Intro

Okay, so you've solved problems where one number describes everything you need. House Robber used $dp[i]$ for "best answer up to house $i$." Fibonacci used $dp[n]$ for "the $n$-th number."

But what happens when one number isn't enough? What if you need to track both your position AND something else, like how many items you've picked or how much capacity you've used?

I'll show you how to add dimensions to your DP state. You'll solve Red Green Towers, Grid 1, and Edit Distance. By the end, two-dimensional DP will feel natural.