Started with the nested loop approach just to show I understood the baseline, then moved to the hash map version where you check the complement on each pass.
Start by clarifying the problem constraints (e.g., exactly one solution, can't use same element twice, return any valid pair). Then present a brute-force O(n²) solution using nested loops, followed by an optimized O(n) solution using a hash map. Finally, discuss follow-up variants by explaining how the approach changes for duplicates, sorted arrays, or counting all pairs.
Pro tip: Always clarify assumptions and edge cases before coding; for example, ask if the array is sorted, if there are duplicates, or if multiple pairs exist. This shows you think like a production engineer, not just a competitive programmer.
Ask questions to understand constraints: input size, sortedness, duplicates, multiple solutions, and whether indices or values are needed. Confirm that each element can be used only once.
Explain the O(n²) solution: iterate over each element and check every other element for a complement. Mention its simplicity but inefficiency for large inputs.
Describe the O(n) solution: use a hash map to store each element's index as you iterate. For each element, check if target - element exists in the map; if so, return the pair.
Compare time/space complexity of both approaches. Highlight that the hash map uses O(n) extra space but is faster. Mention edge cases like empty array, no solution, or negative numbers.
Explain how to handle duplicates (store list of indices or count frequencies), sorted arrays (two-pointer technique), and counting all pairs (use frequency map and combinatorics).
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