2 posts tagged with "learning"

A casual conversation between two software engineers about the subtle differences between recursion, memoization, and "real" DP.

The Setup​

It's late afternoon at the office. Alex just finished implementing a memoized solution to Min Cost Climbing Stairs and walks over to Jamie's desk with their laptop.

Alex: Hey Jamie, can I bug you for a second? I'm confused about something with DP.

Jamie: [looks up from code review] Sure, what's up?

Alex: So I wrote this solution for the climbing stairs problem. I started with recursion, then added memoization like everyone says. But now I'm wondering... is this actually DP? Or is it still just recursion?

A dialogue between an engineer learning DP and a professor clarifying the optimal learning path

The Question​

Engineer: Professor, I've been breaking down how to approach dynamic programming problems, and I want to validate my thinking. Here's my approach:

1. First, I solve the problem using recursion in the worst possible way - not worrying about time or space complexity at all
2. Then, I optimize that recursive solution with memoization, which gives me a top-down DP solution
3. Finally, I convert it to bottom-up DP for an even better solution in terms of both time and space complexity

Am I thinking about this correctly? Or am I missing something critical?