记分治法求最大子序列正确性的一次不完全证明

依旧现贴出程序代码再进行分析：

#include <stdio.h>
#include <stdlib.h>

int sc=0;
int max3(int a,int b, int c)
{
    sc++;
    if(a>b)
    {
        return a>c?a:c;
    }
    else
    {
        return b>c?b:c;
    }
}

int max_sub_sum(const int v[], int left, int right)
{
    int center;
    int maxLeftHalfSum;
    int maxRightHalfSum;
    int leftHalfWithRightBorderSum;
    int rightHalfWithLeftBorderSum;
    int maxLeftHalfWithRightBorderSum;
    int maxRightHalfWithLeftBorderSum;
    int i;

    if(left==right)
    {
        return v[left]>0?v[left]:0;
    }
    center=(left+right)/2;

    maxLeftHalfWithRightBorderSum=leftHalfWithRightBorderSum=
    maxRightHalfWithLeftBorderSum=rightHalfWithLeftBorderSum=0;
    for(i=center;i>=left;i--)
    {
        leftHalfWithRightBorderSum+=v[i];
        if(leftHalfWithRightBorderSum>maxLeftHalfWithRightBorderSum)
        {
            maxLeftHalfWithRightBorderSum=leftHalfWithRightBorderSum;
        }
    }

    for(i=center+1;i<=right;i++)
    {
        rightHalfWithLeftBorderSum+=v[i];
        if(rightHalfWithLeftBorderSum>maxRightHalfWithLeftBorderSum)
        {
            maxRightHalfWithLeftBorderSum=rightHalfWithLeftBorderSum;
        }
    }

    return max3(max_sub_sum(v,left,center),max_sub_sum(v,center+1,right),
                maxLeftHalfWithRightBorderSum+maxRightHalfWithLeftBorderSum);
}

int main()
{
    int v[]={1,-1,2,-2,1,-1,2,-2,1,-1,2,-2,1,-1,2,-2,1,-1,2,-2,1,-1,2,-2,1,-1,2,-2,1,-1,2,-2};
    int r=max_sub_sum(v,0,31);
    printf("the max sub sum is %d in step %d",r,sc);
    return 0;
}

如下为证明分治法求解该问题的有效性，随手写来，好久没做证明题了，如有错误，还望不令赐教