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Explain how to find the longest palindromic substring.

Difficulty: 6/10
center expansion, Manacher's algorithm, dynamic programming

Longest Palindromic Substring

A palindrome reads the same from left to right and right to left. A practical approach for the longest palindromic substring is expand-around-center: every palindrome has a center, which can be a character for odd-length palindromes or a gap between characters for even-length palindromes.

javascript
  1. 1

    Expand-around-center takes O(n²) time in the worst case.

  2. 2

    Auxiliary space is O(1), excluding the returned substring.

  3. 3

    Dynamic programming can also solve the problem in O(n²) time and O(n²) space.

  4. 4

    Manacher's Algorithm solves the problem in O(n) time but is more complex.

  5. 5

    For production code, I would choose the approach based on input size and maintainability requirements.

Scenario Questions

0-2 years experience

  1. 1We have a function that receives a short user‑entered string (max 100 chars) and we need to return its longest palindromic substring. How would you implement it quickly?
  2. 2If you wrote a simple expand‑around‑center solution and it fails on the input 'abacdfgdcaba', what bug might be causing the wrong result?
  3. 3What edge cases would you test for after implementing your solution?

2-5 years experience

  1. 1Our product adds a feature that highlights the longest palindrome in a paragraph of up to 10,000 characters. Which algorithm would you choose and why?
  2. 2During a code review you notice the current implementation uses O(n²) time and O(n²) space. How would you improve its performance without changing the public API?
  3. 3If the service suddenly starts timing out on inputs that contain many repeated characters, what could be the cause and how would you debug it?

5-8 years experience

  1. 1Design a microservice that processes streaming text and needs to emit the longest palindrome seen so far for each message. Discuss algorithm choice, state management, and scaling considerations.
  2. 2Our legacy system uses a naïve O(n³) approach and is now a bottleneck for 1 GB daily logs. How would you refactor the component, and what trade‑offs would you evaluate between Manacher’s algorithm and a parallelized center‑expansion?
  3. 3Explain how you would instrument and monitor the palindrome service to detect regressions in latency after switching to a linear‑time algorithm.

8+ years experience

  1. 1We plan to migrate a monolithic text‑analysis pipeline to a distributed architecture that includes a longest‑palindrome service used by multiple downstream products. What architectural patterns would you adopt to ensure low latency, versioning, and backward compatibility?
  2. 2How would you evaluate the long‑term maintenance impact of embedding Manacher’s algorithm directly in the codebase versus wrapping it behind a language‑agnostic service, considering teams across different tech stacks?
  3. 3If a new requirement emerges to support Unicode grapheme clusters and case‑insensitive matching, how would that affect your current palindrome detection design and what changes would you propose at the system level?

Follow-up Questions

  • What would happen if the input string is extremely long, say 10⁶ characters?
  • How would you modify your solution to also return the start index of the palindrome?
  • Can you discuss the memory trade‑offs between the DP and Manacher approaches?
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