アルゴリズムの導論の第4章:最も大きいサブ配列-再帰、暴力と線形アルゴリズム

#include <iostream>  
#include <vector>  
#include <tuple>
#include <climits>
  
using namespace std;  
  
 tuple<int,int,int> maxCrossSubarray(vector<int> &vec,int low,int mid,int high)  
{  
    int leftSum=INT_MIN;  
    int sum=0;  
    int leftBoard=mid;  
    for(int i=mid;i>=low;--i){  
        sum+=vec[i];  
        if(sum>leftSum){  
            leftSum=sum;  
            leftBoard=i;  
        }  
    }  
  
    int rightSum=INT_MIN;  
    int sum2=0;  
    int rightBoard=mid+1;  
    for(int j=mid+1;j<=high;j++){  
        sum2+=vec[j];  
        if(sum2>rightSum){  
            rightSum=sum2;  
            rightBoard=j;  
        }  
    }  
  
    return (make_tuple(leftBoard,rightBoard,leftSum+rightSum));  
  
}  
  
tuple<int,int,int> maxSubarray(vector<int> &vec,int low,int high)  
{  
    if(high==low)  
        return(make_tuple(low,high,vec[high]));  
    else{  
        size_t mid=(low+high)/2;  
        tuple<int,int,int> leftTuple;  
        tuple<int,int,int> rightTuple;  
        tuple<int,int,int> corssTuple;  
  
        leftTuple=maxSubarray(vec,low,mid);  
        rightTuple=maxSubarray(vec,mid+1,high);  
        corssTuple=maxCrossSubarray(vec,low,mid,high);  
  
        if(get<2>(leftTuple)>get<2>(rightTuple)&&get<2>(leftTuple)>get<2>(corssTuple))  
            return leftTuple;  
        else if(get<2>(rightTuple)>get<2>(leftTuple)&&get<2>(rightTuple)>get<2>(corssTuple))  
            return rightTuple;  
        else  
            return corssTuple;  
  
    }  
}


tuple<int,int,int> naiveMaxSub(const vector<int> &vec)
{
    int maxSum=INT_MIN;
    int  thisSum=0;
    int leftBoard=0,rightBoard=0;

    int i,j;
    for(i=0;i<vec.size()-1;i++)
    {
        thisSum=vec[i];
        if(thisSum>maxSum)
        {
            maxSum=thisSum;
            leftBoard=i;
            rightBoard=i;
        }

        for(j=i+1;j<vec.size();j++)
        {
            thisSum+=vec[j];
            if(thisSum>maxSum)
            {
                maxSum=thisSum;
                leftBoard=i;
                rightBoard=j;
            }
        }
    }

    return(make_tuple(leftBoard,rightBoard,maxSum));  
}

tuple<int,int,int> linerMaxSub(vector<int> &vec)  
{  
    int maxSum=INT_MIN;//    
    int thisSum=0;  
    int leftBoard=0,rightBoard=0;  
    int tmpleftBoard=0,tmprightBoard=0;   
    
    for(int i=0;i<vec.size();++i)  
    {  
        thisSum+=vec[i];  
        if(thisSum>maxSum)  
        {  
            maxSum=thisSum;  
            leftBoard=tmpleftBoard;  
            rightBoard=tmprightBoard=i;  
        }  
      
        if(thisSum<0)  
        {  
            thisSum=0;  
            tmpleftBoard=tmprightBoard=i+1;  
        }  
    }  
    return(make_tuple(leftBoard,rightBoard,maxSum));  
} 


int main()  
{  
    int SIZE=100000;
    int i=0;
    vector<int> vec;
    while(i<SIZE)
    {
        vec.push_back(rand()%1000-500);
        i++;
    }
    cout<<vec.size()<<endl;  
  
    //    ，    nlgn
    clock_t start_time=clock();  
    tuple<int,int,int> t=maxSubarray(vec,0,vec.size()-1); 
    clock_t end_time=clock(); 

    cout<<"Running time is: "<<  
    static_cast<double>(end_time-start_time)/CLOCKS_PER_SEC<<" S"<<endl;  

    cout<<get<0>(t)<<"__"<<get<1>(t)<<" sum: "<<get<2>(t)<<endl;  
  
   
    //    ，    n^2 
    clock_t start_time2=clock(); 
    tuple<int,int,int> t2=naiveMaxSub(vec);
    clock_t end_time2=clock(); 
    cout<<"Running time is: "<<  
    static_cast<double>(end_time2-start_time2)/CLOCKS_PER_SEC<<" S"<<endl;

    cout<<get<0>(t2)<<"__"<<get<1>(t2)<<" sum: "<<get<2>(t2)<<endl;  


    //       
    clock_t start_time3=clock();
    tuple<int,int,int> t3=linerMaxSub(vec);
    clock_t end_time3=clock();
    cout<<"Running time is: "<<  
    static_cast<double>(end_time3-start_time3)/CLOCKS_PER_SEC<<" S"<<endl;
     cout<<get<0>(t3)<<"__"<<get<1>(t3)<<" sum: "<<get<2>(t3)<<endl;

    
}