I jumped straight to the hash map approach without asking about negatives or whether multiple valid answers were possible.
Start by clarifying the problem constraints (e.g., input size, whether the array is sorted, if duplicates exist, and if the same element can be used twice). Then propose an optimal solution using a hash map to store seen values and their indices, achieving O(n) time and O(n) space. Walk through the algorithm with a small example, and discuss edge cases and potential optimizations.
Pro tip: Mention that you would first ask about the expected input size and whether the array is sorted, as this determines whether a two-pointer approach (O(n log n) with sorting) or a hash map (O(n)) is more appropriate. Also, explicitly state that you assume exactly one solution exists unless told otherwise, and handle the case where no solution exists by returning an empty result.
Ask about input size, whether the array is sorted, if there are duplicate values, and if the same element can be used twice. Confirm the expected output format (e.g., return indices in any order, or empty array if no pair).
Decide between a hash map (O(n) time, O(n) space) and sorting with two pointers (O(n log n) time, O(1) space). For unsorted arrays, the hash map is generally preferred for its linear time complexity.
Describe the hash map approach: iterate through the array, for each element check if target - element exists in the map. If it does, return the current index and the stored index; otherwise, store the element and its index.
Use a small example (e.g., nums = [2, 7, 11, 15], target = 9) to demonstrate how the algorithm finds the pair (indices 0 and 1). This shows understanding and helps catch off-by-one errors.
Cover edge cases: no solution, duplicate values, negative numbers, and large input. State time and space complexity (O(n) time, O(n) space for hash map) and mention that the solution returns an empty result if no pair is found.
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