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.

For example,

[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.

Example:

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

Follow up:

1. If all integer numbers from the stream are between 0 and 100, how would you optimize it?
2. If 99% of all integer numbers from the stream are between 0 and 100, how would you optimize it?

用两个heap（min heap和max heap），较小的一半元素放进max heap，较大的一半元素放进min heap，两个heap的size之差不超1，最后的答案在两个堆顶元素中产生（min heap的最小值 -> 较大数里的最小值，max heap的最大值 -> 较小数里的最大值）。在平衡两个heap的大小时，如果大小之差=2了，把元素多的堆的堆顶元素弹出并加入到元素少的堆里。

时间：O(logN) add element into heap + O(1) compute median -> O(NlogN)，空间：O(N)

class MedianFinder {

    /** initialize your data structure here. */
    PriorityQueue<Integer> minHeap;
    PriorityQueue<Integer> maxHeap;
    
    public MedianFinder() {
        minHeap = new PriorityQueue<>();
        maxHeap = new PriorityQueue<>((a, b) -> b - a);
    }
    
    public void addNum(int num) {
        if(maxHeap.isEmpty() || num <= maxHeap.peek())
            maxHeap.add(num);
        else
            minHeap.add(num);
        
        if(maxHeap.size() - minHeap.size() == 2)
            minHeap.add(maxHeap.poll());
        else if(minHeap.size() - maxHeap.size() == 2)
            maxHeap.add(minHeap.poll());
    }
    
    public double findMedian() {
        if(minHeap.size() > maxHeap.size())
            return (double)minHeap.peek();
        else if(maxHeap.size() > minHeap.size())
            return (double)maxHeap.peek();
        else
            return (double)(minHeap.peek() + maxHeap.peek()) / 2;
    }
}

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