort uses binary search to find the proper location to insert the selected item at each iteration. In normal insertion, sorting takes O(i) (at ith iteration) in worst case. We can reduce it to O(logi) by using binary search. The algorithm, as a whole, still has a running worst case running time of O(n2) because of the series of swaps required for each insertion.

Comparison among Bubble Sort, Selection Sort and Insertion Sort
Insertion sort to sort even and odd positioned elements in different orders
Merge Sort vs. Insertion Sort
Time complexity of insertion sort when there are O(n) inversions?
An Insertion Sort time complexity question
Recursive Insertion Sort
Binary Insertion Sort
Insertion Sort for Doubly Linked List
C Program for Insertion Sort
Insertion sort using C++ STL
C Program for Binary Insertion Sort
Java Program for Binary Insertion Sort
Python Program for Binary Insertion Sort
C Program for Recursive Insertion Sort
Java Program for Recursive Insertion Sort
Python Program for Recursive Insertion Sort
Insertion Sort by Swapping Elements
C program for Time Complexity plot of Bubble, Insertion and Selection Sort
Sorting algorithm visualization : Insertion Sort
Why Quick Sort preferred for Arrays and Merge Sort for Linked Lists?

Binary Insertion Sort:
We can use binary search to reduce the number of comparisons in normal insertion sort. Binary Insertion Sort uses binary search to find the proper location to insert the selected item at each iteration.
In normal insertion sort, it takes O(n^2) comparisons(at nth iteration) in worst case. We can reduce it to O(log n) by using binary search.

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