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Classic DP problem but I fumbled the recurrence for a minute.
Start by clarifying the problem and discussing a brute-force approach, then optimize using dynamic programming. Explain the DP recurrence based on comparing characters at both ends and derive the solution for the longest palindromic subsequence. Analyze time and space complexity, and mention potential optimizations.
Pro tip: Relate the problem to the Longest Common Subsequence (LCS) between the string and its reverse, which provides an alternative DP formulation and shows deeper insight. Also, be prepared to discuss space optimization from O(n^2) to O(n) if asked.
Confirm that a subsequence does not require contiguous characters and that we seek the maximum length. Discuss edge cases like empty string or single character.
Mention that a naive recursive approach would explore all subsequences, leading to exponential time. Highlight that the problem exhibits optimal substructure and overlapping subproblems, making DP suitable.
Define dp[i][j] as the length of the longest palindromic subsequence in substring s[i..j]. If s[i] == s[j], dp[i][j] = dp[i+1][j-1] + 2; else dp[i][j] = max(dp[i+1][j], dp[i][j-1]). Base case: dp[i][i] = 1.
Fill the DP table in increasing order of substring length. Discuss time complexity O(n^2) and space complexity O(n^2), and mention that space can be reduced to O(n) by using two rows.
Walk through a small example (e.g., 'bbbab' returns 4) to verify the recurrence. Discuss how to handle large inputs and potential follow-up questions.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.