Start by clarifying the problem constraints and edge cases, then propose an efficient solution using a hash map to store complements. Walk through the algorithm step-by-step, analyze its time and space complexity, and optionally discuss alternative approaches like sorting with two pointers.
Pro tip: Mention that the hash map approach is optimal for unsorted arrays, but if the array is sorted, a two-pointer approach can achieve O(1) space. This shows you consider trade-offs and adapt to constraints.
Ask about input size, whether the array is sorted, if there are duplicate values, and if the solution must be unique. Confirm that exactly one solution exists and elements cannot be reused.
Describe using a hash map to store each element's value and index as you iterate. For each element, check if its complement (target - current) exists in the map; if so, return the indices.
Trace the algorithm on a small example, such as nums = [2, 7, 11, 15], target = 9, to demonstrate correctness and clarity.
State that the time complexity is O(n) because each element is processed once, and space complexity is O(n) for the hash map in the worst case.
Mention that a brute-force approach is O(n^2) and inefficient. If the array is sorted, a two-pointer approach uses O(1) extra space but requires sorting (O(n log n) time) or assumes sorted input.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.