My first instinct was a trie and I ran with it way too long.
Start by clarifying the problem constraints and edge cases, then propose a solution that enumerates all possible contiguous sub-phrases (n-grams) across the input strings. For each candidate, compute its coverage by counting the number of strings where it appears as a contiguous word-boundary match, and track the maximum. Discuss trade-offs between brute-force and optimized approaches using suffix automata or inverted indices.
Pro tip: Mention that the optimal sub-phrase is likely short (1-3 words) because coverage drops exponentially as phrase length increases, so you can limit the maximum n-gram length to keep the solution efficient. Also, highlight that word-boundary matching requires careful tokenization to avoid partial word matches.
Ask about input size, expected phrase lengths, and whether case sensitivity or punctuation matters. Confirm that coverage is computed as word count times the number of strings containing the sub-phrase as a contiguous sequence of whole words.
Generate all contiguous n-grams (n from 1 to max possible) from each string, ensuring they respect word boundaries. Use a set to deduplicate candidates across strings.
For each candidate, count how many strings contain it as a contiguous word-boundary match. Use a hash map to store candidate phrases and their counts, or build an inverted index from n-grams to string IDs.
Iterate through candidates, compute coverage as word count times frequency, and keep the candidate with the highest coverage. Handle ties by returning any or the shortest phrase.
Propose pruning: limit n-gram length based on coverage upper bound (e.g., if max possible coverage for longer phrases is less than current best). Mention advanced data structures like suffix automata or Aho-Corasick for large inputs.
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