295. Find Median from Data Stream

Median is the middle value in an ordered integer list. If the size of the list is even, there is no middle value. So the median is the mean of the two middle value.

Examples: 

[2,3,4] , the median is 3

[2,3], the median is (2 + 3) / 2 = 2.5

Design a data structure that supports the following two operations:

• void addNum(int num) - Add a integer number from the data stream to the data structure.
• double findMedian() - Return the median of all elements so far.

For example:

addNum(1)
addNum(2)
findMedian() -> 1.5
addNum(3) 
findMedian() -> 2

Solution:

We use a max heap to store the values equal or smaller than x, where x is the top of the max heap.

We also use a min heap to store the values bigger than x.

We need to keep the two heap balanced such that we can easily get the median. So the size of max heap will always be equal or larger than the size of min heap.

The time complexity is O(logn) and the space complexity is O(n).



Code:

public class MedianFinder {

    private PriorityQueue<Integer> maxHeap;
    private PriorityQueue<Integer> minHeap;
    /** initialize your data structure here. */
    public MedianFinder() {
        maxHeap = new PriorityQueue<>(Collections.reverseOrder());
        minHeap = new PriorityQueue<>();
    }
    
    public void addNum(int num) {
        maxHeap.offer(num);
        minHeap.offer(maxHeap.poll());
        if (maxHeap.size() < minHeap.size()) {
            maxHeap.offer(minHeap.poll());
        }
    }
    
    public double findMedian() {
        if (maxHeap.size() == minHeap.size()) {
            return 0.5 * (maxHeap.peek() + minHeap.peek());
        }
        return maxHeap.peek();
    }
}

/**
 * Your MedianFinder object will be instantiated and called as such:
 * MedianFinder obj = new MedianFinder();
 * obj.addNum(num);
 * double param_2 = obj.findMedian();
 */