2D DP Problems

Two-dimensional DP problems have two state variables — typically representing indices into two arrays/dimensions. The DP table is a 2D matrix dp[i][j].

📋 Problems

#	Problem	Pattern	Difficulty
1	Unique Paths	Grid traversal	Medium
2	0/1 Knapsack	Take/skip items	Medium
3	Longest Common Subsequence	String alignment	Medium
4	Edit Distance	String transformation	Hard

⚡ Quick Recurrence Reference

Unique Paths:   dp[i][j] = dp[i-1][j] + dp[i][j-1]             (sum of paths)
Knapsack:       dp[i][w] = max(dp[i-1][w], dp[i-1][w-wt] + val) (skip or take)
LCS:            match? dp[i-1][j-1]+1 : max(dp[i-1][j], dp[i][j-1]) (match or skip)
Edit Distance:  match? dp[i-1][j-1] : 1+min(delete, insert, replace) (3 ops)

Start with Unique Paths →