xtu 1268 Strange Optimization 2017年“嘉杰信息杯” 中国大学生程序设计竞赛全国邀请赛（湖南）

最新推荐文章于 2019-10-04 20:37:12 发布

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面对一个特殊的优化挑战，Bob需要找到一个实数α，使得f(12+α)最大化，其中f(t)=mini,j∈Z|in−jm+t|。本问题确保了解总是有理数，并提供了输入输出示例及解决方案。

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Strange Optimization

Bobo is facing a strange optimization problem. Given n,m, he is going to find a real number α such that f(12+α) is maximized, where f(t)=mini,j∈Z|in−jm+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.

Source

XTU OnlineJudge

#include<stdio.h>  
  
#define ll __int64  
ll gcd(ll a,ll b)  
{  
    return a%b==0?b:gcd(b,a%b);  
}  
  
int main()  
{  
    ll a,b;  
    while(~scanf("%I64d %I64d",&a,&b))  
    {  
        printf("1/%I64d\n",2*a*b/gcd(a,b));  
    }  
    return 0;  
}