hdu 4063 福州赛区网络赛 圆 ****

画几个图后，知道路径点集一定是起点终点加上圆与圆之间的交点，枚举每两个点之间是否能走，能走则连上线，然后求一遍最短路即可

 #include<cstdio>
 #include<cstdlib>
 #include<cstring>
 #include<cmath>
 #include<algorithm>
 using namespace std;
 #define sqr(x) ((x)*(x))
 const double eps= 1e-;
 const int maxc=;
 const int maxp=;
 const double inf=1e20;
 double dsgn(double x)//return double
 {
     if(fabs(x)<eps)return ;
     return x;
 }
 int isgn(double x)//return int
 {
     if(fabs(x)<eps)return ;
     if(x<)return -;
     return ;
 }
 struct point
 {
     double x, y;
     point() {}
     point(double xx, double yy):x(xx), y(yy) {}
     double length() const
     {
         return sqrt(sqr(x)+sqr(y));
     }
     point set(const double &m) const
     {
         double len=length();
         return point(x*m/len, y*m/len);
     }
     double sqrdist(const point &a)const
     {
         return sqr(a.x-x)+sqr(a.y-y);
     }
     double dist(const point &a)const
     {
         return sqrt(sqrdist(a));
     }
 } p[maxp];
 struct line
 {
     double a, b, c;
     line() {}
     line(double ta=,  double tb=-,  double tc=):a(ta), b(tb), c(tc) {}
 };
 struct circle
 {
     point o;
     double r;
 } c[maxc];
 int pn, cn;
 double edge[maxp][maxp];

 int cir_relation(circle c1, circle c2)//判断两圆关系
 {
     double d=c1.o.dist(c2.o);
     int a=isgn(d-c1.r-c2.r);
     int b=isgn(d-fabs(c1.r-c2.r));
     if(a==)return -;//外切
     if(b==)return -;//内切
     if(a>)return ;//相离
     if(b<)return ;//内含
     return ;//相交
 }
 point line_intersect(point p1, point p2, point q1, point q2)
 {
     point ans=p1;
     double t=((p1.x-q1.x)*(q1.y-q2.y)-(p1.y-q1.y)*(q1.x-q2.x))/
              ((p1.x-p2.x)*(q1.y-q2.y)-(p1.y-p2.y)*(q1.x-q2.x));
     ans.x += (p2.x-p1.x)*t;
     ans.y += (p2.y-p1.y)*t;
     return ans;
 }
 void line_cross_circle(point p, point q, point o, double r, point &pp, point &qq)
 {
     point tmp=o;
     tmp.x += p.y-q.y;
     tmp.y += q.x-p.x;
     tmp=line_intersect(tmp, o, p, q);
     double t=sqrt(r*r - sqr(tmp.dist(o)))/(p.dist(q));
     pp.x=tmp.x + (q.x-p.x)*t;
     pp.y=tmp.y + (q.y-p.y)*t;
     qq.x=tmp.x - (q.x-p.x)*t;
     qq.y=tmp.y - (q.y-p.y)*t;
 }
 void circle_intersect(circle c1, circle c2, point &p1, point &p2)
 {
     point u, v;
     double t, d;
     d=c1.o.dist(c2.o);
     t= (+ (sqr(c1.r) -sqr(c2.r))/sqr(d))/;
     u.x= c1.o.x+ (c2.o.x-c1.o.x)*t;
     u.y= c1.o.y+ (c2.o.y-c1.o.y)*t;
     v.x= u.x+c1.o.y-c2.o.y;
     v.y= u.y-c1.o.x+c2.o.x;
     line_cross_circle(u, v, c1.o, c1.r, p1, p2);
 }
 point circle_tangent(circle c1, circle c2)
 {
     point t;
     if(isgn(c1.o.dist(c2.o)-c1.r-c2.r)==)
     {
         t.x=(c1.r*c2.o.x + c2.r*c1.o.x)/(c1.r+c2.r);
         t.y=(c1.r*c2.o.y + c2.r*c1.o.y)/(c1.r+c2.r);
         return t;
     }
     t.x=(c1.r*c2.o.x-c2.r*c1.o.x)/(c1.r-c2.r);
     t.y=(c1.r*c2.o.y-c2.r*c1.o.y)/(c1.r-c2.r);
     return t;
 }
 void findallpoint()
 {
     int i, j, rel;
     point p1, p2;
     for(i=; i<=cn; i++)
         for(j=i+; j<=cn; j++)
         {
             rel=cir_relation(c[i], c[j]);
             if(rel==)
             {
                 circle_intersect(c[i], c[j], p1, p2);
                 p[pn++]=p1;
                 p[pn++]=p2;
             }
             else if(rel<)
                 p[pn++]=circle_tangent(c[i], c[j]);
         }
 }

 point tmp[];
 point qq[], base;
 bool cmp(point a, point b)
 {
     return a.dist(base)<b.dist(base);
 }
 bool insideok(point a, point b)
 {
     for(int i=; i<=cn; i++)
     {
         if(isgn(c[i].r-a.dist(c[i].o))<)continue;
         if(isgn(c[i].r-b.dist(c[i].o))<)continue;
         return true;
     }
     return false;
 }
 double multiply(point sp, point ep, point op)
 {
     return (sp.x-op.x)*(ep.y-op.y)-(sp.y-op.y)*(ep.x-op.x);
 }
 bool onsegment(point a, point u, point v)
 {
     return isgn(multiply(v, a, u))== && isgn((u.x-a.x)*(v.x-a.x))<= && isgn((u.y-a.y)*(v.y-a.y))<=;
 }

 bool edgeok(point a, point b)
 {
     int i, j;
     int cnt=, num;

     tmp[cnt++]=a;
     point p1, p2;
     for(i=; i<=cn; i++)
     {
         line_cross_circle(a, b, c[i].o, c[i].r, p1, p2);
         if(onsegment(p1, a, b))tmp[cnt++]=p1;
         if(onsegment(p2, a, b))tmp[cnt++]=p2;
     }
     tmp[cnt++]=b;

     base=a;
     sort(tmp, tmp+cnt, cmp);
     for(i=; i<cnt; i++)
         if(!insideok(tmp[i-], tmp[i]))
             return false;
     return true;
 }
 void findalledge()
 {
     int i, j;
     for(i=; i<pn; i++)
         for(j=i+; j<pn; j++)
         {
             if(edgeok(p[i], p[j]))
                 edge[i][j]=edge[j][i]=p[i].dist(p[j]);
             else
                 edge[i][j]=edge[j][i]=-;
         }
 }
 bool has[maxp];
 double dis[maxp];
 void dijkstra()
 {
     int i, j, num;
     double tmp;
     for(i=; i<pn; i++)has[i]=false, dis[i]=inf;
     dis[]=;
     for(i=; i<pn; i++)
     {
         tmp=inf;
         for(j=; j<pn; j++)
             if(!has[j] && dis[j]<tmp)
             {
                 tmp=dis[j];
                 num=j;
             }
         has[num]=true;
         for(j=; j<pn; j++)
             if(!has[j] && isgn(edge[num][j])>=)
                 dis[j]=min(dis[j], dis[num]+edge[num][j]);
     }
     if(dis[]<inf)printf("%.4lf\n", dis[]);
     else printf("No such path.\n");
 }

 void solve()
 {
     findallpoint();
     findalledge();
     dijkstra();
 }

 int main()
 {
     int t, ca=;
     scanf("%d", &t);
     while(t--)
     {
         scanf("%d", &cn);
         for(int i=; i<=cn; i++)
             scanf("%lf%lf%lf", &c[i].o.x, &c[i].o.y, &c[i].r);
         pn=;
         p[pn++]=c[].o;
         p[pn++]=c[cn].o;
         printf("Case %d: ", ca++);
         solve();
     }
     return ;
 }