随机提取中位数

题目：Numbers are randomly generated and stored into an (expanding) array. How would you keep track of the median?

思路分析：使用两个堆，一个最大堆（存储小于中位数的一半的元素），一个最小堆（存储大于中位数的一半的元素），只要维护好这两个堆，根据堆顶元素就能得到中位数。我们的程序保证左右两个堆的元素个数差不能超过1，设最大堆堆顶元素为x1，最小堆堆顶元素为x2，则若插入元素x>x2,则将该元素插入最小堆中，若最小堆元素个数-最大堆元素个数>1，将最小堆堆顶元素弹出到最大堆中去；若x1<=x<=x2，插入任意一个堆中；若x<x1，同x>x2的情况。

#include<iostream>#include<queue>using namespace std;//最后的> >中间要有一个空格，避免被编译器理解为移位操作//大顶堆 priority_queue<int,vector<int>,less<int> > maxheap;//小顶堆 priority_queue<int,vector<int>, greater<int> > minheap;void insert(int x){//insert into any heapif(maxheap.size()==0&&minheap.size()==0)maxheap.push(x);//rebalance it else if(maxheap.size()==0&&minheap.size()==1){if(x>minheap.top()){maxheap.push(minheap.top());minheap.pop();minheap.push(x);}else{maxheap.push(x);}}//rebalance itelse if(maxheap.size()==1&&minheap.size()==0){if(x<maxheap.top()){minheap.push(maxheap.top());maxheap.pop();maxheap.push(x);}else{minheap.push(x);}}//insertelse{if(x>minheap.top()){minheap.push(x);if(minheap.size()-maxheap.size()>1){int tmp=minheap.top();minheap.pop();maxheap.push(tmp);}}else if(x<maxheap.top()){maxheap.push(x);if(maxheap.size()-minheap.size()>1){int tmp=maxheap.top();maxheap.pop();maxheap.push(tmp);}}else{//插入任意一个 if(maxheap.size()==minheap.size()){maxheap.push(x);}else if(maxheap.size()-minheap.size()==1){minheap.push(x);}else{maxheap.push(x);}}}}int getMid(){if(minheap.size()-maxheap.size()==1)    return minheap.top();else if(maxheap.size()-minheap.size()==1)return maxheap.top();elsereturn min(maxheap.top(),minheap.top());//这一句很重要，可能出现最大堆是：5 5 最小堆是：6 6 这种情况，我们必须取两者中的最小值。}