Clarify the problem constraints and edge cases, then propose an optimal solution using a hash map to achieve O(n) time complexity. Walk through the algorithm step-by-step, analyze its time and space complexity, and discuss potential trade-offs with alternative approaches.
Pro tip: At Amazon, emphasize scalability and efficiency: mention that the hash map solution is optimal for large inputs and aligns with Amazon's leadership principles like 'Invent and Simplify' and 'Deliver Results'.
Ask clarifying questions to confirm assumptions: array size, integer range, whether the array is sorted, and if multiple solutions are possible. Confirm that exactly one solution exists and indices cannot be reused.
Mention the naive O(n^2) approach using nested loops to check all pairs, and explain why it's inefficient for large inputs.
Explain using a hash map to store each element's value and index as you iterate. For each element, check if the complement (target - current) exists in the map; if so, return the indices.
State that the hash map solution runs in O(n) time and O(n) space, as each element is processed once and stored in the map.
Discuss edge cases like negative numbers, zero target, and duplicate values. Walk through a small example to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.