hdu 2225 The nearest fraction （数学题）

Problem - 2225

　　一道简单数学题，要求求出一个分母不超过m的最接近sqrt(n)的分数。

　　做法就是暴力枚举，注意中间过程不能用浮点数比较，误差要求比较高。

代码如下：

 #include <cstdio>
 #include <cstring>
 #include <algorithm>
 #include <iostream>
 #include <cmath>

 using namespace std;

 typedef long long LL;
 template<class T> T sqr(T x) { return x * x;}
 template<class T> T gcd(T a, T b) { return b ? gcd(b, a % b) : a;}

 int main() {
     LL n, m;
     while (cin >> n >> m) {
         LL bx = , by = ;
 //        long double r = sqrt((long double) n);
 //        cout << r << endl;
         for (LL i = ; i <= m; i++) {
             LL t = (int) sqrt((double) sqr(i) * n);
             for (int d = ; d < ; d++) {
 //                if (fabs((long double) (t + d) / i - r) < fabs((long double) bx / by - r)) {
 //                    bx = t + d, by = i;
 //                }
                 if (abs(sqr(t + d) * sqr(by) - n * sqr(by) * sqr(i)) < abs(sqr(bx) * sqr(i) - n * sqr(by) * sqr(i))) bx = t + d, by = i;
             }
         }
         LL GCD = gcd(bx, by);
         cout << bx / GCD << "/" << by / GCD << endl;
     }
     return ;
 }

——written by Lyon