UVa 10256 The Great Divide 凸包, 凸包分离
来源:互联网 发布:淘宝有哪几种营销方式 编辑:程序博客网 时间:2024/05/18 02:13
题目地址:pdf版本
首先可以证明,存在这样的直线的充要条件是,两个点集的凸包实现分离。
而凸包实现分离的充要条件又是。
1 不能有任何线段相交(不是规范相交) 是不能有公共点
2 在1保证了相离的前提下,不能有点在另一个多边形的内部
对凸包退化成点或者线段的时候,需要单独考虑~
代码:
#include<iostream>#include<cmath>#include<cstdio>#include<algorithm>#include<vector>const double eps=1e-10;const double PI=acos(-1.0);using namespace std;struct Point{ double x; double y; Point(double x=0,double y=0):x(x),y(y){} void operator<<(Point &A) {cout<<A.x<<' '<<A.y<<endl;}};int dcmp(double x) {return (x>eps)-(x<-eps); }int sgn(double x) {return (x>eps)-(x<-eps); }typedef Point Vector;Vector operator +(Vector A,Vector B) { return Vector(A.x+B.x,A.y+B.y);}Vector operator -(Vector A,Vector B) { return Vector(A.x-B.x,A.y-B.y); }Vector operator *(Vector A,double p) { return Vector(A.x*p,A.y*p); }Vector operator /(Vector A,double p) {return Vector(A.x/p,A.y/p);}ostream &operator<<(ostream & out,Point & P) { out<<P.x<<' '<<P.y<<endl; return out;}//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;}double Dot(Vector A,Vector B) {return A.x*B.x+A.y*B.y;}double Cross(Vector A,Vector B) {return A.x*B.y-B.x*A.y; }double Length(Vector A) { return sqrt(Dot(A, A));}double Angle(Vector A,Vector B) {return acos(Dot(A,B)/Length(A)/Length(B));}double Area2(Point A,Point B,Point C ) {return Cross(B-A, C-A);}Vector Rotate(Vector A,double rad) { return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));}Vector Normal(Vector A) {double L=Length(A);return Vector(-A.y/L,A.x/L);}Point GetLineIntersection(Point P,Vector v,Point Q,Vector w){ Vector u=P-Q; double t=Cross(w, u)/Cross(v,w); return P+v*t; }double DistanceToLine(Point P,Point A,Point B){ Vector v1=P-A; Vector v2=B-A; return fabs(Cross(v1,v2))/Length(v2); }double DistanceToSegment(Point P,Point A,Point B){ if(A==B) return Length(P-A); Vector v1=B-A; Vector v2=P-A; Vector v3=P-B; if(dcmp(Dot(v1,v2))==-1) return Length(v2); else if(Dot(v1,v3)>0) return Length(v3); else return DistanceToLine(P, A, B); }Point GetLineProjection(Point P,Point A,Point B){ Vector v=B-A; Vector v1=P-A; double t=Dot(v,v1)/Dot(v,v); return A+v*t;}// 已针对本题优化bool SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2){ double c1=Cross(b1-a1, a2-a1); double c2=Cross(b2-a1, a2-a1); double c3=Cross(a1-b1, b2-b1); double c4=Cross(a2-b1, b2-b1); return dcmp(c1)*dcmp(c2)<=0&&dcmp(c3)*dcmp(c4)<=0 ; }bool OnSegment(Point P,Point A,Point B){ return dcmp(Cross(P-A, P-B))==0&&dcmp(Dot(P-A,P-B))<=0;}double PolygonArea(Point *p,int n){ double area=0; for(int i=1;i<n-1;i++) { area+=Cross(p[i]-p[0], p[i+1]-p[0]); } return area/2; }Point read_point(){ Point P; scanf("%lf%lf",&P.x,&P.y); return P;}// ---------------与圆有关的--------struct Circle{ Point c; double r; Circle(Point c=Point(0,0),double r=0):c(c),r(r) {} Point point(double a) { return Point(c.x+r*cos(a),c.y+r*sin(a)); } };struct Line{ Point p; Vector v; Line(Point p=Point(0,0),Vector v=Vector(0,1)):p(p),v(v) {} Point point(double t) { return Point(p+v*t); } };int getLineCircleIntersection(Line L,Circle C,double &t1,double &t2,vector<Point> &sol){ double a=L.v.x; double b=L.p.x-C.c.x; double c=L.v.y; double d=L.p.y-C.c.y; double e=a*a+c*c; double f=2*(a*b+c*d); double g=b*b+d*d-C.r*C.r; double delta=f*f-4*e*g; if(dcmp(delta)<0) return 0; if(dcmp(delta)==0) { t1=t2=-f/(2*e); sol.push_back(L.point(t1)); return 1; } else { t1=(-f-sqrt(delta))/(2*e); t2=(-f+sqrt(delta))/(2*e); sol.push_back(L.point(t1)); sol.push_back(L.point(t2)); return 2; } }// 向量极角公式double angle(Vector v) {return atan2(v.y,v.x);}int getCircleCircleIntersection(Circle C1,Circle C2,vector<Point> &sol){ double d=Length(C1.c-C2.c); if(dcmp(d)==0) { if(dcmp(C1.r-C2.r)==0) return -1; // 重合 else return 0; // 内含 0 个公共点 } if(dcmp(C1.r+C2.r-d)<0) return 0; // 外离 if(dcmp(fabs(C1.r-C2.r)-d)>0) return 0; // 内含 double a=angle(C2.c-C1.c); double da=acos((C1.r*C1.r+d*d-C2.r*C2.r)/(2*C1.r*d)); Point p1=C1.point(a-da); Point p2=C1.point(a+da); sol.push_back(p1); if(p1==p2) return 1; // 相切 else { sol.push_back(p2); return 2; }}// 求点到圆的切线int getTangents(Point p,Circle C,Vector *v){ Vector u=C.c-p; double dist=Length(u); if(dcmp(dist-C.r)<0) return 0; else if(dcmp(dist-C.r)==0) { v[0]=Rotate(u,PI/2); return 1; } else { double ang=asin(C.r/dist); v[0]=Rotate(u,-ang); v[1]=Rotate(u,+ang); return 2; } }// 求两圆公切线int getTangents(Circle A,Circle B,Point *a,Point *b){ int cnt=0; if(A.r<B.r) { swap(A,B); swap(a, b); // 有时需标记 } double d=Length(A.c-B.c); double rdiff=A.r-B.r; double rsum=A.r+B.r; if(dcmp(d-rdiff)<0) return 0; // 内含 double base=angle(B.c-A.c); if(dcmp(d)==0&&dcmp(rdiff)==0) return -1 ; // 重合 无穷多条切线 if(dcmp(d-rdiff)==0) // 内切 外公切线 { a[cnt]=A.point(base); b[cnt]=B.point(base); cnt++; return 1; } // 有外公切线的情形 double ang=acos(rdiff/d); a[cnt]=A.point(base+ang); b[cnt]=B.point(base+ang); cnt++; a[cnt]=A.point(base-ang); b[cnt]=B.point(base-ang); cnt++; if(dcmp(d-rsum)==0) // 外切 有内公切线 { a[cnt]=A.point(base); b[cnt]=B.point(base+PI); cnt++; } else if(dcmp(d-rsum)>0) // 外离 又有两条外公切线 { double ang_in=acos(rsum/d); a[cnt]=A.point(base+ang_in); b[cnt]=B.point(base+ang_in+PI); cnt++; a[cnt]=A.point(base-ang_in); b[cnt]=B.point(base-ang_in+PI); cnt++; } return cnt;}// 几何算法模板int isPointInPolygon(Point p,Point * poly,int n){ int wn=0; for(int i=0;i<n;i++) { if(OnSegment(p, poly[i], poly[(i+1)%n])) return -1; int k=dcmp(Cross(poly[(i+1)%n]-poly[i], p-poly[i])); int d1=dcmp(poly[i].y-p.y); int d2=dcmp(poly[(i+1)%n].y-p.y); if(k>0&&d1<=0&&d2>0) wn++; if(k<0&&d2<=0&&d1>0) wn--; } if(wn!=0) return 1; else return 0; }// Andrew 算法求凸包int ConvexHull(Point *p,int n,Point *ch){ int m=0; sort(p,p+n); n=unique(p, p+n)-p; for(int i=0;i<n;i++) { while(m>1&&Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--; ch[m++]=p[i]; } int k=m; for(int i=n-2;i>=0;i--) { while(m>k&&Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--; ch[m++]=p[i]; } if(n>1) m--; return m; }Point p1[10010];Point ch1[10010];Point p2[10010];Point ch2[10010];int main(){ int n1,n2; while(cin>>n1>>n2) { bool ok=1; if(!n1&&!n2) break; for(int i=0;i<n1;i++) p1[i]=read_point(); for(int i=0;i<n2;i++) p2[i]=read_point(); int m1=ConvexHull(p1, n1, ch1); int m2=ConvexHull(p2, n2, ch2); if(m1>=3&&m2>=3) { bool breakout=0; // 判断线段相交 for(int i=0;i<m1;i++) { for(int j=0;j<m2;j++) { if(SegmentProperIntersection(ch1[i], ch1[i+1], ch2[j], ch2[j+1])) { ok=0; breakout=1; break; } } if(breakout) break; } // 判断点在多边形内 for(int i=0;i<m1;i++) { if(isPointInPolygon(ch1[i],ch2, m2)) { ok=0; break; } } for(int i=0;i<m2;i++) { if(isPointInPolygon(ch2[i],ch1, m1)) { ok=0; break; } } } else if(m1==1&&m2>=3) { if(isPointInPolygon(ch1[0],ch2, m2)) { ok=0; } } else if(m1==2&&m2>=3) { if(isPointInPolygon(ch1[0],ch2, m2)) { ok=0; } if(isPointInPolygon(ch1[1],ch2, m2)) { ok=0; } } else if(m1>=3&&m2==1) { if(isPointInPolygon(ch2[0],ch1, m1)) { ok=0; break; } } else if(m1>=3&&m2==2) { if(isPointInPolygon(ch2[0],ch1, m1)) { ok=0; break; } if(isPointInPolygon(ch2[1],ch1, m1)) { ok=0; break; } } else if(m1==1&&m2==1) { if(ch1[0]==ch2[0]) { ok=0; } } else if(m1==1&&m2==2) { if(OnSegment(ch1[0],ch2[0], ch2[1])) { ok=0; } } else if(m1==2&&m2==1) { if(OnSegment(ch2[0],ch1[0], ch1[1])) { ok=0; } } else if(m1==2&&m2==2) { if(SegmentProperIntersection(ch1[0], ch1[1], ch2[0], ch2[1])) { ok=0; } } if(ok) cout<<"Yes"<<endl; else cout<<"No"<<endl; }}
0 0
- UVa 10256 The Great Divide 凸包, 凸包分离
- UVA 10256 The Great Divide 凸包
- UVA 10256 The Great Divide 凸包 .
- UVA 10256 The Great Divide(凸包应用)
- uva 10256 - The Great Divide(凸包)
- Uva 10256 The Great Divide(凸包)
- UVa 10256 The Great Divide,判断两个凸包是否相离
- UVA 10256 The Great Divide(凸包应用 即凸包+线段相交判定+点是否在凸包内判断)
- uva10256 The Great Divide(凸包+判断)
- UVA 10256 The Great Divide
- UVA 10256 - The Great Divide
- UVA 10256 The Great Divide
- UVA 10256 The Great Divide
- uva 10256 The Great Divide
- uva 10256(凸包)
- uva 10256 凸包
- uva10256 The Great Divide
- UVA 10078 The Art Gallery(凸包)
- ZOJ 1203 Swordfish
- fedora20+Nginx+Mysql+PHP配置
- Free Type True Type的字体外形信息,及angelcode.com的.fnt格式的baseline
- Eclipse快速添加get/set方法
- 网页屏蔽右键以及防止css被查看方法
- UVa 10256 The Great Divide 凸包, 凸包分离
- 《MQL4实用编程》读书笔记(9) - 简单编程:外建指标 ROC (价格变化速度)
- 设计模式(6)-结构性模式-Adapter模式
- 明智行动的艺术2
- 设计模式(7)-结构型模式-Bridge模式
- 关于c#中networkstream.read 方法的问题
- 虚函数,静态与动态绑定
- c语言深度学习
- javaIO流-1