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120 | #include<bits/stdc++.h>
using namespace std;
template<typename T>
struct point{
T x,y;
point(){}
point(const T&dx,const T&dy):x(dx),y(dy){}
inline const point operator+(const point &b)const{
return point(x+b.x,y+b.y);
}
inline const point operator-(const point &b)const{
return point(x-b.x,y-b.y);
}
inline const point operator*(const T &b)const{
return point(x*b,y*b);
}
inline const point operator/(const T &b)const{
return point(x/b,y/b);
}
inline const T dot(const point &b)const{
return x*b.x+y*b.y;
}
inline const T cross(const point &b)const{
return x*b.y-y*b.x;
}
inline point normal()const{/*求法向量*/
return point(-y,x);
}
inline const T abs2()const{/*向量長度的平方*/
return dot(*this);
}
};
template<typename T>
struct line{
line(){}
point<T> p1,p2;
line(const point<T>&x,const point<T>&y):p1(x),p2(y){}
inline bool parallel(const line &l)const{/*直線平行*/
return (p1-p2).cross(l.p1-l.p2)==0;
}
inline T cross(const point<T> &p)const{/*點和有向直線的關係，>0左邊、=0在線上<0右邊*/
return (p2-p1).cross(p-p1);
}
inline point<T> line_intersection(const line &l)const{/*直線交點*/
point<T> a=p2-p1,b=l.p2-l.p1,s=l.p1-p1;
return p1+a*s.cross(b)/a.cross(b);
}
};
template<typename T>
struct polygon{
polygon(){}
std::vector<point<T> > p;
inline const point<T>& operator[](int id)const{
return p[id];
}
inline static char sign(const T&x){
return x>=0?1:-1;
}
inline static bool angle_cmp(const line<T>& A,const line<T>& B){
point<T>a=A.p2-A.p1,b=B.p2-B.p1;
char ay=sign(a.y),by=sign(b.y),ax=sign(a.x),bx=sign(b.x);
return ay>by||(ay==by&&(ax*ay>bx*by||(ax*ay==bx*by&&a.cross(b)>0)));
}
inline int halfplane_intersection(std::vector<line<T> > &s){
sort(s.begin(),s.end(),angle_cmp);
int L,R,n=s.size();
std::vector<point<T> > px(n);
std::vector<line<T> > q(n);
q[L=R=0]=s[0];
for(int i=1;i<n;++i){
while(L<R&&s[i].cross(px[R-1])<=0)--R;
while(L<R&&s[i].cross(px[L])<=0)++L;
q[++R]=s[i];
if(q[R].parallel(q[R-1])){
--R;
if(q[R].cross(s[i].p1)>0)q[R]=s[i];
}
if(L<R)px[R-1]=q[R-1].line_intersection(q[R]);
}
while(L<R&&q[L].cross(px[R-1])<=0)--R;
p.clear();
if(R-L<=1)return 0;
px[R]=q[R].line_intersection(q[L]);
for(int i=L;i<=R;++i)p.push_back(px[i]);
return R-L+1;
}
};
const int maxn=105;
const double bw=10000;
polygon<double> poly;
vector<line<double> >s;
int n,v[maxn],u[maxn],w[maxn];
int main(){
while(~scanf("%d",&n)&&n){
for(int i=0;i<n;++i)scanf("%d%d%d",&v[i],&u[i],&w[i]);
for(int i=0;i<n;++i){
s.clear();
bool ok=1;
for(int j=0;j<n;++j)if(i!=j){
if(v[i]<=v[j]&&u[i]<=u[j]&&w[i]<=w[j]){ok=0;break;}
if(v[i]>=v[j]&&u[i]>=u[j]&&w[i]>=w[j])continue;
double a=(bw/v[j]-bw/w[j])-(bw/v[i]-bw/w[i]);
double b=(bw/u[j]-bw/w[j])-(bw/u[i]-bw/w[i]);
double c=bw/w[j]-bw/w[i];
point<double> t,x(b,-a);
if(fabs(a)>fabs(b))t=point<double>(-c/a,0);
else t=point<double>(0,-c/b);
s.push_back(line<double>(t,t+x));
}
if(ok){
s.push_back(line<double>(point<double>(0,0),point<double>(0,-1)));
s.push_back(line<double>(point<double>(0,0),point<double>(1,0)));
s.push_back(line<double>(point<double>(0,1),point<double>(-1,2)));
if(!poly.halfplane_intersection(s))ok=0;
}
puts(ok?"Yes":"No");
}
}
return 0;
}
|
