I went straight to backtracking and it felt fine.
Use a backtracking (recursive) approach to build combinations digit by digit, mapping each digit to its corresponding letters. Start with an empty combination, iterate through the letters for the current digit, and recurse to the next digit. Handle edge cases like empty input and digits '1' or '0' which have no letters.
Pro tip: Clarify upfront that digits 1 and 0 have no letters and that an empty input should return an empty list, not a list with an empty string. This shows attention to detail and prevents incorrect assumptions.
Confirm the mapping of digits to letters (standard phone keypad), and ask about handling of digits 1 and 0, empty input, and whether the output should be sorted or not.
Select backtracking as the optimal approach, explaining that it explores all combinations efficiently by building the solution incrementally.
Write a recursive function that takes the current index and the current combination string. At each step, iterate over the letters for the current digit and recurse to the next index.
State that the time complexity is O(4^n * n) where n is the number of digits (since each digit maps to at most 4 letters), and space complexity is O(n) for recursion depth plus output storage.
Walk through a simple example like '23' to verify the output, and test edge cases such as empty string and digits with no letters.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.