LeetCode 295. Find Median from Data Stream数据流的中位数 (C++/Java)

题目：

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

分析：

中位数是有序列表中间的数。如果列表长度是偶数，中位数则是中间两个数的平均值。

很明显我们最好不要每调用一次求中位数函数就重新计算一遍，这样做时间复杂度较高。

 剑指offer中有一道相同的题目，可以参考这篇理解这道题，剑指Offer-63.数据流中的中位数(C++/Java)。

程序：

C++

class MedianFinder {
public:
    /** initialize your data structure here. */
    MedianFinder() {
        index = 0;
    }
    
    void addNum(int num) {
        if(index % 2 == 0){
            minHeap.push(num);
            maxHeap.push(minHeap.top());
            minHeap.pop();
        }
        else{
            maxHeap.push(num);
            minHeap.push(maxHeap.top());
            maxHeap.pop();
        }
        index++;
    }
    
    double findMedian() {
        double res = 0;
        if(index % 2 == 0){
            res = (double)(maxHeap.top() + minHeap.top()) / 2;
            return res;
        }
        else{
            res = (double)maxHeap.top();
            return res;
        }
    }
private:
    priority_queue <int, vector<int>, less<int> > maxHeap;
    priority_queue <int, vector<int>, greater<int> > minHeap;
    int index;
};

Java

class MedianFinder {

    /** initialize your data structure here. */
    public MedianFinder() {
        minHeap = new PriorityQueue<Integer>();
        maxHeap = new PriorityQueue<Integer>(11,new Comparator<Integer>(){
            @Override
            public int compare(Integer i1,Integer i2){
                return i2-i1;
            }
        });
        index = 0;
    }
    
    public void addNum(int num) {
        if(index % 2 == 0){
            minHeap.offer(num);
            maxHeap.offer(minHeap.poll());
        }
        else{
            maxHeap.offer(num);
            minHeap.offer(maxHeap.poll());
        }
        index++;
    }
    
    public double findMedian() {
        double res = 0;
        if(index % 2 == 0){
            res = (minHeap.peek() + maxHeap.peek()) / 2.0;
            return res;
        }
        else{
            res =  maxHeap.peek();
            return res;
        }
    }
    private PriorityQueue<Integer> minHeap;
    private PriorityQueue<Integer> maxHeap;
    private int index;
}