I knew the brute force immediately but sat there second-guessing whether O(n^2) was good enough.
Clarify the problem constraints (e.g., string length, character set) and discuss brute-force vs. optimized approaches. Present an O(n^2) expand-around-center solution that counts all palindromic substrings, including duplicates, and analyze its time and space complexity.
Pro tip: Mention that duplicates are counted separately because each occurrence at a different position is a distinct substring, and note that Manacher's algorithm can achieve O(n) if needed, but expand-around-center is simpler and often sufficient.
Ask about input size, character set, and whether empty substrings or single characters count. Confirm that duplicates at different positions are counted separately.
Explain that checking all O(n^2) substrings and verifying each palindrome takes O(n^3) time, which is inefficient for large inputs.
For each character (and each pair of adjacent characters), expand outward while characters match, counting each valid palindrome. This runs in O(n^2) time and O(1) extra space.
State time complexity O(n^2) and space O(1). Handle edge cases: empty string (0), single character (1), all same characters (n(n+1)/2).
Briefly note Manacher's algorithm can solve this in O(n) time, but it's more complex; expand-around-center is usually preferred for interviews unless O(n) is explicitly required.
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