I started with the naive backtracking approach, generate every combination then filter against a set.
Clarify the problem constraints, then discuss a backtracking approach that generates all possible letter combinations and checks each against the dictionary. Optimize by using a trie for the dictionary to prune invalid prefixes early, and analyze time and space complexity.
Pro tip: Mention that you can preprocess the dictionary into a trie and then perform DFS on the digit string, pruning branches that don't match any word prefix. This shows you think about efficiency and real-world scalability.
Ask about input size, dictionary size, whether the output should be sorted, and if duplicates are possible. Confirm the mapping of digits to letters.
Explain generating all possible letter combinations using backtracking and then filtering by dictionary lookup. Mention time complexity O(4^n * m) where n is digit length and m is average word length.
Propose building a trie from the dictionary and performing DFS on the digit string, only continuing down paths that are prefixes in the trie. This reduces unnecessary combinations.
Discuss time and space complexity of the optimized solution, and cover edge cases like empty input, no matches, and digits mapping to multiple letters.
Write clean code for the chosen approach, and walk through a test case to verify correctness.
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