分数拆分（刘汝佳紫书P183）

枚举，由已知条件推得y大于k，小于等于2K

AC代码：

#include"iostream"
#include"cstring"
using namespace std;
const int maxn=20002;
int a[maxn];
int b[maxn];
int main()
{
int i,y;
int x,f,k;
while(cin>>k&&k)
{
memset(a,0,sizeof(a));
memset(b,0,sizeof(b));
f=0;
for(y=k+1;y<=2*k;y++)
{
if(((k*y)%(y-k))==0)
{
a[f]=(k*y)/(y-k);
b[f]=y;
f++;
}
}
cout<<f<<endl;
for(int j=0;j<f;j++)
{
cout<<"1/"<<k<<" = "<<"1/"<<a[j]<<" + "<<"1/"<<b[j]<<endl;
}
}
return 0;
}

 

 

 

疑问（未解决）

同样的代码codeblock运行正常，VC6.0错误

#include"iostream"
#include"cstring"
using namespace std;
const int maxn=10001;
int a[maxn];
int b[maxn];
int main()
{
    double k,i,y;
    int x,f;
    while(cin>>k&&k)
    {
        memset(a,0,sizeof(a));
        memset(b,0,sizeof(b));
        f=0;
     for(y=k+1;y<=2*k;y++)
     {
         i=1/(1/k-1/y);
         x=i;
         if(x-i==0)
         {
         a[f]=x;
         b[f]=y;
         f++;
         }
     }
     cout<<f<<endl;
     for(int j=0;j<f;j++)
     {
          cout<<"1/"<<k<<" = "<<"1/"<<a[j]<<" + "<<"1/"<<b[j]<<endl;
     }
    }
    return 0;
}

 codeblock：

2
2
1/2 = 1/6 + 1/3
1/2 = 1/4 + 1/4
12
8
1/12 = 1/156 + 1/13
1/12 = 1/84 + 1/14
1/12 = 1/60 + 1/15
1/12 = 1/48 + 1/16
1/12 = 1/36 + 1/18
1/12 = 1/30 + 1/20
1/12 = 1/28 + 1/21
1/12 = 1/24 + 1/24

 

VC6.0

2
1
1/2 = 1/4 + 1/4
12
4
1/12 = 1/84 + 1/14
1/12 = 1/36 + 1/18
1/12 = 1/28 + 1/21
1/12 = 1/24 + 1/24