Knew the brute force immediately but sat there second-guessing whether to just code it up or explain the optimal path first.
Start by clarifying the problem constraints (e.g., array size, k value, data types) and then propose an efficient solution using a monotonic deque to achieve O(n) time complexity. Explain the algorithm step-by-step, emphasizing how the deque maintains indices of potential maximums, and then discuss edge cases and complexity.
Pro tip: Mention that a naive O(n*k) solution is straightforward but suboptimal; by using a deque, you can achieve O(n) and handle large inputs gracefully. Also, proactively discuss how you would test the solution with edge cases like k=1, k=n, and arrays with negative numbers.
Ask about input size, possible values, and whether the array can be empty or k can be larger than the array. Confirm the expected output format.
Acknowledge the O(n*k) brute-force method, then introduce the monotonic deque approach that processes each element once, achieving O(n) time.
Describe how to maintain a deque of indices where values are in decreasing order. For each element, remove indices out of the window and smaller elements from the back, then add the current index. The front of the deque is the maximum for the current window.
Choose a small array (e.g., [1,3,-1,-3,5,3,6,7] with k=3) and trace the deque operations to demonstrate correctness and build intuition.
State that time complexity is O(n) and space is O(k). Discuss handling k=1, k=n, empty array, and negative numbers, and mention potential pitfalls like integer overflow.
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