Find Median from Data Stream

The problem. Design a class MedianFinder for a stream of integers. addNum(num) adds a number. findMedian() returns the median of all numbers added so far: the middle value in sorted order, or the average of the two middle values when the count is even.

The numbers 5, 2, 8, 1 and 9 arrive one by one. Sorted, they read 1, 2, 5, 8, 9, so the median is 5, the middle one. After a sixth number, 3, they read 1, 2, 3, 5, 8, 9 and the median is the average of 3 and 5: 4.

Example

addNum(1)
addNum(2)
findMedian()  ->  1.5      (1 and 2: the average of the two middle values)
addNum(3)
findMedian()  ->  2        (1, 2, 3: the middle value)

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Still to come

1. Brute force: sort on every query
2. Optimal: keep the numbers sorted
The key idea: you only need the two middle values
3. Best solution: two heaps
Comparing the approaches
Edge cases to test
Variations

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Find Median from Data Stream

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