uva 1298 - Triathlon

半平面交的题；

这个题目的亮点就是建模；

 #include<cstdio>
 #include<algorithm>
 #include<cmath>
 #define maxn 109
 #define eps 1e-6
 using namespace std;

 int dcmp(double x)
 {
     return fabs(x) < eps ?  : (x >  ?  : -);
 }

 struct Point
 {
     double x;
     double y;
     Point(double x = , double y = ):x(x), y(y) {}
 };
 typedef Point Vector;

 Vector operator + (Point A, Point B)
 {
     return Vector(A.x + B.x, A.y + B.y);
 }

 Vector operator - (Point A, Point B)
 {
     return Vector(A.x - B.x, A.y - B.y);
 }

 Vector operator * (Point A, double p)
 {
     return Vector(A.x * p, A.y * p);
 }

 Vector operator / (Point A, double p)
 {
     return Vector(A.x / p, A.y / p);
 }
 double dot(Point a,Point b)
 {
     return a.x*b.x+a.y*b.y;
 }
 double cross(Point a,Point b)
 {
     return a.x*b.y-a.y*b.x;
 }

 Vector nomal(Vector a)
 {
     double l=sqrt(dot(a,a));
     return Vector(-a.y/l,a.x/l);
 }

 struct line
 {
     Point p;
     Vector v;
     double ang;
     line() {}
     line(Point p,Vector v):p(p),v(v)
     {
         ang=atan2(v.y,v.x);
     }
     bool operator<(const line &t)const
     {
         return ang<t.ang;
     }
 };

 bool onleft(line l,Point p)
 {
     return (cross(l.v,p-l.p)>);
 }

 Point getintersection(line a,line b)
 {
     Vector u=a.p-b.p;
     double t=cross(b.v,u)/cross(a.v,b.v);
     return a.p+a.v*t;
 }

 int halfplanintersection(line *l,int n,Point *poly)
 {
     sort(l,l+n);
     int first,last;
     Point *p=new Point[n];
     line *q=new line[n];
     q[first=last=]=l[];
     for(int i=; i<n; i++)
     {
         while(first<last && !onleft(l[i],p[last-]))last--;
         while(first<last && !onleft(l[i],p[first]))first++;
         q[++last]=l[i];
         if(fabs(cross(q[last].v,q[last-].v))<eps)
         {
             last--;
             if(onleft(q[last],l[i].p))q[last]=l[i];
         }
         if(first<last)p[last-]=getintersection(q[last-],q[last]);
     }
     while(first<last && !onleft(q[first],p[last-]))last--;
     if((last-first )<=)return ;
     p[last]=getintersection(q[last],q[first]);
     int m=;
     for(int i=first; i<=last; i++)poly[m++]=p[i];
     return m;
 }

 Point poly[maxn];
 line l[maxn];
 double v[maxn],u[maxn],w[maxn];

 int main()
 {
     int n;
     while(scanf("%d",&n)!=EOF)
     {
         for(int i=;i<n;i++)scanf("%lf%lf%lf",&v[i],&u[i],&w[i]);
         for(int i=;i<n;i++)
         {
             double k=;
             bool flag=;
             int cnt=;
             for(int j=;j<n;j++)
             {
                 if(i==j)continue;
                 if(v[j]>=v[i]&&u[j]>=u[i]&&w[j]>=w[i]){flag=;break;}
                 if(v[j]<=v[i]&&w[j]<=u[i]&&w[j]<=w[i])continue;
                 double a=(k/v[j]-k/w[j])-(k/v[i]-k/w[i]);
                 double b=(k/u[j]-k/w[j])-(k/u[i]-k/w[i]);
                 double c=k/w[j]-k/w[i];
                 Point p;
                 Vector v(b,-a);
                 if(fabs(a)>fabs(b))p=Point(-c/a,);
                 else p=Point(,-c/b);
                 l[cnt++]=line(p,v);
             }
             if(flag)
             {
                 l[cnt++]=line(Point(,),Vector(,-));
                 l[cnt++]=line(Point(,),Vector(,));
                 l[cnt++]=line(Point(,),Vector(-,));
                 if(halfplanintersection(l,cnt,poly)==)flag=;
             }
             if(flag)puts("Yes");
             else puts("No");
         }

     }return ;
 }