Cracking the Code Interview (1): 跟踪数组的中位数

题目：

随机生成一些数字，并保存到一个（可扩展的）数组中，如何跟踪数组的中位数？

题解：

用multiset分别实现最大堆和最小堆，最大堆保存数组的前半部分，最小堆保存数组的后半部分，每次添加新数字时和堆顶元素比较。同时保证两个堆的元素个数之差不超过1.

////  main.cpp//  Combination////  Created by  on 14-2-3.//  Copyright (c) 2014年 . All rights reserved.//#include <iostream>#include <string>#include <vector>#include <set>#include <cstdlib>#include <ctime>using namespace std;typedef struct {    bool operator()( int i, int j) {        return i < j;    }} Increase;typedef struct {    bool operator()( int i, int j) {        return i >= j;    }} Decrease;typedef multiset<int, Increase> minHeap;typedef multiset<int, Decrease> maxHeap;class Solution {public:    void FindMedian()    {        cout << "Please enter the number of integers in your array:";        int count;        cin >> count;        int i = 0;        srand(static_cast<unsigned int>(time(0)));        maxHeap heap1;        minHeap heap2;        while( i < count )        {            int temp = rand()%100;            cout << temp  << " is added into the integer array" << endl;            if(!heap1.size() && !heap2.size())            {                heap1.insert(temp);                i++;                continue;            }            if(temp > *heap1.begin())            {                heap2.insert(temp);                if(static_cast<int>(heap1.size() - heap2.size()) >= 2)                {                    int temp = *heap1.begin();                    heap1.erase(heap1.begin());                    heap2.insert(temp);                }                else if(static_cast<int>(heap2.size() - heap1.size()) >= 2)                {                    int temp = *heap2.begin();                    heap2.erase(heap2.begin());                    heap1.insert(temp);                }            }            else{                heap1.insert(temp);                if(static_cast<int>(heap1.size() - heap2.size()) >= 2)                {                    int temp = *heap1.begin();                    heap1.erase(heap1.begin());                    heap2.insert(temp);                }                else if(static_cast<int>(heap2.size() - heap1.size()) >= 2)                {                    int temp = *heap2.begin();                    heap2.erase(heap2.begin());                    heap1.insert(temp);                }            }                        cout << "Intergers in the first heap (max heap) are:";            for(auto iter: heap1)                cout << iter << " ";            cout << endl;                        cout << "Intergers in the second heap (max heap) are:";            for(auto iter: heap2)                cout << iter << " ";            cout << endl;                        cout << "The median of the entire integer array is: ";            if( heap1.size() > heap2.size())                cout << *heap1.begin() << endl << endl;            else if(heap1.size() < heap2.size())                cout << *heap2.begin() << endl << endl;            else                cout << (*heap1.begin() + *heap2.begin())/2 << endl << endl;            i++;        }            }    };int main(int argc, const char * argv[]){    // insert code here...10        Solution a;    a.FindMedian();    return 0;}