Use a two-pointer technique starting from both ends of the sorted array, comparing absolute values and placing the larger square at the end of the result array. For the follow-up, either extend the two-pointer approach to stop at the k-th element or use a binary search on the squared value range to find the k-th smallest square.
Pro tip: Clarify whether the input array can be modified and discuss time/space complexity trade-offs. For the follow-up, mention that binary search on the value range is O(n log(max-min)) but can be optimized to O(n) with a heap or by using the two-pointer method with early termination.
Confirm that the array is sorted, may contain negatives, and that the output should be sorted squares. Discuss edge cases like empty array, all negatives, all positives, and duplicates.
Describe initializing two pointers at the start and end, comparing absolute values, and filling the result array from the end to the beginning. This yields O(n) time and O(n) space.
Propose either modifying the two-pointer approach to stop after k elements or using binary search on the squared value range to count how many squares are ≤ a given value, then find the k-th smallest.
Compare the two-pointer method (O(n) time, O(n) space) with binary search (O(n log(max-min)) time, O(1) space). Mention that for the follow-up, a heap can also be used but may be less efficient.
Implement the chosen solution, handle edge cases, and walk through a few examples to verify correctness. Discuss potential optimizations if needed.
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