Maintain median of a data stream

Q: Maintain median of a data stream

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Question

Design a data structure that supports:

addNum(int x) : Add an integer from a stream.
findMedian() : Return the median of all inserted numbers so far.

Median definition:

If the count is odd: the middle element after sorting.
If the count is even: average of the two middle elements.

Requirements

Aim for O(log n) per insertion and O(1) (or O(log n) ) per median query.
Implement in C++.

Constraints

Up to ~10^5 insertions/queries.
Values may be negative and can repeat.

Maintain median of a data stream

Requirements

Constraints

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