I knew sliding window was the right direction but fumbled on how to track min and max efficiently inside the window.
Use a sliding window with two monotonic deques to maintain the min and max in the current window, expanding the right pointer and shrinking the left when the difference exceeds the limit. This yields O(n) time and O(n) space, which is optimal for this problem.
Pro tip: Mention that the monotonic deque approach is preferred over a heap-based solution because it achieves O(n) time and avoids O(log n) operations, and clarify that the absolute difference condition is equivalent to max - min <= limit.
Confirm that the subarray must be contiguous, the limit is inclusive, and discuss edge cases like empty array or limit < 0. Ask about input size to determine if O(n) is necessary.
Briefly describe checking all subarrays in O(n^2) time to establish a baseline, then explain why it's inefficient for large inputs.
Explain that you'll maintain two deques: one for minimum and one for maximum in the current window. Expand the right pointer, update deques, and shrink from the left while max - min > limit.
Trace the algorithm on a small array to demonstrate correctness. State that each element is added and removed at most once, giving O(n) time and O(n) space.
Compare with a heap-based approach (O(n log n)) or a balanced BST, and mention that the deque method is optimal for this problem. Also note that if the array is sorted, a simpler two-pointer approach works.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.