The core idea clicked pretty fast for me, you want a sliding window but maintaining the running min and max efficiently is where it gets annoying.
Clarify the problem and constraints, then propose an efficient solution using a sliding window with two monotonic deques to track min and max in O(n) time. Walk through the algorithm, analyze complexity, and provide test cases including edge cases and large inputs.
Pro tip: Mention that a naive O(n^2) approach is too slow for n=10^5, and emphasize that the monotonic deque solution is optimal because each element is added and removed at most once. Also, proactively discuss how to handle duplicates and negative numbers.
Confirm the definition of subarray (contiguous), the condition (max - min >= k), and the expected input size (up to 10^5). Ask about edge cases like k <= 0 or no valid subarray.
Describe a sliding window approach with two monotonic deques to maintain the min and max of the current window. Explain how to expand the right pointer and shrink the left pointer when the condition is met.
State that each element is added and removed from each deque at most once, giving O(n) time. Space is O(n) for the deques in the worst case.
Include at least three test cases: a small array with a valid subarray, an array with no valid subarray, and a large array of length 10^5 (e.g., random or increasing) to demonstrate efficiency.
Mention alternative approaches (e.g., sorting, binary search) and why they are less efficient. Address edge cases like k <= 0, empty array, and all elements equal.
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