My first instinct was brute force and I actually coded it up before catching myself.
Clarify the problem and edge cases, then propose an efficient solution using a sliding window with two monotonic deques to track the min and max in O(n) time. Explain the algorithm step-by-step, analyze its complexity, and test with examples.
Pro tip: Mention that a naive O(n^2) approach would be too slow for large inputs, and that the monotonic deque technique is a common pattern for sliding window min/max problems. Also, discuss how you would handle edge cases like k <= 0 or empty arrays.
Restate the problem in your own words, ask clarifying questions about input constraints, and confirm edge cases (e.g., k <= 0, empty array, no valid subarray).
Acknowledge that checking all subarrays is O(n^2) and too slow; then introduce the sliding window with monotonic deques to achieve O(n).
Detail how to maintain two deques for min and max, expand the right pointer, and shrink the left pointer while the condition holds, updating the minimum length.
State that time complexity is O(n) and space is O(n) in the worst case; discuss handling of negative numbers and large k.
Walk through a small example to demonstrate correctness, and consider edge cases like k=0 or no valid subarray.
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