LeetCode 1143 Longest Common Subsequence - State Design

Define $dp[i][j]$ as the length of the LCS (Longest Common Subsequence) of the first $i$ characters of A and the first $j$ characters of B. Why this definition? At each step, you're either matching characters or skipping one.

You need to track progress in both strings independently. Base cases: $dp[0][j] = 0$ for all $j$ (empty A has no common subsequence with anything). $dp[i][0] = 0$ for all $i$ (empty B has no common subsequence with anything).