牛客网剑指offer-数据流中的中位数

题目描述

如何得到一个数据流中的中位数？如果从数据流中读出奇数个数值，那么中位数就是所有数值排序之后位于中间的数值。如果从数据流中读出偶数个数值，那么中位数就是所有数值排序之后中间两个数的平均值。

class Solution {
public:
    //思路就是把数据分半,前半部分用最大堆，后半部分用最小堆
    //然后中位数，就是堆顶数中做运算
    void Insert(int num)
    {
        if (MaxHeap.empty())
            pushMax(num);
        else
        {
            int d = MaxHeap.size() - MinHeap.size();
            if (num <= MaxHeap[0])
            {
                pushMax(num);
                if (d == 1)
                {
                    int x = MaxHeap[0];
                    popMax();
                    pushMin(x);
                }
            }
            else
            {
                pushMin(num);
                if (d == -1)
                {
                    int x = MinHeap[0];
                    popMin();
                    pushMax(x);
                }
            }
        }
    }

    double GetMedian()
    { 
        if (MaxHeap.size() == 0 && MinHeap.size() == 0)
            return 0;
        int d = MaxHeap.size() - MinHeap.size();
        double ans = 0;
        if (d == 0)
            ans = (MaxHeap[0] + MinHeap[0])/2.0;
        else if (d == 1)
            ans = MaxHeap[0];
        else
            ans = MinHeap[0];
        return ans;
    }
private:
    vector<int> MaxHeap, MinHeap;
    void pushMax(int num)
	{
		MaxHeap.push_back(num);
		push_heap(MaxHeap.begin(), MaxHeap.end(), less<int>());
	}
	void popMax()
	{
		pop_heap(MaxHeap.begin(), MaxHeap.end(), less<int>());
		MaxHeap.pop_back();
	}
	void pushMin(int num)
	{
		MinHeap.push_back(num);
		push_heap(MinHeap.begin(), MinHeap.end(), greater<int>());
	}
	void popMin()
	{
		pop_heap(MinHeap.begin(), MinHeap.end(), greater<int>());
		MinHeap.pop_back();
	}
};