HDU 4617

题目多读几次就明白了。主要是求异面直线的距离，然后用距离和两圆半径之和作比较。

空间直线的距离d=|AB*n| / |n| （AB表示异面直线任意2点的连线，n表示法向量,法向量为两条异面直线方向向量的叉积，|n|表示模。

 

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#include <iostream> #include <cstdio> #include <cstring> #include <algorithm> #include <cmath>   using namespace std; const int MAXN=50; const double eps=1e-8; struct point {     double x,y,z; }; struct line {     point a,b;     double r; }; int n; point tmp[3]; line le[MAXN]; point vectical;   point operator - (const point &a, const point &b){  //减法     point t;     t.x=a.x-b.x; t.y=a.y-b.y; t.z=a.z-b.z;     return t; } point operator ^ (const point &u, const point &v){  //叉乘     point t;     t.x=u.y*v.z-v.y*u.z; t.y=u.z*v.x-u.x*v.z; t.z=u.x*v.y-u.y*v.x;     return t; }   point operator + (const point &a, const point &b){     point t;     t.x=a.x+b.x; t.y=a.y+b.y; t.z=a.z+b.z;     return t; }   double operator *(const point &a, const point &b){     return a.x*b.x+a.y*b.y+a.z*b.z; }   double dist(point &a, point &b){     double tx=a.x-b.x; double ty=a.y-b.y; double tz=a.z-b.z;     return sqrt(tx*tx+ty*ty+tz*tz); }   double len (point &t){     return sqrt(t.x*t.x+t.y*t.y+t.z*t.z); }   int main(){     int T;     scanf("%d",&T);     while(T--){         scanf("%d",&n);         for(int i=0;i<n;i++){             for(int j=0;j<3;j++)             scanf("%lf%lf%lf",&tmp[j].x,&tmp[j].y,&tmp[j].z);             le[i].a=tmp[0];             vectical=(tmp[1]-tmp[0])^(tmp[2]-tmp[0]);             le[i].b=le[i].a+vectical;             le[i].r=dist(tmp[1],tmp[0]);         }         bool flag=false;         double ans=1e10;         for(int i=0;i<n;i++){             for(int j=0;j<n;j++){                 if(i!=j){                     vectical=(le[i].a-le[i].b)^(le[j].a-le[j].b);                     point tt=le[i].a-le[j].a;                     double dd=fabs((tt*vectical))/len(vectical);                     if(dd<=le[i].r+le[j].r){                         flag=true;                         break;                     }                     else ans=min(ans,dd-le[i].r-le[j].r);                 }             }             if(flag)break;         }         if(flag) printf("Lucky\n");         else printf("%.2lf\n",ans);     }     return 0; }