Problem Description

Design a data structure that efficiently supports two operations:

• addNum(int x): Adds an integer x from a continuous stream of data.
• findMedian(): Returns the median of all integers added to the data structure so far.

Median Definition

• If the total count of numbers is odd, the median is the middle element after sorting.
• If the total count of numbers is even, the median is the average of the two middle elements after sorting.

Performance Requirements

• The addNum operation should aim for an average time complexity of O(log n), where n is the number of elements currently in the data structure.
• The findMedian operation should aim for an average time complexity of O(1) or O(log n).

Constraints

• The total number of addNum and findMedian operations can be up to approximately 10^5.
• Input integers (x) can be negative, positive, or zero, and duplicate values are allowed.
• The implementation should be in C++.