I jumped straight to the sort-after-squaring approach because my brain went blank on anything cleverer.
Start by clarifying the problem constraints and edge cases, then propose a two-pointer approach that leverages the sorted order to achieve O(n) time. Explain how the largest squares come from the extremes, and walk through the algorithm step-by-step, including handling negatives and duplicates.
Pro tip: Mention that a naive approach of squaring and sorting would be O(n log n), but the two-pointer method is optimal at O(n). Also, discuss how this approach can be extended to handle large inputs or streaming data.
Ask clarifying questions about input size, range of integers, and whether the output should be a new array or in-place. Confirm that the array is sorted in non-decreasing order.
Recognize that squaring preserves order for non-negative numbers but reverses for negatives. Use two pointers starting at both ends to pick the larger square and fill the result array from the end.
Explain the two-pointer process: compare absolute values at left and right, square the larger, place it at the current position in the result, and move the corresponding pointer. Continue until pointers meet.
State that time complexity is O(n) because each element is processed once, and space complexity is O(n) for the output array. Mention that this is optimal since we must examine each element.
Run through a few test cases, including all negatives, all positives, mixed, and duplicates, to verify correctness and edge cases.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.