Clarify the problem requirements first, then propose an efficient solution using a hash map to store runtimes and their indices, allowing a single-pass O(n) time and O(n) space algorithm. Walk through the algorithm with an example, discuss trade-offs with brute force, and handle edge cases like no solution or duplicate runtimes.
Pro tip: Demonstrate Amazon Leadership Principles by proactively discussing trade-offs (e.g., time vs. space) and asking clarifying questions about input constraints and expected output format. This shows customer obsession and ownership.
Ask the interviewer to confirm the output format (indices or runtimes), whether the list can contain duplicates, and if a solution is guaranteed to exist.
Mention the brute force O(n^2) approach and then propose the optimal O(n) hash map solution, explaining why it's better.
Describe the single-pass hash map algorithm: iterate through the list, for each runtime check if its complement (flight duration - runtime) exists in the map; if yes, return indices; else store the runtime and index.
Use a concrete example (e.g., runtimes [90, 120, 150], flight duration 240) to illustrate how the algorithm finds the pair.
State time and space complexity (O(n) each) and discuss edge cases: no solution, multiple solutions, duplicate runtimes, and negative or zero durations.
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