The naive solution is just square everything and sort again, which works but they clearly wanted better.
Start by clarifying the problem and edge cases, then propose a brute-force solution and analyze its complexity. Follow up with an optimal two-pointer approach that leverages the sorted order to achieve O(n) time and O(n) space, and walk through an example to demonstrate correctness.
Pro tip: Explicitly mention that the two-pointer technique works because the largest squares come from the extremes of the sorted array, and offer to code it with clear variable names and comments to show production-quality coding.
Ask about input size, duplicates, negative numbers, and whether the output should be a new array. Confirm the expected time/space complexity.
Mention the naive approach: square each element and sort, which takes O(n log n) time. Acknowledge it's simple but not optimal.
Explain that since the array is sorted, the largest square is at either end. Use two pointers starting at both ends, compare absolute values, and fill the result array from the end to the beginning.
Trace the algorithm on a sample array like [-4, -1, 0, 3, 10] to show how pointers move and the result is built.
State that the optimal solution runs in O(n) time and O(n) space. Mention edge cases: empty array, single element, all negatives, all positives, and zeros.
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