The naive approach of just grabbing the last N elements and sorting them every time is obviously too slow given the constraints.
Clarify the requirements first, especially the definition of 'most recent N comments' and whether N is fixed or variable. Then propose a solution using two heaps (max-heap for lower half, min-heap for upper half) to maintain the median in O(log N) per insertion, with a queue to track the sliding window of N comments. Discuss trade-offs between this approach and alternatives like balanced BSTs or order-statistic trees, and handle edge cases like even/odd counts and duplicate ratings.
Pro tip: Mention that you would use lazy deletion to handle expired comments from the sliding window, avoiding O(N) removal from heaps. Also, proactively discuss how to handle ties and the median definition for even counts (average of two middle values).
Ask about the expected volume of comments, whether N is fixed or can change, and the definition of median for even counts. Confirm if ratings are integers and if there are any memory constraints.
Describe using two heaps: a max-heap for the lower half and a min-heap for the upper half, keeping their sizes balanced. This allows O(log N) insertion and O(1) median retrieval.
Use a queue to track the order of comments. When a new comment arrives, add it to the heaps and enqueue it; if the queue size exceeds N, remove the oldest comment from the heaps (using lazy deletion) and dequeue it.
Explain how to handle expired comments that are still in the heaps: maintain a count of invalid entries and skip them when they reach the top during rebalancing or median retrieval.
Compare with other approaches like balanced BSTs (e.g., order-statistic tree) or Fenwick trees over a rating range. Highlight time/space complexity and suitability for streaming data.
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