Question

When implementing Insertion Sort, a binary search could be used to locate the position within the first i−1i-1i−1 records of the array into which record iii should be inserted. In this implementation, the worst case time will be:

Answer 1

Insertion Sort implementation with binary search can locate the correct position for insertion quickly. Worst case time complexity is O(n^2).

Step-by-step explanation:

It iterates through the unsorted portion and inserts each element into its correct position within the sorted portion. In this implementation, a binary search can be used to quickly locate the correct position for insertion.

The worst case time for this implementation of Insertion Sort is O(n^2), where n is the number of elements in the array. This worst case occurs when the array is in reverse order, as each element needs to be inserted at the beginning of the sorted portion.

For example, suppose we have an array [5, 3, 2, 4, 1]. After the first iteration, the sorted portion is [3, 5] and the unsorted portion is [2, 4, 1]. The next element, 2, is found to be smaller than 3 and larger than 1. So, it is inserted at index 1, resulting in the sorted portion [2, 3, 5]. The same process continues for the remaining elements.