6.Which of the following is an example of a divide and conquer algorithm?Bubble SortSelection SortMerge SortInsertion Sort

Step 1: Break Down the Problem

We need to identify which algorithm from the given options is an example of a divide and conquer algorithm. The options are:

1. Bubble Sort
2. Selection Sort
3. Merge Sort
4. Insertion Sort

Step 2: Relevant Concepts

A divide and conquer algorithm works by recursively breaking down a problem into smaller subproblems, solving each of these subproblems independently, and then combining their solutions to solve the original problem.

• Bubble Sort: Works by repeatedly stepping through the list, comparing adjacent elements and swapping them if they are in the wrong order. Not a divide and conquer algorithm.
• Selection Sort: Divides the list into a sorted and an unsorted segment. It iteratively selects the smallest element from the unsorted segment and moves it to the end of the sorted segment. Not a classic divide and conquer algorithm.
• Merge Sort: Recursively divides the list into two halves until each sub-list contains a single element, and then merges the sorted sub-lists to produce the sorted list. This is a classic example of a divide and conquer algorithm.
• Insertion Sort: Builds the final sorted array one item at a time. It is not based on dividing the problem into subproblems.

Step 3: Analysis and Detail

Based on the definitions:

• Bubble Sort and Insertion Sort are simple sorting algorithms that do not use the divide and conquer technique.
• Selection Sort also does not have the characteristic of divide and conquer.
• Merge Sort perfectly embodies the divide and conquer approach by continuously breaking down the array and merging back together in a sorted manner.

Step 4: Verify and Summarize

Upon reviewing the characteristics of each sorting algorithm, it is clear that Merge Sort is the only algorithm that uses the divide and conquer strategy.

Final Answer

Merge Sort is an example of a divide and conquer algorithm.