Maintain the Median of an Integer Stream with Two Heaps

Support addNum(value), which adds an integer to a stream, and findMedian(), which returns the median of all values received so far. For an even count, return the arithmetic mean of the two middle values. ### Constraints and Clarifications The source names the standard data-stream median problem and asks heap follow-ups. Use the [official reference](https://leetcode.com/problems/find-median-from-data-stream/description/) for the practice interface: values between-100000 and100000, at most50000 operations, and at least one value before every median query. These bounds are reference context, not separately recalled interview constraints. Serialized add operations emit null; queries emit numeric medians. The reference accepts absolute error within1e-5, though integer and half-integer medians in this domain are exactly representable in ordinary binary floating point. ### What a Strong Answer Covers Maintain a max-heap for the lower half and a min-heap for the upper half, prove ordering and balance invariants, and explain insertion and query complexity. ### Follow-up Questions - What heap operations are required, and why are they logarithmic? - Does the two-heap method use bounded memory for an arbitrarily long stream?