I knew the general DP approach but fumbled explaining the recurrence relation out loud.
Start by clarifying the problem and edge cases, then explain the dynamic programming approach using a 2D table where dp[i][j] represents the length of the longest palindromic subsequence in substring s[i..j]. Derive the recurrence relation and discuss time and space complexity, mentioning possible optimizations.
Pro tip: Emphasize that this is a classic DP problem and relate it to the Longest Common Subsequence (LCS) by reversing the string, showing deeper understanding. Also, mention that for large strings, space can be optimized to O(n) using a 1D array.
Restate the problem in your own words and ask clarifying questions about input size, character set, and expected output. Discuss edge cases like empty string or single character.
Define dp[i][j] as the length of the longest palindromic subsequence in substring s[i..j]. Explain that the answer will be dp[0][n-1].
If s[i] == s[j], then dp[i][j] = dp[i+1][j-1] + 2. Otherwise, dp[i][j] = max(dp[i+1][j], dp[i][j-1]). Handle base cases: dp[i][i] = 1, and dp[i][j] = 0 for i > j.
Describe filling the table in increasing order of substring length. Analyze time complexity O(n^2) and space complexity O(n^2), and mention space optimization to O(n).
Walk through a small example like 'bbbab' to demonstrate the DP table and verify the result. Discuss potential pitfalls and how to avoid them.
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