The brute force answer comes out naturally but you have to get to the HashMap solution on your own.
Start by clarifying the problem constraints and edge cases, then propose a brute-force solution and analyze its inefficiency. Introduce the optimal hash map approach, explaining how it reduces time complexity to O(n) by trading space for time. Walk through a concrete example to demonstrate correctness and discuss potential trade-offs.
Pro tip: Mention that the hash map approach can be done in a single pass, and highlight that you would handle edge cases like duplicate values or negative numbers gracefully. This shows attention to detail and real-world robustness.
Ask about input size, whether the array is sorted, if there are duplicate values, and if the solution can be returned in any order. Confirm that exactly one solution exists and elements cannot be reused.
Describe the naive O(n^2) solution using nested loops to check all pairs. Acknowledge its simplicity but highlight inefficiency for large inputs.
Explain how to use 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 time complexity is O(n) and space complexity is O(n) due to the hash map. Compare with brute-force O(n^2) time and O(1) space, and justify why the hash map is preferable for large n.
Use a sample array like [2, 7, 11, 15] with target 9 to demonstrate the algorithm. Mention edge cases such as negative numbers, duplicates, and the need to avoid using the same element twice.
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