題意:
求光線能達到的最大橫坐標
注意光線可以和管道重合
也可以經過轉折點
解法:
枚舉每種光線是否能通過每個轉折點的截面(線段)即可
//大白p263 #include <cmath> #include <cstdio> #include <cstring> #include <string> #include <queue> #include <functional> #include <set> #include <iostream> #include <vector> #include <algorithm> using namespace std; const double eps=1e-8;//精度 const int INF=1<<29; const double PI=acos(-1.0); int dcmp(double x){//判斷double等於0或。。。 if(fabs(x)<eps)return 0;else return x<0?-1:1; } struct Point{ double x,y; Point(double x=0,double y=0):x(x),y(y){} }; typedef Point Vector; typedef vector<Point> Polygon; Vector operator+(Vector a,Vector b){return Vector(a.x+b.x,a.y+b.y);}//向量+向量=向量 Vector operator-(Point a,Point b){return Vector(a.x-b.x,a.y-b.y);}//點-點=向量 Vector operator*(Vector a,double p){return Vector(a.x*p,a.y*p);}//向量*實數=向量 Vector operator/(Vector a,double p){return Vector(a.x/p,a.y/p);}//向量/實數=向量 bool operator<( const Point& A,const Point& B ){return dcmp(A.x-B.x)<0||(dcmp(A.x-B.x)==0&&dcmp(A.y-B.y)<0);} bool operator==(const Point&a,const Point&b){return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;} bool operator!=(const Point&a,const Point&b){return a==b?false:true;} struct Segment{ Point a,b; Segment(){} Segment(Point _a,Point _b){a=_a,b=_b;} bool friend operator<(const Segment& p,const Segment& q){return p.a<q.a||(p.a==q.a&&p.b<q.b);} bool friend operator==(const Segment& p,const Segment& q){return (p.a==q.a&&p.b==q.b)||(p.a==q.b&&p.b==q.a);} }; struct Circle{ Point c; double r; Circle(){} Circle(Point _c, double _r):c(_c),r(_r) {} Point point(double a)const{return Point(c.x+cos(a)*r,c.y+sin(a)*r);} bool friend operator<(const Circle& a,const Circle& b){return a.r<b.r;} }; struct Line{ Point p; Vector v; double ang; Line() {} Line(const Point &_p, const Vector &_v):p(_p),v(_v){ang = atan2(v.y, v.x);} bool operator<(const Line &L)const{return ang < L.ang;} }; double Dot(Vector a,Vector b){return a.x*b.x+a.y*b.y;}//|a|*|b|*cosθ 點積 double Length(Vector a){return sqrt(Dot(a,a));}//|a| 向量長度 double Angle(Vector a,Vector b){return acos(Dot(a,b)/Length(a)/Length(b));}//向量夾角θ double Cross(Vector a,Vector b){return a.x*b.y-a.y*b.x;}//叉積 向量圍成的平行四邊形的面積 double Area2(Point a,Point b,Point c){return Cross(b-a,c-a);}//同上 參數為三個點 double DegreeToRadius(double deg){return deg/180*PI;} double GetRerotateAngle(Vector a,Vector b){//向量a順時針旋轉theta度得到向量b的方向 double tempa=Angle(a,Vector(1,0)); if(a.y<0) tempa=2*PI-tempa; double tempb=Angle(b,Vector(1,0)); if(b.y<0) tempb=2*PI-tempb; if((tempa-tempb)>0) return tempa-tempb; else return tempa-tempb+2*PI; } double torad(double deg){return deg/180*PI;}//角度化為弧度 Vector Rotate(Vector a,double rad){//向量逆時針旋轉rad弧度 return Vector(a.x*cos(rad)-a.y*sin(rad),a.x*sin(rad)+a.y*cos(rad)); } Vector Normal(Vector a){//計算單位法線 double L=Length(a); return Vector(-a.y/L,a.x/L); } Point GetLineProjection(Point p,Point a,Point b){//點在直線上的投影 Vector v=b-a; return a+v*(Dot(v,p-a)/Dot(v,v)); } Point GetLineIntersection(Point p,Vector v,Point q,Vector w){//求直線交點 有唯一交點時可用 Vector u=p-q; double t=Cross(w,u)/Cross(v,w); return p+v*t; } int ConvexHull(Point* p,int n,Point* sol){//計算凸包 sort(p,p+n); int m=0; for(int i=0;i<n;i++){ while(m>1&&Cross(sol[m-1]-sol[m-2],p[i]-sol[m-2])<=0) m--; sol[m++]=p[i]; } int k=m; for(int i=n-2;i>=0;i--){ while(m>k&&Cross(sol[m-1]-sol[m-2],p[i]-sol[m-2])<=0) m--; sol[m++]=p[i]; } if(n>0) m--; return m; } double Heron(double a,double b,double c){//海倫公式 double p=(a+b+c)/2; return sqrt(p*(p-a)*(p-b)*(p-c)); } bool SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2){//線段規范相交判定 double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1); double c3=Cross(b2-b1,a1-b1),c4=Cross(b2-b1,a2-b1); return dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0; } double CutConvex(const int n,Point* poly, const Point a,const Point b, vector<Point> result[3]){//有向直線a b 切割凸多邊形 vector<Point> points; Point p; Point p1=a,p2=b; int cur,pre; result[0].clear(); result[1].clear(); result[2].clear(); if(n==0) return 0; double tempcross; tempcross=Cross(p2-p1,poly[0]-p1); if(dcmp(tempcross)==0) pre=cur=2; else if(tempcross>0) pre=cur=0; else pre=cur=1; for(int i=0;i<n;i++){ tempcross=Cross(p2-p1,poly[(i+1)%n]-p1); if(dcmp(tempcross)==0) cur=2; else if(tempcross>0) cur=0; else cur=1; if(cur==pre){ result[cur].push_back(poly[(i+1)%n]); } else{ p1=poly[i]; p2=poly[(i+1)%n]; p=GetLineIntersection(p1,p2-p1,a,b-a); points.push_back(p); result[pre].push_back(p); result[cur].push_back(p); result[cur].push_back(poly[(i+1)%n]); pre=cur; } } sort(points.begin(),points.end()); if(points.size()<2){ return 0; } else{ return Length(points.front()-points.back()); } } double DistanceToSegment(Point p,Segment s){//點到線段的距離 if(s.a==s.b) return Length(p-s.a); Vector v1=s.b-s.a,v2=p-s.a,v3=p-s.b; if(dcmp(Dot(v1,v2))<0) return Length(v2); else if(dcmp(Dot(v1,v3))>0) return Length(v3); else return fabs(Cross(v1,v2))/Length(v1); } bool isPointOnSegment(Point p,Segment s){ return Cross(s.a-p,s.b-p)==0&&Dot(s.a-p,s.b-p)<0; } int isPointInPolygon(Point p, Point* poly,int n){//點與多邊形的位置關系 int wn=0; for(int i=0;i<n;i++){ Point& p2=poly[(i+1)%n]; if(isPointOnSegment(p,Segment(poly[i],p2))) return -1;//點在邊界上 int k=dcmp(Cross(p2-poly[i],p-poly[i])); int d1=dcmp(poly[i].y-p.y); int d2=dcmp(p2.y-p.y); if(k>0&&d1<=0&&d2>0)wn++; if(k<0&&d2<=0&&d1>0)wn--; } if(wn) return 1;//點在內部 else return 0;//點在外部 } double PolygonArea(vector<Point> p){//多邊形有向面積 double area=0; int n=p.size(); for(int i=1;i<n-1;i++) area+=Cross(p[i]-p[0],p[i+1]-p[0]); return area/2; } int GetLineCircleIntersection(Line L,Circle C,Point& p1,Point& p2){//圓與直線交點 返回交點個數 double a = L.v.x, b = L.p.x - C.c.x, c = L.v.y, d = L.p.y-C.c.y; double e = a*a + c*c, f = 2*(a*b+c*d), g = b*b + d*d -C.r*C.r; double delta = f*f - 4*e*g; if(dcmp(delta) < 0) return 0;//相離 if(dcmp(delta) == 0) {//相切 p1=p1=C.point(-f/(2*e)); return 1; }//相交 p1=(L.p+L.v*(-f-sqrt(delta))/(2*e)); p2=(L.p+L.v*(-f+sqrt(delta))/(2*e)); return 2; } double rotating_calipers(Point *ch,int n)//旋轉卡殼 { int q=1; double ans=0; ch[n]=ch[0]; for(int p=0;p<n;p++) { while(Cross(ch[q+1]-ch[p+1],ch[p]-ch[p+1])>Cross(ch[q]-ch[p+1],ch[p]-ch[p+1])) q=(q+1)%n; ans=max(ans,max(Length(ch[p]-ch[q]),Length(ch[p+1]-ch[q+1]))); } return ans; } Polygon CutPolygon(Polygon poly,Point a,Point b){//用a->b切割多邊形 返回左側 Polygon newpoly; int n=poly.size(); for(int i=0;i<n;i++){ Point c=poly[i]; Point d=poly[(i+1)%n]; if(dcmp(Cross(b-a,c-a))>=0) newpoly.push_back(c); if(dcmp(Cross(b-a,c-d))!=0){ Point ip=GetLineIntersection(a,b-a,c,d-c); if(isPointOnSegment(ip,Segment(c,d))) newpoly.push_back(ip); } } return newpoly; } int GetCircleCircleIntersection(Circle c1,Circle c2,Point& p1,Point& p2){ double d=Length(c1.c-c2.c); if(dcmp(d)==0){ if(dcmp(c1.r-c2.r)==0) return -1;//兩圓重合 return 0; } if(dcmp(c1.r+c2.r-d)<0) return 0; if(dcmp(fabs(c1.r-c2.r)-d)>0) return 0; double a=Angle(c2.c-c1.c,Vector(1,0)); double da=acos((c1.r*c1.r+d*d-c2.r*c2.r)/(2*c1.r*d)); p1=c1.point(a-da);p2=c1.point(a+da); if(p1==p2) return 1; return 2; } //-------------------------------------- //-------------------------------------- //-------------------------------------- //-------------------------------------- //-------------------------------------- int n; Point arr[25],arr2[25]; double fuck(Line l){ Point p; int i; for(i=0;i<n;i++){ p=GetLineIntersection(l.p,l.v,arr[i],arr2[i]-arr[i]); if(dcmp(p.y-arr[i].y)>0||dcmp(p.y-arr2[i].y)<0){ if(i==0) return arr[0].x; Point q=GetLineIntersection(l.p,l.v,arr[i],arr[i]-arr[i-1]); p=GetLineIntersection(l.p,l.v,arr2[i],arr2[i]-arr2[i-1]); return max(p.x,q.x); } } return arr[n-1].x; } int main() { while(scanf("%d",&n)!=EOF&&n){ for(int i=0;i<n;i++){ scanf("%lf%lf",&arr[i].x,&arr[i].y); arr2[i].x=arr[i].x; arr2[i].y=arr[i].y-1; } double ans=arr[0].x; for(int i=0;i<n;i++){ for(int j=0;j<n;j++)if(i!=j){ Line l1(arr[i],arr[i]-arr2[j]); ans=max(ans,fuck(l1)); } } if(dcmp(ans-arr[n-1].x)<0) printf("%.2lf\n",ans); else puts("Through all the pipe."); } return 0; }