I started with the brute force: enumerate all substrings and count occurrences, which is roughly cubic time.
Clarify the tie-breaking rule and constraints first, then propose a suffix automaton or suffix array solution that finds the shortest unique substring in O(n) or O(n log n) time. Walk through the algorithm, analyze complexity, and discuss trade-offs versus simpler but slower approaches.
Pro tip: Mention that the shortest unique substring can be found by computing for each position the longest repeated prefix using suffix structures, then the answer is the minimum over positions of that length plus one. This shows deep insight and often impresses interviewers.
Ask about input size, character set, tie-breaking (any vs lexicographically smallest), and whether the substring must be contiguous. Confirm expected time/space complexity.
Start with brute-force O(n^3) or O(n^2) using hash maps, then improve using suffix arrays or suffix automaton to achieve O(n log n) or O(n). Explain why naive is insufficient for large n.
Describe building a suffix automaton or suffix array with LCP array. For each suffix, compute the longest prefix that appears at least twice; the shortest unique substring starting at that position has length LCP+1. Track the minimum over all positions.
If lexicographically smallest is required, compare candidates of the same minimal length. Handle empty string, all characters repeated, and single-character unique cases.
State time and space complexity of the chosen approach. Compare with alternatives (e.g., suffix tree, rolling hash) and justify why the chosen method is optimal for the given constraints.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.