Longest Palindromic Substring
Given a string `s`, return the longest palindromic substring in `s`. Consider the 'Expand Around Center' approach.
Why Interviewers Ask This
Meta evaluates candidates on their ability to optimize brute-force solutions into efficient algorithms. This question specifically tests your understanding of string manipulation, edge case handling like odd versus even length palindromes, and your capacity to implement the 'Expand Around Center' technique with O(n^2) time complexity while maintaining clean, readable code.
How to Answer This Question
1. Clarify constraints: Ask about input size and character set to determine if O(n^2) is acceptable. 2. Define the strategy: Explicitly state you will use the 'Expand Around Center' approach rather than dynamic programming for better space efficiency. 3. Handle dual cases: Explain that every palindrome has a center, which could be a single character (odd length) or between two characters (even length). 4. Walk through logic: Describe initializing pointers at each potential center, expanding outward while characters match, and tracking the maximum length found. 5. Validate edge cases: Mention handling empty strings, single characters, or inputs with no palindromes longer than one. 6. Analyze complexity: Conclude by stating the time complexity is O(n^2) and space complexity is O(1), demonstrating Meta's focus on optimal resource usage.
Key Points to Cover
- Explicitly distinguishing between odd and even length palindrome centers
- Demonstrating O(1) space complexity compared to Dynamic Programming approaches
- Clearly articulating boundary conditions for pointer movement
- Justifying the choice of algorithm based on time complexity trade-offs
- Providing a concrete walkthrough with a specific example string
Sample Answer
I would start by clarifying that for a string up to 1000 characters, an O(n^2) solution is perfectly acceptable. My preferred approach is 'Expand Around Center' because it avoids the O(n) space overhead of dynamic programming tables. I recognize that every palindrome expands from a center point. For a string like 'babad', the centers are individual characters for odd-length palindromes, such as 'a' in 'bab'. However, for even-length palindromes like 'abba', the center exists between the two 'b's. I would iterate through every index in the string. At each index, I'd run two expansion functions: one treating the current index as the sole center, and another treating the current and next indices as the center pair. Inside these functions, I'd move left and right pointers outward as long as they remain within bounds and the characters match. Whenever a valid expansion finishes, I compare the new length against my recorded maximum. If it is larger, I update the result substring. Finally, I return the stored longest substring. This ensures we handle all cases efficiently without nested loops checking every possible substring blindly. This method aligns well with Meta's engineering standards for balancing readability and performance.
Common Mistakes to Avoid
- Failing to check for even-length palindromes by ignoring the center between two characters
- Using brute force O(n^3) methods without attempting to optimize to O(n^2)
- Neglecting to handle edge cases like null inputs or strings with only one character
- Not explaining the time and space complexity analysis after writing the code
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