I knew the center-expansion trick going in, which saved me.
Start by clarifying the problem and edge cases, then propose an efficient algorithm like expanding around centers or Manacher's algorithm. Explain the time and space complexity, and walk through a small example to demonstrate correctness.
Pro tip: Mention that expanding around centers is often preferred in interviews because it's easier to implement correctly under pressure, but also note Manacher's algorithm for optimal O(n) time if the interviewer wants maximum efficiency.
Confirm that substrings are contiguous, count each occurrence separately, and handle edge cases like empty string or single character.
Mention the naive O(n^3) approach of checking all substrings, but note it's inefficient and set the stage for optimization.
Explain expanding around centers: for each of the 2n-1 centers (including between characters), expand while characters match, counting palindromes. This is O(n^2) time and O(1) space.
State that the expanding around centers approach takes O(n^2) time in the worst case (e.g., all same characters) and O(1) extra space.
Use a short string like 'aaa' to show how the algorithm counts 6 palindromic substrings, ensuring the interviewer follows your logic.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.