Use a backtracking (DFS) approach to build combinations digit by digit, leveraging a mapping from digits to letters. Start with an empty string, iterate through each digit's letters, and recurse to the next digit until the combination length equals the input length. Collect and return all combinations.
Pro tip: Clarify edge cases upfront (empty input, '1' or '0') and discuss iterative BFS as an alternative to recursion, showing awareness of trade-offs. Also, mention that the maximum input length is 4, so the solution is efficient without optimization.
Confirm the digit-to-letter mapping (standard phone keypad) and handle edge cases: empty string, digits '1' or '0' (which have no letters), and maximum length 4. Ask if the output order matters.
Select backtracking (DFS) for simplicity and clarity, or BFS for an iterative solution. Explain the choice and its time/space complexity.
Write code: define the mapping, then recursively build combinations by appending each letter for the current digit and moving to the next digit. Base case: when the current combination length equals the input length, add to results.
Walk through the example '23' to show the recursion tree and verify output. Test edge cases like empty string and single digit.
State time complexity O(4^n * n) where n is input length (max 4), and space O(n) for recursion stack. Discuss potential optimizations if needed.
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