最大子段和（分而治之求解）

 

#include<iostream>

#include<vector>

 

using namespace std;

const int Min=-99999;

void MaxSum(const vector<int>&v,int &besti,int &bestj,int& sum,int low,int high)

{

       int i;

       if(low==high) //当low==high,递归截止,sum存放一个元素和

       {

              sum=v[low];

              return;

       }

       else if(low<high) //当low<high,产生递归

       {

              int mid=(low+high)/2; //mid是low...high区间的中值

              int lsum;

              MaxSum(v,besti,bestj,lsum,low,mid); //左区间递归,求low...mid区间最大子段和

              int rsum;

              MaxSum(v,besti,bestj,rsum,mid+1,high);//右区间递归,求mid+1...high区间最大子段和

              //最大子段和可能出现在i...j中,low<=i<=mid, mid<j<=high

              int lbestsum=Min; //lbestsum是i...mid区间最大子段和

              int s=0; //s用于求和

              int L_index; //L_index...mid区间是最大子段和区间

              for(i=mid;i>=low;i--) //求i...mid区间最大子段和

              {

                     s+=v[i];

                     if(s>lbestsum)

                     {

                            L_index=i;

                            lbestsum=s;

                     }

              }

              int rbestsum=Min; //rbestsum是mid+1...high区间最大子段和

              s=0;

              int R_index; //mid_1...R_index区间是最大子段和区间

              for(i=mid+1;i<=high;i++)

              {

                     s+=v[i];

                     if(s>rbestsum)

                     {

                            R_index=i;

                            rbestsum=s;

                     }

              }

              if(lsum>rsum && lsum>(lbestsum+rbestsum)) //最大子段和是出现在low...mid区间内

              {

                     besti=low;

                     bestj=mid;

                     sum=lsum;

              }

              else if(rsum>lsum && rsum>(lbestsum+rbestsum)) //最大子段和是出现在mid+1...high区间内

              {

                     besti=mid+1;

                     bestj=high;

                     sum=rsum;

              }

              else

              {

                     besti=L_index;

                     bestj=R_index;

                     sum=lbestsum+rbestsum;

              }

       }

}

 

void main()

{

       vector<int>v;

       int i,j,sum;

       sum=0;

       int e;

       const int end=-9999;

       cin>>e;

       while(e!=end)

       {

              v.push_back(e);

              cin>>e;

       }

       for(i=0;i<v.size();i++) cout<<i<<":"<<v[i]<<endl;

       MaxSum(v,i,j,sum,0,v.size()-1);

       cout<<"最大子段和从位置"<<i<<"到"<<"位置"<<j<<endl;

       cout<<"最大子段和是:"<<sum<<endl;

}