Memoization

If I choose not to stash, I'm going to spend time and save space, right? Essentially, that's the trade-off here, right? And it's very clear to explain with memoization.

And then you can say, OK, but now if you look at the structure of the memoization problems, there's this interesting duality that if you really stare at the structure of memoization, you realize there's actually a trade-off.

Do I want to check whether I've already solved the subproblem or not? Do I want to compute bottom-up or top-down? Memoization is a top-down, depth-first process.

So you can ask, well, what if I wanted to work bottom-up instead? Well, you're going to have to rewrite your problem to express it bottom-up.

But if you do it bottom-up, you can go bottom-up breadth first and that's called dynamic programming.