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

可以采用两个优先队列，第一个存放所有小于中间元素的元素，第二个存放大于中间元素的元素；

class MedianFinder {
public:
    /** initialize your data structure here. */
    private:
    priority_queue<int, vector<int>, less<int>> res1;//大顶堆
    priority_queue<int, vector<int>, greater<int>> res2;//小顶堆
    public:

    MedianFinder() {

    }

    void addNum(int num) {
        //保证大顶堆中的所有元素小于小顶堆中的所有元素；
        if (res1.empty() || num <= res1.top())res1.push(num);
        else res2.push(num);
        //调整两个堆的大小，使得大顶堆和小顶堆各含有一半元素，若元素总数为奇数，则将中位数存放在大顶堆中；
        if (res1.size() + 1 == res2.size())res1.push(res2.top()), res2.pop();
        if (res1.size() == res2.size() + 2)res2.push(res1.top()), res1.pop();
    }

    double findMedian() {
        return (res1.size() == res2.size()) ? (res1.top() + res2.top()) / 2.0 : res1.top();
    }
};