I got the sliding part pretty quickly but fumbled on efficiently dropping the k largest.
Clarify the problem constraints and edge cases, then propose an efficient algorithm using a sliding window with a data structure that supports fast removal of the k largest elements, such as a max-heap or a balanced BST. Analyze the time and space complexity, and discuss potential optimizations or trade-offs.
Pro tip: Mention that if k is small relative to the window size, a heap-based approach is efficient, but if k is large, consider using order-statistic trees or sorting-based methods. Also, handle edge cases like k >= window size by returning 0 or an empty array.
Ask about constraints: array size, window size, k, possible negative numbers, and what to return if k >= window size. Confirm output format (e.g., floating-point averages).
Propose maintaining a data structure for each window that allows efficient removal of the k largest elements. For example, use a max-heap to extract k largest, then compute the sum of remaining elements.
Discuss how to update the data structure when the window slides: remove the outgoing element and add the incoming element. Consider using a balanced BST or two heaps to maintain order statistics.
Calculate time complexity: O(n * (k log w + w)) if using a heap per window, or O(n log w) with a more advanced structure. Space complexity O(w).
Address cases where k >= window size (return 0), empty array, or window size > array length. Also discuss integer overflow and floating-point precision.
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