My first instinct was brute force, comparing each string against all others character by character.
Build a trie from all strings, then for each string traverse the trie until reaching a node with exactly one child (or the string's end), which marks the shortest unique prefix. Alternatively, sort the strings and compare adjacent strings to find the minimal distinguishing prefix for each. Discuss trade-offs between trie (O(total characters) time and space) and sorting (O(n log n * L) time, O(1) extra space).
Pro tip: Clarify edge cases upfront: duplicate strings, empty strings, and strings where one is a prefix of another. Mention that if duplicates exist, no unique prefix is possible, so you must handle that explicitly.
Ask about input constraints (string length, number of strings, character set) and edge cases like duplicates, empty strings, and prefix relationships. Confirm expected output for duplicates.
Decide between a trie and sorting. Explain that a trie naturally groups strings by common prefixes and allows efficient prefix extraction, while sorting leverages lexicographic order to find minimal distinguishing prefixes.
For trie: insert all strings, then for each string traverse until the current node has only one child or the string ends. For sorting: sort strings, then for each string compare with its neighbors to find the shortest prefix that differs.
State time and space complexity for both approaches. Trie: O(N * L) time and space, where N is number of strings and L is average length. Sorting: O(N log N * L) time, O(1) extra space (if in-place).
Walk through examples including duplicates, empty strings, and one string being a prefix of another. Verify that the algorithm returns correct unique prefixes or handles impossible cases.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.