题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=3400

这题就是一道简单的两重三分

首先设e点为从ab上离开的点，f为从cd上进入的点

显然对固定点e,f从距c的距离的长度是一个单调函数或者先减后增的函数，这里可以三分算出最优解。这里是第一个三分

然后对e点的最优解易证也存在这个性质，所以再来一个三分，就能解除最优解

代码如下：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;

const double EPS = 1e-10;

typedef struct
{
    double x,y;
}point;

double sulAB(point a, point b, point c, point d, double p, double q, double r);
double sulCD(point e, point c, point d, double q, double r);
double getSulCD(double l,const point &e,const point &c,const point &d,const double &q,const double &r);
double getSulAB(double l,const point &a,const point &b, const point &c,const point &d
    , const double &p,const double &q,const double &r);
double getDis(point a, point b)
{
    return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
}
int main()
{
    long t,p,q,r;
    double res;
    point a,b,c,d;
    scanf("%ld", &t);
    while(t --)
    {
        scanf("%lf %lf %lf %lf", &a.x, &a.y, &b.x, &b.y);
        scanf("%lf %lf %lf %lf", &c.x, &c.y, &d.x, &d.y);
        scanf("%ld %ld %ld", &p, &q, &r);
        res = sulAB(a, b, c, d, p, q, r);
        printf("%.2lf\n", res);
    }
    return 0;
}

double sulAB(point a, point b, point c, point d, double p, double q, double r)
{
    double l,rr,m,mm;
    double tmp1, tmp2;
    l = 0;
    rr = 1.0;
    while(l + EPS < rr)
    {
        m = (l + rr) / 2;
        mm = (m + rr) / 2;
        tmp1 = getSulAB(m, a, b, c, d, p, q, r);
        tmp2 = getSulAB(mm, a, b, c, d, p, q, r);
        if(tmp1 < tmp2)
            rr = mm;
        else
            l = m;
    }

    return getSulAB(l, a, b, c, d, p, q, r);
}

double sulCD(point e, point c, point d, double q, double r)
{
    double l,rr,m,mm;
    double tmp1, tmp2;
    l = 0;
    rr = 1.0;
    while(l + EPS < rr)
    {
        m = (l + rr) / 2;
        mm = (m + rr) / 2;
        tmp1 = getSulCD(m, e, c, d, q, r);
        tmp2 = getSulCD(mm, e, c, d, q, r);
        if(tmp1 < tmp2)
            rr = mm;
        else
            l = m;
    }

    return getSulCD(l, e, c, d, q, r);
}

double getSulCD(double l,const point &e,const point &c,const point &d,const double &q,const double &r)
{
    point p;
    p.x = c.x + (d.x - c.x) * l;
    p.y = c.y + (d.y - c.y) * l;
    return getDis(e, p) / r + getDis(p, d) / q;
}

double getSulAB(double l,const point &a,const point &b, const point &c,const point &d
    , const double &p,const double &q,const double &r)
{
    point pp;
    pp.x = a.x + (b.x - a.x) * l;
    pp.y = a.y + (b.y - a.y) * l;
    return getDis(a, pp) / p + sulCD(pp, c, d, q, r);
}