Gym - 101981D The 2018 ICPC Asia Nanjing Regional Contest D.Country Meow 最小球覆盖

题面

题意:给你100个三维空间里的点,让你求一个点,使得他到所有点距离最大的值最小,也就是让你找一个最小的球覆盖掉这n个点

题解:红书模板题,这题也因为数据小,精度也不高,所以也可以用随机算法,模拟退火之类的

 #include<bits/stdc++.h>
 using namespace std;
 int npoint,nouter;
 struct Tpoint
 {
     double x,y,z;
 };
 Tpoint pt[],outer[],res;
 #define eps 1e-9
 double radius,tmp;
 inline double dist(Tpoint p1,Tpoint p2)
 {
     double dx=p1.x-p2.x,dy=p1.y-p2.y,dz=p1.z-p2.z;
     return (dx*dx+dy*dy+dz*dz);
 }
 inline double dot(Tpoint p1,Tpoint p2)
 {
     return p1.x*p2.x+p1.y*p2.y+p1.z*p2.z;
 }
 void ball()
 {
     Tpoint q[];
     double m[][],sol[],L[],det;
     int i,j;
     res.x=res.y=res.z=radius=;
     switch (nouter)
     {
         case :res=outer[];break;
         case :
                res.x=(outer[].x+outer[].x)/;
                res.y=(outer[].y+outer[].y)/;
                res.z=(outer[].z+outer[].z)/;
                radius=dist(res,outer[]);
                break;
         case :
                for (int i=;i<;i++)
                {
                    q[i].x=outer[i+].x-outer[].x;
                    q[i].y=outer[i+].y-outer[].y;
                    q[i].z=outer[i+].z-outer[].z;
                }
                for (int i=;i<;i++)
                    for (int j=;j<;j++)
                        m[i][j]=dot(q[i],q[j])*;
                for (int i=;i<;i++) sol[i]=dot(q[i],q[i]);
                if (fabs(det=m[][]*m[][]-m[][]*m[][])<eps) return;
                L[]=(sol[] * m[][] - sol[] * m[][])/det;
                L[]=(sol[] * m[][] - sol[] * m[][])/det;
                res.x=outer[].x+q[].x*L[]+q[].x*L[];
                res.y=outer[].y+q[].y*L[]+q[].y*L[];
                res.z=outer[].z+q[].z*L[]+q[].z*L[];
                radius=dist(res,outer[]);
                break;
         case :
                for (int i=;i<;i++)
                {
                    q[i].x=outer[i+].x-outer[].x;
                    q[i].y=outer[i+].y-outer[].y;
                    q[i].z=outer[i+].z-outer[].z;
                    sol[i]=dot(q[i],q[i]);
                }
                for (int i=;i<;i++)
                    for (int j=;j<;j++) m[i][j]=dot(q[i],q[j])*;
                det=m[][]*m[][]*m[][]
                   +m[][]*m[][]*m[][]
                   +m[][]*m[][]*m[][]
                   -m[][]*m[][]*m[][]
                   -m[][]*m[][]*m[][]
                   -m[][]*m[][]*m[][];
                if (fabs(det)<eps) return ;
                for (int j=;j<;j++)
                {
                    for (int i=;i<;i++)
                        m[i][j]=sol[i];
                    L[j]=( m[][]*m[][]*m[][]
                          +m[][]*m[][]*m[][]
                         +m[][]*m[][]*m[][]
                        -m[][]*m[][]*m[][]
                    -m[][]*m[][]*m[][]
                     -m[][]*m[][]*m[][]
                           )/det;
                    for  (int i=;i<;i++)
                        m[i][j]=dot(q[i],q[j])*;
                 }
                 res=outer[];
                 for (int i=;i<;i++)
                 {
                     res.x+=q[i].x*L[i];
                     res.y+=q[i].y*L[i];
                     res.z+=q[i].z*L[i];
                 }
                 radius=dist(res,outer[]);
     }
 }
 void minball(int n)
 {
     ball();
     if (nouter<)
     {
         for (int i=;i<n;i++)
             if (dist(res,pt[i])-radius>eps)
             {
                 outer[nouter]=pt[i];
                 ++nouter;
                 minball(i);
                 --nouter;
                 if (i>)
                 {
                     Tpoint Tt=pt[i];
                     memmove(&pt[],&pt[],sizeof(Tpoint)*i);
                     pt[]=Tt;
                 }
             }
     }
 }
 int main()
 {
     radius=-;
     scanf("%d",&npoint);
     for (int i=;i<npoint;i++)
     {
         scanf("%lf%lf%lf",&pt[i].x,&pt[i].y,&pt[i].z);
     }
     for (int i=;i<npoint;i++)
         if (dist(res,pt[i])-radius>eps)
         {
             nouter=;
             outer[]=pt[i];
             minball(i);
         }
     printf("%.10lf\n",sqrt(radius));
 }