Question

What is meant by the phrase "divide and conquer"?

Short answer

Answer: Divide and conquer is a problem-solving approach that involves dividing a given problem into smaller, more manageable subproblems, solving these subproblems individually, and combining their solutions to find the overall solution. An example of this strategy is the Merge Sort algorithm used in computer programming to sort a list of elements. The algorithm divides the list into halves, recursively applies Merge Sort to these halves, and then merges the sorted halves to arrive at the final sorted list. This approach allows for more efficient problem-solving compared to other methods like Bubble Sort.

Step-by-step solution

Definition of Divide and Conquer

Divide and conquer is a problem-solving approach in which a given problem is divided into smaller, more manageable subproblems. These subproblems are solved individually, and their solutions are combined to arrive at a solution for the original problem.

Example of Divide and Conquer

One example of a divide and conquer algorithm is the Merge Sort algorithm, used in computer programming to sort a list of elements. Here's how Merge Sort works using divide and conquer: 1. If the list contains only one element, it is already sorted. 2. If the list contains more than one element, divide it into two equal parts - the left half and the right half. 3. Apply the Merge Sort algorithm recursively to both the left and right halves of the list. 4. Combine the sorted left and right halves by merging them together into a new, sorted list. The Merge Sort algorithm is efficient and has a time complexity of O(n log n), where n is the number of elements in the list to be sorted. By breaking the problem into smaller subproblems and solving them individually, the divide and conquer strategy allows for more efficient problem-solving compared to other methods like Bubble Sort, which has a time complexity of O(n^2).