The naive approach is obvious and I almost went with it just to get something on the board.
Start by clarifying the problem constraints (e.g., array size, window size, data types) and then propose an efficient solution using a deque to maintain indices of potential maximums in O(n) time. Explain the algorithm step-by-step, emphasizing how the deque maintains a decreasing order of values and removes out-of-window indices.
Pro tip: Mention that while a naive O(n*k) solution is straightforward, the optimal O(n) deque approach is preferred for large inputs, and discuss trade-offs such as memory usage and edge cases like k=1 or k=n.
Ask about input size, window size range, data types, and whether the array can be empty. Confirm expected output format (e.g., array of maximums).
Mention the O(n*k) brute-force method, then introduce the O(n) deque-based solution. Explain why the deque approach is more efficient.
Describe how to maintain a deque of indices where values are in decreasing order. For each element, remove indices out of the window from the front, remove smaller elements from the back, then add the current index. The front is the maximum.
Choose a small array and window size, and step through the algorithm to demonstrate correctness and how the deque updates.
State time and space complexity (O(n) time, O(k) space). Discuss edge cases: k=1, k=n, empty array, negative numbers, and large inputs.
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