Solution: Find Median from Data Stream

Explore how to implement a MedianOfStream class that dynamically stores integers and finds the median efficiently. Understand the optimized approach using max and min heaps to maintain balanced halves for quick median computation. Learn the time and space complexity implications for each operation in this approach.

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Statement
Solution
- Naive approach
- Optimized approach using heaps

Statement

Design a data structure that stores a dynamically changing list of integers and can find the median in constant time, $O(1)$ , as the list grows. To do that, implement a class named MedianOfStream with the following functionality:

Constructor(): Initializes an instance of the class.
insertNum(int num): Adds a new integer num to the data structure.
findMedian(): Returns the median of all integers added so far.

Note: The median is the middle value in a sorted list of integers.
For an odd-sized list (e.g., $[4, 5, 6]$ ), the median is the middle element: $5$ .
For an even-sized list (e.g., $[2, 4, 6, 8]$ ), the median is the average of the two middle elements: $(4 + 6) / 2 = 5$ .

Constraints: