{5, 2, 4, 6,1,3} INSERTION-S ORT .A/ 1 for j = 2 to A.lengt…
{5, 2, 4, 6,1,3} INSERTION-S ORT .A/ 1 for j = 2 to A.length 2 key = A[j] 3 // Insert A[j ] into the sorted sequence A[1. . j – 1] 4 i = j – 1 5 while i > 0 and A
Answer
The insertion sort algorithm is a simple sorting algorithm that works by repeatedly inserting an element into a sorted portion of the list until the entire list is sorted. It is an efficient algorithm for small data sets or nearly sorted lists.
The algorithm operates by dividing the list into two portions: a sorted portion and an unsorted portion. Initially, the sorted portion is empty, and the unsorted portion contains all the elements of the list. The algorithm iterates through the unsorted portion, taking one element at a time and inserting it into the correct position in the sorted portion.
In the given pseudocode, the algorithm starts with j = 2, which represents the second element of the list A. The key variable is assigned the value of A[j]. The algorithm then enters a loop with i = j – 1, which represents the index of the last element in the sorted portion.
The loop continues as long as i > 0 and the element at index i in the sorted portion is greater than the key. The algorithm compares the key with each element in the sorted portion, moving each element one position to the right until it finds the correct position for the key. This shifting of elements allows room for the insertion of the key.
Once the correct position is found, the algorithm assigns the value of the key to the element at index i+1, effectively inserting the element into the sorted portion. After this insertion step, the algorithm increments j by 1 and continues with the next iteration, repeating the process until j reaches the length of the list.
The insertion sort algorithm has an average and worst-case time complexity of O(n^2), where n is the number of elements in the list. This makes it less efficient than other sorting algorithms such as merge sort or quicksort for large data sets. However, insertion sort has advantages in certain scenarios, such as when the list is nearly sorted or when the list is small.
In conclusion, the insertion sort algorithm is a simple and efficient algorithm for sorting small data sets or nearly sorted lists. It works by repeatedly inserting elements into a sorted portion of the list until the entire list is sorted. The algorithm has a time complexity of O(n^2), making it less efficient than other sorting algorithms for large data sets, but it has advantages in specific scenarios.