How does memoization compare to dynamic programming?

Can you explain how memoization differs from dynamic programming?

Sure! Memoization is an optimization technique that stores the results of expensive function calls and returns the cached result when the same inputs occur again. Dynamic programming, on the other hand, is a broader algorithmic paradigm that solves problems by breaking them down into simpler subproblems and storing the results of these subproblems to avoid redundant calculations.

Are there specific scenarios where one is preferred over the other?

Yes, memoization is often preferred for problems with overlapping subproblems, like the Fibonacci sequence. Dynamic programming is more suitable for optimization problems where you need to consider all possible solutions, like the knapsack problem.

Can you give an example of a problem that uses dynamic programming?

Certainly! A classic example is the 'Longest Common Subsequence' problem, where you find the longest subsequence present in both sequences. It uses dynamic programming to build a solution based on previously computed results.

What about the space complexity of both techniques?

Memoization can have higher space complexity due to storing results in a cache, while dynamic programming often uses a table to store results, which can be optimized to reduce space usage depending on the problem.