Hdu 4717 The Moving Points (three-way)

Give the two-dimensional coordinates of n starting points and the size and direction of the velocity. Ask at which time the maximum distance between all two points is the smallest.

// Time 78 ms; Memory 1316K  

 

#include<iostream>  #include<cstdio>  #include<cmath>  #define maxn 50000  #define maxm 305  #define sqr(x) ((x)*(x))  #define eps 1e-5    using namespace std;    double a[maxn],b[maxn],c[maxn];  int cas,cnt;    int sig(double x)  {      return (x>eps)-(x<-eps);  }    typedef struct point  {      double x,y;      point(double xx=0,double yy=0):x(xx),y(yy){}  }vector;    point pt[maxm];  vector vt[maxm];    vector operator - (point p,point q)  {      return vector(p.x-q.x,p.y-q.y);  }  double dot(vector p,vector q)  {      return p.x*q.x+p.y*q.y;  }  double cal(double t)  {      double tmp,res=a[0]*t*t+b[0]*t+c[0];      for(int i=1;i<cnt;i++)      {          tmp=a[i]*t*t+b[i]*t+c[i];          if(res<tmp) res=tmp;      }      return res;  }    int main()  {      int i,j,t,n;      double l,r,m1,m2,tmp;      vector v,w;      scanf("%d",&t);      while(t--)      {          scanf("%d",&n);          cnt=0;          l=r=0.0;          for(i=0;i<n;i++)              scanf("%lf%lf%lf%lf",&pt[i].x,&pt[i].y,&vt[i].x,&vt[i].y);          for(i=0;i<n;i++) for(j=i+1;j<n;j++)          {              v=vt[j]-vt[i],              w=pt[j]-pt[i],              a[cnt]=dot(v,v),              b[cnt]=2*dot(v,w),              c[cnt]=dot(w,w);              tmp=-b[cnt]/(2*a[cnt]);              if(r<tmp) r=tmp;              cnt++;          }          while(sig(r-l)>0)          {               m1=l+(r-l)/3;m2=r-(r-l)/3;              if(cal(m1)<cal(m2)) r=m2;              else l=m1;          }          printf("Case #%d: %.2lf %.2lf\n",++cas,l,sqrt(cal(l)));      }      return 0;  }