I knew this problem but still fumbled the explanation a bit.
Start by clarifying the problem constraints (e.g., exactly one solution, cannot use same element twice, return indices in any order). Then present the optimal hash map solution: iterate through the array, for each element check if target minus element exists in the map, and if so return the indices; otherwise store the element and its index. Discuss time and space complexity (O(n) time, O(n) space) and compare with brute force (O(n^2)).
Pro tip: Mention that while the hash map solution is optimal for unsorted arrays, if the array is sorted you could use two pointers for O(1) space. Also, briefly discuss edge cases like duplicate values and negative numbers to show thoroughness.
Ask if the array is sorted, if there is exactly one solution, if the same element can be used twice, and what to return if no solution exists. This shows attention to detail.
Mention the naive O(n^2) solution using nested loops to establish a baseline, but note it's inefficient for large datasets.
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) is in the map; if yes, return the indices.
State time complexity O(n) and space complexity O(n). Discuss handling duplicates, negative numbers, and no solution scenario.
Write clean code (in a language of choice) and walk through a simple example like [2,7,11,15], target=9 to verify correctness.
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