[2017HNCPC] Strange Optimization 简单数论

给出正整数$n,m\le 1e9$，并且定义函数$f(t)={\min }_{i,j\in Z}|\frac{i}{n}-\frac{j}{m}+t|$，求一实数$\alpha$使得$f(\frac{1}{2}+\alpha )$最大，求出值。
由于$\alpha$是任意实数，所以等价于求$f(\alpha )$。$|\frac{i}{n}-\frac{j}{m}|=|\frac{mi-nj}{nm}|=|\frac{kgcd(n,m)}{nm}|$，$\alpha$取$\frac{gcd(n,m)}{2nm}$的时候有最大值答案即为$\frac{gcd(n,m)}{2nm}$。

#include 
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
static const int maxn = 100010;
static const int INF = 0x3f3f3f3f;
static const int mod = (int)1e9 + 7;
static const double eps = 1e-6;
static const double pi = acos(-1);
 
void redirect(){
    #ifdef LOCAL
        freopen("test.txt","r",stdin);
    #endif
}
 
int main(){
    redirect();
    int n,m;
    while(~scanf("%d %d",&n,&m)){
        ll a = __gcd(n,m);
        ll b = 2ll*m*n;
        ll tmp = __gcd(a,b);
        printf("%lld/%lld\n",a/tmp,b/tmp);
    }
    return 0;
}