Memoization or Tabulation approach for Dynamic programming

Question

There are many problems that can be solved using Dynamic programming e.g. Longest increasing subsequence. This problem can be solved by using 2 approaches

1. Memoization (Top Down) - Using recursion to solve the sub-problem and storing the result in some hash table.
2. Tabulation (Bottom Up) - Using Iterative approach to solve the problem by solving the smaller sub-problems first and then using it during the execution of bigger problem.

My question is which is better approach in terms of time and space complexity?

Answer 1

Short answer: it depends on the problem!

Memoization usually requires more code and is less straightforward, but has computational advantages in some problems, mainly those which you do not need to compute all the values for the whole matrix to reach the answer.

Tabulation is more straightforward, but may compute unnecessary values. If you do need to compute all the values, this method is usually faster, though, because of the smaller overhead.

Answer 2

Asymptotically a dynamic programming implementation that is top down is the same as going bottom up, assuming you're using the same recurrence relation. However, bottom up is generally more efficient because of the overhead of recursion which is used in memoization.