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I knew it was a DP problem pretty quickly but then fumbled explaining the recurrence relation out loud.
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 analyze time and space complexity, mentioning potential optimizations.
Pro tip: Mention that this DP pattern is fundamental for sequence alignment tasks in ML, such as comparing text or DNA sequences, and that space can be optimized to O(min(m,n)) using rolling arrays.
Confirm that subsequence means characters appear in order but not necessarily consecutively, and discuss edge cases like empty strings or no common characters.
Let dp[i][j] be the length of LCS of first i characters of string1 and first j characters of string2. Initialize a (m+1) x (n+1) table with zeros.
If characters match, dp[i][j] = dp[i-1][j-1] + 1; else dp[i][j] = max(dp[i-1][j], dp[i][j-1]). Explain why this works.
Fill the table iteratively and return dp[m][n]. Discuss time complexity O(m*n) and space complexity O(m*n), with possible optimization to O(min(m,n)).
Connect LCS to ML applications like evaluating text generation, sequence alignment in bioinformatics, or diff algorithms, showing broader understanding.
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