Memoization

Memoization is a technique mainly used to speed up algorithms that solve problems by breaking them into smaller overlapping subproblems. The results of these smaller subproblems are stored and reused when needed again. This avoids redundant computations and can significantly speed up algorithms, especially those with a high degree of overlapping subproblems, like dynamic programming solutions.

However, in the case of divide-and-conquer algorithms like merge sort, memoization does not offer a speed-up. This is primarily for two reasons:

1. No Overlapping Subproblems: Merge sort breaks down the original problem into disjoint subsets. Each subset is independent and doesn’t overlap with others. Because there are no overlapping subproblems, there’s nothing to memoize.

2. Already Efficient: Merge sort has a time complexity of (O(n \log n)), which is already efficient for sorting algorithms. Memoization aims to improve efficiency by avoiding re-computation, but since merge sort doesn’t re-compute any subproblem, memoization has no role to play here.

So, memoization fails to speed up algorithms like merge sort because these algorithms are designed to efficiently solve non-overlapping subproblems in the first place.