My first instinct was a brute force O(n^2) scan and I actually started coding it before catching myself.
Clarify the problem constraints and edge cases, then propose an efficient solution using a sliding window with a monotonic deque to track the min and max in the current window. Explain how the window expands and shrinks to maintain the condition that max - min < N, and analyze the time and space complexity.
Pro tip: Mention that the condition 'difference between any two elements is less than N' is equivalent to max - min < N, and highlight that using two deques gives O(n) time, which is optimal. Also, proactively discuss how to handle negative numbers and large inputs.
Restate the problem in your own words and ask clarifying questions about constraints, input size, and edge cases (e.g., empty array, N <= 0, duplicates).
Start with a brute-force O(n^2) approach to check all subarrays, then identify the inefficiency and propose a sliding window with deques for O(n) time.
Describe how to maintain a window [left, right] and use two deques to track indices of min and max. Expand right, update deques, and while max - min >= N, move left and remove out-of-window indices.
Trace the algorithm on a small example to demonstrate correctness, showing how the window adjusts and the length is updated.
State that each element is added and removed from deques at most once, giving O(n) time and O(n) space. Discuss handling of negative numbers and large N.
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