I knew the two-pointer approach going in, but I fumbled the initialization for a second because I kept second-guessing which end to write into first.
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. This achieves O(n) time and O(n) space without explicitly sorting.
Pro tip: Clarify that the input array is sorted in non-decreasing order and may contain negative numbers; the key insight is that the largest squared values come from the extremes. Mention that you can optimize space by reusing the input array if allowed, but typically a new array is required.
Confirm that the array is sorted, may contain negatives, and that the output must be in non-decreasing order of squares. Note the linear time requirement.
Recognize that the largest square must come from either the leftmost (most negative) or rightmost (most positive) element. Use two pointers to compare absolute values.
Set left pointer at 0, right pointer at n-1, and create a result array of size n. Use a write pointer starting at n-1 to fill from the end.
While left <= right, compare absolute values of elements at left and right. Place the larger square at the write position, move the corresponding pointer, and decrement write position.
After the loop, the result array contains squares in non-decreasing order. Return it.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This one I actually had pre-thought, so it went smoother.
First, clarify that the input is a sorted array of integers (possibly negative) and we need the K-th smallest square. Then propose a two-pointer approach from both ends to generate squares in sorted order, or a binary search on the value range to count how many squares are ≤ a candidate. Discuss trade-offs between O(n) time with O(1) space (two-pointer) and O(n log n) time with O(1) space (binary search).
Pro tip: Mention that the two-pointer method can be adapted to find the K-th smallest without generating all squares by stopping early, but binary search is often simpler to reason about and avoids potential off-by-one errors. Also, consider edge cases like duplicate squares and negative numbers.
Confirm that the input array is sorted in non-decreasing order, may contain negative numbers, and that K is 1-indexed. Ask about the expected time/space complexity and whether duplicates are allowed.
Mention that computing all squares, sorting them, and picking the K-th element takes O(n log n) time and O(n) space, which is suboptimal. This sets the stage for better approaches.
Use two pointers starting at both ends of the array, compare absolute values, and generate squares in non-decreasing order. To find the K-th smallest, you can either generate all squares and pick the K-th (O(n) time, O(n) space) or use a modified approach to stop after K steps (O(K) time, O(1) space if not storing all).
The K-th smallest square lies between 0 and max(|first|, |last|)^2. Binary search on the value, and for each candidate, count how many squares are ≤ candidate using two pointers. Adjust the search range based on the count. This takes O(n log(max_value)) time and O(1) space.
Highlight that the two-pointer method is optimal for small K, while binary search is better when K is large or when we want a predictable O(n log M) time. Choose based on constraints and mention potential optimizations like early termination.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.