Solution: Find Median from Data Stream

Explore how to implement a MedianOfStream data structure that efficiently tracks the median as integers are inserted. Learn to use two heaps—a max-heap and a min-heap—to balance dynamically changing data and compute the median in constant time. Understand the time and space complexity tradeoffs for constructions, insertions, and median calculations.

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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: $5$ ...