分治法，求最大字段和

问题： 给定n个整数（可能为负数）组成的序列a[1],a[2],a[3],…,a[n],求该序列如a[i]+a[i+1]+…+a[j]的子段和的最大值。当所给的整均为负数时定义子段和为0，依此定义，所求的最优值为： Max{0,a[i]+a[i+1]+…+a[j]},1<=i<=j<=n 例如，当（a[1],a[2],a[3],a[4],a[5],a[6]）=(-2,11,-4,13,-5,-2)时，最大子段和为20。

 

分为三种情况，以中间划分，1.全在左边，2.全在右边 3.跨越了中间的mid(这种情况是易求的)

1,2情况按原问题做递归即可

 

// MaxChildArray.cpp : Defines the entry point for the console application.
//

#include "stdafx.h"
#include <VECTOR>
#include <iostream>
using namespace std;


//返回值，result[0]-> lindex  result[1]-> rindex  result[2]-> sum(lindex,rindex)

vector<int> GetMaxAcross(vector<int> & v,int mid,int begin,int end){
    int lsum = 0 ,maxlsum= -9999;
    int rsum = 0 ,maxrsum= -9999;
    vector<int >  result(3,0);
    int i = 0;
    for(i = mid;i>=begin;i--){
        lsum+=v[i];
        if(maxlsum < lsum){
            maxlsum = lsum;
            result[0] = i;
        }
    }

    for(i = mid+1;i<=end;i++){
        rsum+=v[i];
        if(maxrsum < rsum){
            maxrsum = rsum;
            result[1] = i;
        }
    }

    result[2] = maxlsum+maxrsum;

    return result;
}

vector<int> GetMaxChildArray(vector<int> & v,int begin,int end){ 
    vector<int >  result(3,0);                  
    if(begin == end){                             //递归截止点
        result[0] = begin; 
        result[1] = end;
        result[2] = v[end];
        return result;
    }

    int mid = (begin+end)/2;
    vector<int> lresult = GetMaxChildArray(v,begin,mid);
    vector<int> rresult = GetMaxChildArray(v,mid+1,end);
    vector<int> midresult = GetMaxAcross(v,mid,begin,end);

    if(lresult[2] >= rresult[2] && lresult[2] >= midresult[2])
        return lresult;
    if(rresult[2] >= lresult[2] && rresult[2] >= midresult[2])
        return rresult;
    return midresult;

}
int main(int argc, char* argv[])
{
    int array[] = {-2,11,-4,13,-5,-2};
    vector<int> elements(array,array+sizeof(array)/sizeof(int));
    vector<int> result = GetMaxChildArray(elements,0,sizeof(array)/sizeof(int)-1);
    
    cout<<"leftindex = "<<result[0]<<endl;
    cout<<"rightindex = "<<result[1]<<endl;
    cout<<"maxsubarray = "<<result[2]<<endl;
    
    int i;
    cin>>i;
    return 0;
}