Solution: Find Median from Data Stream

Explore how to implement a data structure that maintains a dynamic list of integers and finds the median in constant time using two heaps. Learn to insert numbers, balance heaps, and calculate medians with optimized time complexity, as well as understand the trade-offs in different approaches.

We'll cover the following...

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: $5$ ...