My first instinct was the DP table approach because it felt safe and I could explain it cleanly.
Start by clarifying the problem constraints (e.g., input size, character set) and discussing brute-force versus optimized solutions. Then present an O(n^2) expand-around-center approach as a balance of simplicity and efficiency, and optionally mention Manacher's algorithm for O(n) if needed. Walk through the algorithm with a small example and analyze time/space complexity.
Pro tip: Demonstrate awareness of trade-offs: expand-around-center is easier to implement and less error-prone than Manacher's, which is complex and rarely expected in interviews unless explicitly asked. Also, handle edge cases like empty string and single character early.
Ask about input size, character set, and whether the palindrome must be contiguous. Confirm return type (substring vs. length) and handle edge cases like empty string.
Mention brute-force O(n^3), dynamic programming O(n^2), expand-around-center O(n^2), and Manacher's O(n). Compare their trade-offs in terms of implementation complexity and performance.
Select expand-around-center for its simplicity and good average performance. Explain how to expand around each character (odd length) and each pair (even length) to find the longest palindrome.
Trace the algorithm on a sample string like 'babad' to show how it finds 'bab' or 'aba'. Highlight how you track the start index and max length.
State time complexity O(n^2) and space O(1). Discuss edge cases: empty string, single character, all same characters, and no palindrome longer than 1.
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