I knew this one but still fumbled the explanation a bit.
Start by clarifying edge cases (empty array, single string, empty strings) and then propose a vertical scanning approach: compare characters column by column across all strings until a mismatch is found. This is efficient and easy to reason about, with O(N*M) time and O(1) space where N is the number of strings and M is the length of the shortest string.
Pro tip: Mention that you can optimize by first finding the shortest string to limit comparisons, and discuss trade-offs with other methods like divide-and-conquer or binary search. Also, explicitly state that you would test with edge cases like empty input, single string, and strings with no common prefix.
Ask about input constraints: can the array be empty? Can strings be empty? What should be returned in those cases? Confirm that the function should return an empty string if no common prefix exists.
Select a strategy such as vertical scanning, horizontal scanning, divide-and-conquer, or binary search. Explain why vertical scanning is often preferred for its simplicity and efficiency.
Describe the step-by-step process: iterate over characters of the first string (or shortest string), and for each character, check if all other strings have the same character at that position. Stop at the first mismatch or when a string ends.
State the time complexity: O(N * M) where N is the number of strings and M is the length of the shortest string. Space complexity is O(1) extra space (or O(M) if building the result string).
Walk through a few test cases: e.g., ['flower','flow','flight'] returns 'fl'; ['dog','racecar','car'] returns ''; empty array returns ''; single string returns itself.
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