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：
1: #include <stdio.h> 2: #include <stdlib.h> 3: 4: int sc=0;
5: int max3(int a,int b, int c)
6: { 7: sc++;8: if(a>b)
9: {10: return a>c?a:c;
11: }12: else
13: {14: return b>c?b:c;
15: } 16: } 17: 18: int max_sub_sum(const int v[], int left, int right)
19: {20: int center;
21: int maxLeftHalfSum;
22: int maxRightHalfSum;
23: int leftHalfWithRightBorderSum;
24: int rightHalfWithLeftBorderSum;
25: int maxLeftHalfWithRightBorderSum;
26: int maxRightHalfWithLeftBorderSum;
27: int i;
28: 29: if(left==right)
30: {31: return v[left]>0?v[left]:0;
32: } 33: center=(left+right)/2; 34: 35: maxLeftHalfWithRightBorderSum=leftHalfWithRightBorderSum= 36: maxRightHalfWithLeftBorderSum=rightHalfWithLeftBorderSum=0;37: for(i=center;i>=left;i--)
38: { 39: leftHalfWithRightBorderSum+=v[i];40: if(leftHalfWithRightBorderSum>maxLeftHalfWithRightBorderSum)
41: { 42: maxLeftHalfWithRightBorderSum=leftHalfWithRightBorderSum; 43: } 44: } 45: 46: for(i=center+1;i<=right;i++)
47: { 48: rightHalfWithLeftBorderSum+=v[i];49: if(rightHalfWithLeftBorderSum>maxRightHalfWithLeftBorderSum)
50: { 51: maxRightHalfWithLeftBorderSum=rightHalfWithLeftBorderSum; 52: } 53: } 54: 55: return max3(max_sub_sum(v,left,center),max_sub_sum(v,center+1,right),
56: maxLeftHalfWithRightBorderSum+maxRightHalfWithLeftBorderSum); 57: } 58: 59: int main()
60: {61: 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};
62: int r=max_sub_sum(v,0,31);
63: printf("the max sub sum is %d in step %d",r,sc);
64: return 0;
65: }
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
