What does the divide and conquer strategy entail in algorithm design?

The divide and conquer strategy in algorithm design is fundamentally about breaking a problem down into smaller, more manageable subproblems that can be solved independently before combining their results to solve the original problem. This method typically involves three key steps: dividing the problem into smaller subproblems, solving each of those subproblems independently, and then combining their solutions to form a complete solution to the original problem.

The focus on solving smaller instances of the same problem is essential because this allows complex problems to be approached more easily and can lead to more efficient algorithms. Classic examples of algorithms that use this strategy are mergesort and quicksort, where the list to be sorted is divided and sorted independently before merging the sorted lists back together. This approach not only simplifies the problem-solving process but often improves efficiency through recursion and reduced computational complexity.