What is the difference between memoization and tabulation?

What is the difference between memoization and tabulation?

Memoization and tabulation are both techniques used in dynamic programming to optimize recursive algorithms. Memoization is a top-down approach where you store the results of expensive function calls and reuse them when the same inputs occur again. Tabulation, on the other hand, is a bottom-up approach where you solve all related subproblems first and store their results in a table.

Can you give me an example of each?

Sure! For memoization, consider the Fibonacci sequence. You can use a recursive function and store results in a dictionary to avoid recalculating. For tabulation, you would create an array to store Fibonacci numbers iteratively, filling it from the base cases up to the desired index.

Which method is generally more efficient?

It depends on the problem. Memoization can be more efficient for problems with overlapping subproblems, while tabulation can be better for problems with a clear iterative structure. However, tabulation often uses less memory since it doesn't require the overhead of recursive calls.

Are there any downsides to using either method?

Yes, memoization can lead to high memory usage if the recursion depth is large, while tabulation can be less intuitive and harder to implement for complex problems. Additionally, tabulation may require more upfront computation.