Two heaps, max-heap for the lower half and min-heap for the upper half.
Use two heaps (a max-heap for the lower half and a min-heap for the upper half) to maintain the median in O(log n) insertion and O(1) retrieval. Explain the balancing logic and how to handle even and odd total counts.
Pro tip: Mention that this approach is optimal for streaming data and discuss potential follow-ups like handling duplicates or memory constraints, showing you think beyond the basic implementation.
Ask about input constraints, expected time complexity, and whether the median should be returned as a float or integer. Confirm if the stream is unbounded.
Describe using a max-heap for the lower half and a min-heap for the upper half. Explain that the heaps are kept balanced such that their sizes differ by at most one.
Explain the addNum operation: insert into the appropriate heap, then rebalance by moving the top element if sizes differ by more than one. Ensure the max-heap's top is <= min-heap's top.
If both heaps are equal size, median is the average of their tops; otherwise, it's the top of the larger heap. Emphasize O(1) time.
State that insertion is O(log n) and retrieval is O(1). Discuss edge cases like empty stream, single element, and duplicate values.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the problem constraints (e.g., what 'extremely large' means, whether the stream is sorted, memory limits, and what exactly needs to be optimized). Then propose optimizations that exploit duplicates, such as using a hash map to count frequencies and a heap of unique elements, or a streaming algorithm like Misra-Gries for approximate top-k. Discuss trade-offs between exactness, memory, and speed, and tie your answer to Tinder's scale and real-time needs.
Pro tip: Mention that in many real-world systems, approximate answers with bounded error (e.g., using Count-Min Sketch) are acceptable and far more scalable than exact solutions—showing you understand practical trade-offs beyond textbook algorithms.
Ask about stream size, memory limits, whether exact or approximate results are needed, and if the stream is sorted or has any known distribution. This ensures you optimize for the right objective.
Explain that two heaps store every element, leading to O(n) memory and O(log n) per insertion, which is wasteful when many duplicates exist. Also, heaps don't naturally handle duplicates efficiently.
Suggest using a hash map to count frequencies of unique elements, then maintain a heap (or sorted structure) of unique elements with their counts. This reduces memory to O(u) where u is the number of unique elements, and each insertion updates a count in O(1) average time.
If memory is still a bottleneck, introduce approximate algorithms like Misra-Gries or Count-Min Sketch for frequent items, or reservoir sampling for random sampling. Discuss error bounds and probabilistic guarantees.
Compare exact vs. approximate, memory vs. accuracy, and implementation complexity. Recommend a solution based on the specific constraints, and mention how it could be distributed (e.g., using MapReduce or streaming frameworks like Flink).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.