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Start by clarifying the problem and edge cases, then explain the dynamic programming approach with a 2D table where dp[i][j] represents the LCS length of prefixes. Walk through the recurrence relation and provide time/space complexity, and if time permits, mention space optimization.
Pro tip: Emphasize the connection to sequence alignment and diff algorithms, which are relevant in ML for tasks like text similarity and DNA sequence analysis. Also, proactively discuss space optimization to show depth.
Confirm definitions: subsequence vs substring, whether characters are case-sensitive, and if empty strings are allowed. Ask about constraints on string lengths to determine if O(n*m) is acceptable.
Let dp[i][j] be the LCS length of first i characters of string A and first j characters of string B. If A[i-1] == B[j-1], dp[i][j] = dp[i-1][j-1] + 1; else dp[i][j] = max(dp[i-1][j], dp[i][j-1]).
Initialize first row and column to 0. Iterate i from 1 to n and j from 1 to m, filling dp according to the recurrence. The answer is dp[n][m].
Time complexity is O(n*m), space O(n*m). Mention that space can be reduced to O(min(n,m)) by keeping only the previous row, and briefly explain how.
Relate LCS to ML: e.g., evaluating text generation, DNA sequence alignment, or diff tools. Mention possible extensions like printing the LCS or handling multiple strings.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.