Seems easy until you remember negative numbers exist.
Clarify the problem constraints (e.g., array size, element range, duplicates) and discuss edge cases. Then explain that the maximum product can come from either the two largest positive numbers or the two smallest negative numbers (if their product is positive). Present an O(n) solution that finds the top two maximums and bottom two minimums in a single pass.
Pro tip: Always consider negative numbers—many candidates forget that two large negatives yield a positive product. Also, mention that sorting is O(n log n) but a linear scan is more efficient and shows deeper understanding.
Ask about array size, possible values (negatives, zeros, duplicates), and whether the pair must be distinct indices. Discuss edge cases like arrays with fewer than two elements.
Explain that the maximum product is either the product of the two largest numbers or the two smallest numbers (most negative). This covers all possibilities.
Propose a single-pass O(n) solution that tracks the two largest and two smallest elements. Alternatively, mention sorting as a simpler O(n log n) approach but highlight the linear solution's efficiency.
Walk through examples including all positive, all negative, mixed, and arrays with zeros. Ensure the algorithm correctly returns the pair and handles duplicates.
State time and space complexity (O(n) time, O(1) space for the linear approach). Discuss trade-offs between sorting and linear scan in terms of simplicity and performance.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.