I went with the brute force first, nested loops checking every pair of substrings.
Clarify the problem constraints (string length, character set) and discuss possible approaches: binary search with rolling hash, suffix automaton, or suffix array. Then implement a solution using binary search on length with a rolling hash to check for duplicate substrings, ensuring to handle hash collisions or use double hashing. Analyze time and space complexity, aiming for O(n log n) time.
Pro tip: Mention that while rolling hash is practical, it has collision risks; using double hashing or a suffix automaton can guarantee correctness. Also, note that the problem is equivalent to finding the longest repeated substring, which can be solved in linear time with a suffix automaton, but a binary search + hash approach is often sufficient in interviews.
Ask about string length, character set, and whether overlapping occurrences are allowed (they are). Discuss edge cases like empty string, no repeated substring, and all characters same.
Decide between binary search + rolling hash, suffix automaton, or suffix array. Explain trade-offs: rolling hash is simpler but probabilistic; suffix automaton is deterministic but complex.
For binary search + rolling hash: binary search on length L, compute hashes of all substrings of length L, and check for duplicates using a hash set. Use double hashing to reduce collisions.
Test with provided examples and edge cases. If using rolling hash, consider adding a collision check or using a deterministic method if time permits.
State time complexity: O(n log n) for binary search + rolling hash, O(n) for suffix automaton. Space complexity: O(n) for storing hashes or automaton states.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Talked through binary search on the answer length combined with rolling hash to check each candidate length in linear time.
Start by clarifying the brute-force approach and its inefficiencies, then systematically apply optimizations such as hashing, suffix structures, or binary search with rolling hashes. Discuss trade-offs between time and space, and consider practical constraints like input size and memory.
Pro tip: Mention that the optimal solution depends on whether you need to find all duplicates or just detect existence, and that suffix automaton or suffix array with LCP can solve it in O(n) time, but may be overkill for small inputs.
Define what 'duplicate substrings' means (e.g., any repeated substring of length >= 2) and state the brute-force approach: generate all substrings and compare, which is O(n^3) or O(n^2) with hashing.
Point out that brute-force recompares many substrings; aim to reduce time complexity to O(n log n) or O(n) while managing space.
Propose using rolling hash with binary search for longest duplicate substring, or suffix arrays/trees/automata for linear-time detection. Explain how each works.
Compare time/space complexity, implementation complexity, and suitability for different input sizes. For example, rolling hash is simpler but has collision risk; suffix automaton is optimal but complex.
Summarize that for interviews, binary search + rolling hash is a good balance, but mention suffix automaton for production systems needing guaranteed performance.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Wasn't expecting this as a standalone follow-up.
Start by clarifying that hash collisions are inherent to rolling hash and must be handled to ensure correctness. Explain the trade-offs between different collision resolution strategies, focusing on double hashing and verification, and relate them to practical scenarios like substring search or plagiarism detection. Emphasize that the choice depends on the application's tolerance for false positives and performance constraints.
Pro tip: Mention that using two independent hash functions (double hashing) drastically reduces collision probability, and for critical applications, always verify a hash match with a direct string comparison. This shows you balance theoretical guarantees with practical engineering.
State that rolling hash can produce collisions where different substrings yield the same hash, and ignoring them can lead to incorrect results.
Describe common methods: using a large prime modulus, double hashing, or verifying matches with actual string comparison.
Compare techniques in terms of time/space overhead, false positive rate, and implementation complexity. For example, double hashing reduces collisions but doubles computation.
Suggest a combination: use double hashing for low collision probability and verify with direct comparison when a match is found, especially in critical applications.
Mention how this applies to problems like Rabin-Karp substring search or detecting duplicate content, where collisions must be handled to avoid false positives.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.