分治政策之最大子數組問題

問題描述：

問題：一個整數數組中的元素有正有負，在該數組中找出一個連續子數組，要求該連續子數組中各元素的和最大，這個連續子數組便被稱作最大連續子數組。比如數組{2,4,-7,5,2,-1,2,-4,3}的最大連續子數組為{5,2,-1,2}，最大連續子數組的和為+-+=。
           

解問題：

一、暴力解法：

#include<iostream>
using namespace std;

class solution
{
public:

    int FIND_MAXMUM_SUBARRAY(int A[], int length)
    {
        int i, j;
        int sum = ;
        for (i = ; i < length; i++)
        {
            int cursum = ;
            for (int j = i; j < length; j++)
            {
                cursum += A[j];
                if (cursum > sum)
                {
                    sum = cursum;
                }

            }

        }
        return sum;
    }


     };

int main()
{
    int A[] = { -,,-,,,,,-,- };
    solution S1;
    cout << S1.FIND_MAXMUM_SUBARRAY(A, );
    system("pause");
}
           

二、分治解法：

#include<iostream>
using namespace std;

class solution
{
public:

    int FIND_MAXMUM_SUBARRAY(int A[],int low,int high)
    {
        if (low == high)
            return A[low];
        else
        {
            int mid = (low + high) / ;
            int leftmax, rightmax,  crossmax;

            leftmax = FIND_MAXMUM_SUBARRAY(A, low, mid);
            rightmax = FIND_MAXMUM_SUBARRAY(A, mid + , high);
            crossmax = findcross(A, low,  high);
            if (leftmax >= rightmax&&leftmax >= crossmax)
            {
                return leftmax;
            }
            else if (rightmax >= leftmax&&rightmax >= crossmax)
            {
                return rightmax;
            }
            else
                return crossmax;
        }



    }
    int findcross(int A[],int low,int high)
    {
        int left_sum = -;

        int sum = ;
        int right_sum = -;
        int mid = (low + high) / ;

        for (int i = mid; i>=; i--)
        {
            sum += A[i];
            if (sum > left_sum)
            {
                left_sum = sum;

            }

        }
        sum = ;
        for (int i = mid + ; i <=high; i++)
        {
            sum = sum + A[i];
            if (sum > right_sum)
            {
                right_sum = sum;

            }
        }
        return left_sum + right_sum;
    }




};

int main()
{
    int A[] = { -,,-,,,,,-,- };
    solution S1;
    cout<<S1.FIND_MAXMUM_SUBARRAY(A, ,);
    system("pause");
}
           

三 、線性解法：

#include<iostream>
/*
@author zsj


*/
using namespace std;

int find(int a[], int length)
{
    int temp=;
    int max=;
    for (int i = ; i < length; i++)
    {
        temp += a[i];
        if (temp > max)
            max = temp;
        if (temp < )
            temp = ;


    }

}