Classic DP problem and I knew it, but I still fumbled explaining the recurrence relation out loud.
Clarify the problem and constraints, then explain the dynamic programming approach using a 2D table where dp[i][j] represents the LCS length of prefixes. Walk through the recurrence relation and analyze time and space complexity, mentioning possible optimizations.
Pro tip: Mention that you can reduce space complexity to O(min(m,n)) by keeping only two rows, and discuss how this applies to real-world scenarios like diff tools or DNA sequence alignment, showing practical awareness.
Confirm understanding: subsequence vs substring, return 0 if none, and constraints like string length. Ask if there are any memory or time limits.
Explain that the LCS problem exhibits optimal substructure and overlapping subproblems, making it suitable for dynamic programming.
Define dp[i][j] as LCS of first i chars of string1 and first j chars of string2. Recurrence: if chars match, dp[i][j] = dp[i-1][j-1] + 1; else dp[i][j] = max(dp[i-1][j], dp[i][j-1]).
Describe bottom-up implementation with a 2D array, then mention space optimization to two rows. Analyze time O(m*n) and space O(min(m,n)).
Walk through a small example, test edge cases like empty strings, no common characters, and identical strings. Discuss potential follow-ups like reconstructing the LCS.
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