164 lines
4.0 KiB
C++
164 lines
4.0 KiB
C++
#include<cstdio>
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#include<cstring>
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#include<algorithm>
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#include<cmath>
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#include<vector>
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#define eps 1e-8
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#define N 200
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using namespace std;
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const double PI=acos(-1.0);
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int dlcmp(double x)
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{
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return x<-eps?-1:x>eps;
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}
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struct Point
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{
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double x,y;
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Point(){}
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Point(double a,double b):x(a),y(b){}
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Point operator + (const Point a) const {return Point(x+a.x,y+a.y);}
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Point operator - (const Point a) const {return Point(x-a.x,y-a.y);}
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Point operator * (const double a) const {return Point(x*a,y*a);}
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Point operator / (const double a) const {return Point(x/a,y/a);}
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bool operator == (const Point a)
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{
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return !dlcmp(x-a.x)&&!dlcmp(y-a.y);
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}
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Point trunc(double d) const
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{
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double dis(Point,Point);
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double len=dis(*this,Point(0,0));
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return Point(x*d/len,y*d/len);
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}
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Point rotate(double a)
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{
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return Point(x*cos(a)-y*sin(a),y*cos(a)+x*sin(a));
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}
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};
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struct Circle
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{
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Point o;
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double r;
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Circle(){}
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Circle(Point a,double l):o(a),r(l){}
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};
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struct node
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{
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double s,e;
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node(){}
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node(double a,double b):s(a),e(b){}
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};
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Circle c[N],red,purple;
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vector<node>arc;
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double sqr(double x)
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{
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return x*x;
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}
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double fix(double x)
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{
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if (dlcmp(x-1)>=0)
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return 1;
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if (dlcmp(x+1)<=0)
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return -1;
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return x;
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}
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double dis(Point a,Point b)
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{
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return sqrt(sqr(a.x-b.x)+sqr(a.y-b.y));
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}
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void get_InCommonTangent(Circle c1,Circle c2,Point &s1,Point &e1,Point &s2,Point &e2)
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{
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double l=dis(c1.o,c2.o);
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double d=l*c1.r/(c1.r+c2.r);
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double tmp=c1.r/d;
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tmp=fix(tmp);
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double theta=acos(tmp);
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Point vec=c2.o-c1.o;
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vec=vec.trunc(c1.r);
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s1=c1.o+vec.rotate(theta);
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s2=c1.o+vec.rotate(-theta);
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vec=c1.o-c2.o;
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vec=vec.trunc(c2.r);
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e1=c2.o+vec.rotate(theta);
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e2=c2.o+vec.rotate(-theta);
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}
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void inter_circle_ray(Circle c,Point s,Point e,Point &p)
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{
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Point vec=e-s;
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double A=sqr(vec.x)+sqr(vec.y);
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double B=2*(vec.x*(s.x-c.o.x)+vec.y*(s.y-c.o.y));
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double C=sqr(s.x-c.o.x)+sqr(s.y-c.o.y)-sqr(c.r);
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double delta=sqr(B)-4*A*C;
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delta=fabs(delta);
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double k=(-B+sqrt(delta))/(2*A);
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p=s+vec*k;
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}
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double get_angle(Point a)
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{
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return atan2(a.y,a.x);
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}
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double cmp(node a,node b)
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{
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if (dlcmp(a.s-b.s)==0)
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return dlcmp(a.e-b.e)<0;
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else
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return dlcmp(a.s-b.s)<0;
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}
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int main()
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{
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int n,p,x,y,r,i,j;
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double ans,sum,cur;
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node u,v;
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Point s1,e1,s2,e2,vec,p1,p2;
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while (scanf("%d%d%d%d%d",&n,&p,&x,&y,&r),n||p||x||y||r)
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{
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purple.o=Point(0,0);
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purple.r=(double)p;
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red.o.x=(double)x;
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red.o.y=(double)y;
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red.r=(double)r;
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arc.clear();
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for (i=0;i<n;i++)
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scanf("%lf%lf%lf",&c[i].o.x,&c[i].o.y,&c[i].r);
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for (i=0;i<n;i++)
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{
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get_InCommonTangent(red,c[i],s1,e1,s2,e2);
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if (s1==e1)
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{
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vec=c[i].o-red.o;
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e1=s1+vec.rotate(PI/2);
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e2=s2+vec.rotate(-PI/2);
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}
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inter_circle_ray(purple,s1,e1,p1);
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inter_circle_ray(purple,s2,e2,p2);
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u.s=get_angle(p1);
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u.e=get_angle(p2);
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if (u.s>u.e)
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{
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arc.push_back(node(u.s,PI));
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arc.push_back(node(-PI,u.e));
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}
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else
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arc.push_back(u);
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}
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sort(arc.begin(),arc.end(),cmp);
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sum=arc[0].e-arc[0].s;
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cur=arc[0].e;
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for (i=1;i<arc.size();i++)
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{
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if (dlcmp(arc[i].e-cur)<=0)
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continue;
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if (dlcmp(arc[i].s-cur)>0)
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sum+=arc[i].e-arc[i].s;
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else
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sum+=arc[i].e-cur;
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cur=arc[i].e;
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}
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ans=(2*PI-sum)/(2*PI);
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if (ans<0)
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ans=0;
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printf("%.4f\n",ans);
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}
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return 0;
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}
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