I kept assuming there had to be a linear solution and burned the entire interview trying to find it.
Start by clarifying the problem: what condition must pairs satisfy, are there duplicates, and what are the input constraints? Then discuss the brute-force nested iteration approach (O(n^2)) and optimize using a hash map or sorting/two-pointer technique to achieve O(n) or O(n log n). Finally, walk through code and analyze time/space complexity.
Pro tip: Always mention the trade-off between time and space: the hash map solution is faster but uses extra memory, while sorting modifies the input and may be preferred if memory is constrained. Also, handle edge cases like empty arrays or no valid pairs.
Ask questions to understand the exact condition (e.g., sum equals target, difference, etc.), input size, data types, and whether the array is sorted or can be modified.
Explain that nested loops can check all pairs in O(n^2) time and O(1) space, which is simple but inefficient for large inputs.
Suggest using a hash map to store seen elements for O(n) time, or sorting followed by two pointers for O(n log n) time if the array can be sorted.
Write clean code for the chosen approach, and test with edge cases like empty array, single element, duplicates, and no solution.
State time and space complexity for each approach, and discuss when to prefer one over the other based on constraints.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.