最大子序列和

#include "stdafx.h"
#include <iostream>
#include <vector>
using namespace std;
int flag = 0;
long maxsum(const vector<int>& a)//时间复杂度O（n3）
{
    if (flag == 0)
    {
        return 0;
    }
    long maxsum = 0;
    for (int i = 0; i < a.size(); i++)
    {
        for (int j = i; j < a.size(); j++)
        {
            long thissum = 0;
            for (int k = i; k <= j; k++)
            {
                thissum += a[k];

            }
            if (thissum>maxsum)
                maxsum = thissum;
        }
    }
    return maxsum;
}
long maxsum2(const vector<int>& a)//时间复杂度O（n2）
{
    if (flag == 0)
    {
        return 0;
    }
    long maxsum = 0;
    for (int i = 0; i < (int)a.size(); i++)
    {
        long thissum = 0;
        for (int j = i; j < (int)a.size(); j++)
        {
            thissum += a[j];
            if (thissum > maxsum)
                maxsum = thissum;
        }
    }
    return maxsum;
}
long maxsum3(const vector<int>& a)//时间复杂度O（n）
{
    if (flag == 0)
    {
        return 0;
    }
    long maxsum = 0, thissum = 0;
    for (int i = 0; i < (int)a.size(); i++)
    {
            thissum += a[i];

            if (thissum > maxsum)
                maxsum = thissum;
            else if (thissum < 0)
            {
                thissum = 0;
            }
        }
    return maxsum;
}
long maxsum4(const vector<int>& a,int left,int right) //时间复杂度n*log（n）
{
    if (flag == 0)
    {
        return 0;
    }
    if (left == right)
    {
        if (a[left] > 0)
        {
            return a[left];
        }
        else
        {
            return 0;
        }
        
    }
    int center = (left + right) / 2;
    long maxleftsum = maxsum4(a, left, center);
    long maxrightsum = maxsum4(a, center + 1, right);

    long LBorder_maxsum = 0, LBorder_thissum = 0;
    for (int i = center; i >= left; i--)
    {
        LBorder_thissum += a[i];
        if (LBorder_thissum > LBorder_maxsum)
        {
            LBorder_maxsum = LBorder_thissum;
        }
    }
    long RBorder_maxsum = 0, RBorder_thissum = 0;
    for (int j = center + 1; j <= right; j++)
    {
        RBorder_thissum += a[j];
        if (RBorder_thissum > RBorder_maxsum)
        {
            RBorder_maxsum = RBorder_thissum;
        }
    }

    if (maxleftsum < maxrightsum)
    {
        maxleftsum = maxrightsum;
    }
    if (maxleftsum>(LBorder_maxsum + RBorder_maxsum))
    {
        return maxleftsum;
    }
    else
    {
        return (LBorder_maxsum + RBorder_maxsum);
    }
        
}
int main(void)
{
    int K;
    int temp;
    
    cin >> K;
    vector<int>arry;
    for (int i = 0; i < K; i++)
    {
        cin >> temp;
        arry.push_back(temp);
        if (temp >= 0)
        {
            flag = 1;
        }

    }
    //cout <<maxsum(arry)<< endl;
    //cout <<maxsum2(arry)<< endl;
    //cout <<maxsum3(arry)<< endl;
    cout << maxsum4(arry,0,arry.size()-1) << endl; 
    return 0;
}