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;
}