UVA10976-Fractions Again?!【枚举】

1. 链接

   Fractions Again?!

2. 思路

   因为$\frac{1}{k}-\frac{1}{x}=\frac{1}{y}$，又因为$x\ge y$，所以$\frac{1}{k}-\frac{1}{y}\le \frac{1}{y}$，即$y\le 2k$，枚举y判断x即可。

3. 代码

   #include
   using namespace std;
   
   typedef long long ll;
   const int maxn = 2e5+10;
   const int mod = 1e9+7;
   
   int a[maxn];
   
   int main(void){
   	int k;
   	while(cin>>k){
   		int cnt = 0;
   		for(int y = k+1; y <= 2*k; y++){
   			int a1 = k*y;
   			int a2 = y-k;
   			if(a1%a2==0) cnt++;
   		}
   		cout<<cnt<<endl;
   		for(int y = k+1; y <= 2*k; y++){
   			int a1 = k*y;
   			int a2 = y-k;
   			if(a1%a2==0){
   				int x = a1/a2;
   				printf("1/%d = 1/%d + 1/%d\n",k,x,y); 
   			}
   		}
   	} 
   	return 0;
   }