Problem Description

There are N points in total. Every point moves in certain direction and certain speed. We want to know at what time that the largest distance between any two points would be minimum. And also, we require you to calculate that minimum distance. We guarantee that no two points will move in exactly same speed and direction.

 

Input

The rst line has a number T (T <= 10) , indicating the number of test cases.
For each test case, first line has a single number N (N <= 300), which is the number of points.
For next N lines, each come with four integers X_i, Y_i, VX_i and VY_i (-10⁶ <= X_i, Y_i <= 10⁶, -10² <= VX_i , VY_i <= 10²), (X_i, Y_i) is the position of the i^th point, and (VX_i , VY_i) is its speed with direction. That is to say, after 1 second, this point will move to (X_i + VX_i , Y_i + VY_i).

 

Output

For test case X, output "Case #X: " first, then output two numbers, rounded to 0.01, as the answer of time and distance.

 

Sample Input

 

Sample Output

 

Source

 

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 #include <iostream>

 #include <cstdio>

 #include <cstring>

 #include <cmath>

 using namespace std;

 const double eps=1e-;

 const double INF=0x3f3f3f3f;

 struct point

 {

     double x,y;

     double vx,vy;

     point() {}

     point(double a,double b,double c,double d):x(a),y(b),vx(c),vy(d){}

 }P[];

 double getP2Pdist(point a,point b,double t)

 {

     double x1=a.x+t*a.vx,y1=a.y+t*a.vy;

     double x2=b.x+t*b.vx,y2=b.y+t*b.vy;

     return sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));

 }

 double LMdist(int n,double t)

 {

     double ans=-INF;

     for(int i=;i<n;i++)

     {

         for(int j=i+;j<n;j++)

         {

             ans=max(ans,getP2Pdist(P[i],P[j],t));

         }

     }

     return ans;

 }

 int main()

 {

     int t,n,cas=;

     scanf("%d",&t);

     while(t--)

     {

         scanf("%d",&n);

         for(int i=;i<n;i++)

         {

             double a,b,c,d;

             scanf("%lf%lf%lf%lf",&a,&b,&c,&d);

             P[i]=point(a,b,c,d);

         }

         double low=,high=,midlow,midhigh;

         int cnt=;

         while(cnt<=)

         {

             cnt++;

             midlow=(low*+high)/.,midhigh=(low+high*)/.;

             double distlow=LMdist(n,midlow);

             double disthigh=LMdist(n,midhigh);

             if(distlow>disthigh) low=midlow;

             else high=midhigh;

         }

         double anstime=low;

         double ansdist=LMdist(n,low);

         printf("Case #%d: %.2lf %.2lf\n",cas++,anstime,ansdist);

     }

     return ;

 }

 * This source code was highlighted by YcdoiT. ( style: Codeblocks )