Problem Description

In a two-dimensional plane there are two line belts, there are two segments AB and CD, lxhgww's speed on AB is P and on CD is Q, he can move with the speed R on other area on the plane.
How long must he take to travel from A to D?

 

Input

The first line is the case number T.
For each case, there are three lines.
The first line, four integers, the coordinates of A and B: Ax Ay Bx By.
The second line , four integers, the coordinates of C and D:Cx Cy Dx Dy.
The third line, three integers, P Q R.
0<= Ax，Ay，Bx，By，Cx，Cy，Dx，Dy<=1000
1<=P，Q，R<=10

 

Output

The minimum time to travel from A to D, round to two decimals.

 

Sample Input

 

Sample Output

 

Author

lxhgww&&momodi

 

 #include <iostream>

 #include <cstdio>

 #include <cstring>

 #include <cstdlib>

 #include <cmath>

 #include <algorithm>

 #define LL __int64

 const int maxn = 1e2 + ;

 const double eps = 1e-;

 using namespace std;

 double p, q, r;

 struct node

 {

     double x, y;

 }a, b, c, d;

 double dis(node a, node b)

 {

     return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));

 }

 double solve2(node t)

 {

     double d1, d2;

     node le = c;

     node ri = d;

     node mid, midmid;

     do

     {

         mid.x = (le.x+ri.x)/2.0;

         mid.y = (le.y+ri.y)/2.0;

         midmid.x = (mid.x+ri.x)/2.0;

         midmid.y = (mid.y+ri.y)/2.0;

         d1 = dis(t, mid)/r + dis(mid, d)/q;

         d2 = dis(t, midmid)/r + dis(midmid, d)/q;

         if(d1 > d2)

         le = mid;

         else ri = midmid;

     }while(dis(le, ri)>=eps);

     return d1;

 }

 double solve1()

 {

     double d1, d2;

     node le = a;

     node ri = b;

     node mid, midmid;

     do

     {

         mid.x = (le.x+ri.x)/2.0;

         mid.y = (le.y+ri.y)/2.0;

         midmid.x = (mid.x+ri.x)/2.0;

         midmid.y = (mid.y+ri.y)/2.0;

         d1 = dis(a, mid)/p + solve2(mid);

         d2 = dis(a, midmid)/p + solve2(midmid);

         if(d1 > d2)

         le = mid;

         else ri = midmid;

     }while(dis(le, ri)>=eps);

     return d1;

 }

 int main()

 {

     int t;

     scanf("%d", &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("%lf%lf%lf", &p, &q, &r);

         printf("%.2lf\n", solve1());

     }

     return ;

 }