Strange Optimization
Accepted : 89		Submit : 350
Time Limit : 1000 MS		Memory Limit : 65536 KB

Strange Optimization

Bobo is facing a strange optimization problem. Given n,m , he is going to find a real number α such that f(1/2+α) is maximized, where f(t)=mini,j∈Z|i/n−j/m+t| . Help him!

Note: It can be proved that the result is always rational.

Input

The input contains zero or more test cases and is terminated by end-of-file.

Each test case contains two integers n,m .

1≤n,m≤10⁹
The number of tests cases does not exceed 10⁴ .

Output

For each case, output a fraction p/q which denotes the result.

Sample Input

1 1
1 2

Sample Output

1/2
1/4

Note

For the first sample, α=0 maximizes the function.

解法：猜的结论...

 1 #include <bits/stdc++.h>
 2 using namespace std;
 3 #define ll long long
 4 int main()
 5 {
 6     ll n,m;
 7     while(cin>>n>>m)
 8     {
 9         if(n==m)
10         {
11             cout<<"1/2"<<endl;
12         }
13         else
14         {
15             printf("1/%lld\n",n/__gcd(n,m)*m*2);
16         }
17     }
18     return 0;
19 }

转载于:https://www.cnblogs.com/yinghualuowu/p/6875498.html

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