My first instinct was to just do GCD on prefix lengths and call it done.
First, clarify the problem and edge cases. Then, propose an efficient algorithm using rolling hashes or frequency vectors to compare the prefix signature with block signatures, and analyze time/space complexity. Finally, discuss trade-offs and potential optimizations.
Pro tip: Demonstrate Amazon's Leadership Principles by proactively discussing scalability and edge cases, and by comparing multiple approaches with clear trade-offs.
Restate the problem in your own words and ask clarifying questions about constraints, input size, and expected output. Confirm that the signature is the frequency count of each character.
Describe a naive solution that, for each prefix, tries all possible block sizes and checks if all blocks match the prefix signature. Analyze its time complexity (e.g., O(n^3)) to establish a baseline.
Suggest using rolling hashes or frequency vectors to compute signatures in O(1) per block. Explain how to iterate over prefixes and possible block sizes efficiently, possibly using divisors of the string length.
Compare the optimized approach with the brute-force in terms of time and space. Discuss scenarios where one might be preferred, and mention any assumptions or limitations.
Walk through a small example (e.g., 'ABAB') to validate the algorithm and edge cases like single-character strings or strings with all identical characters.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.