My first instinct was to just iterate through all stored words and check prefix for each query, which is obviously what they told you not to do.
Clarify the operations and constraints, then propose a trie (prefix tree) as the core data structure. Explain how insertion and prefix query work in O(L) time, and discuss trade-offs like memory usage and alternative approaches.
Pro tip: Mention that a trie can be optimized with a hash map for children to save space, and that you can early-terminate the query if a word-end marker is found. This shows awareness of practical optimizations beyond the textbook solution.
Ask about the expected number of operations, word lengths, and whether memory is a concern. Confirm that duplicates can be ignored and that the query checks if any stored word is a prefix of the input string.
Explain that a trie stores words character by character, allowing O(L) insertion and O(L) prefix query, where L is the word length. This avoids scanning all stored words.
Describe the trie node structure: a map or array of children and a boolean flag indicating the end of a word. For insertion, traverse or create nodes; for query, traverse the input string and return true if a word-end is encountered.
Compare trie with other approaches like sorting words and binary search, or using a set of prefixes. Highlight trie's efficiency for prefix queries but note its memory overhead, and suggest optimizations like using a hash map for children.
State time complexity: O(L) for both operations. Space complexity: O(total characters stored). Discuss edge cases: empty string, duplicate insertions, and querying a prefix that is also a complete word.
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