题意：给出一多边形。判断多边形是否存在一点，使得多边形边界上的所有点都能看见该点。
sol：在纸上随手画画就可以找出规律：按逆时针顺序连接所有点。然后找出这些line的半平面交。
题中给出的点已经按顺时针排好序了，所以只要倒过来一下就可以了。很简单的模板题。
#include<vector>
#include<list>
#include<map>
#include<set>
#include<deque>
#include<queue>
#include<stack>
#include<bitset>
#include<algorithm>
#include<functional>
#include<numeric>
#include<utility>
#include<iostream>
#include<sstream>
#include<iomanip>
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cctype>
#include<string>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<ctime>
#include<climits>
#include<complex>
#define mp make_pair
#define pb push_back
using namespace std;
const double eps=1e-;
const double pi=acos(-1.0);
const double inf=1e20;
const int maxp=;
int dblcmp(double d)
{
if (fabs(d)<eps)return ;
return d>eps?:-;
}
inline double sqr(double x){return x*x;}
struct point
{
double x,y;
point(){}
point(double _x,double _y):
x(_x),y(_y){};
void input()
{
scanf("%lf%lf",&x,&y);
}
void output()
{
printf("%.2f %.2f\n",x,y);
}
bool operator==(point a)const
{
return dblcmp(a.x-x)==&&dblcmp(a.y-y)==;
}
bool operator<(point a)const
{
return dblcmp(a.x-x)==?dblcmp(y-a.y)<:x<a.x;
}
double len()
{
return hypot(x,y);
}
double len2()
{
return x*x+y*y;
}
double distance(point p)
{
return hypot(x-p.x,y-p.y);
}
point add(point p)
{
return point(x+p.x,y+p.y);
}
point sub(point p)
{
return point(x-p.x,y-p.y);
}
point mul(double b)
{
return point(x*b,y*b);
}
point div(double b)
{
return point(x/b,y/b);
}
double dot(point p)
{
return x*p.x+y*p.y;
}
double det(point p)
{
return x*p.y-y*p.x;
}
double rad(point a,point b)
{
point p=*this;
return fabs(atan2(fabs(a.sub(p).det(b.sub(p))),a.sub(p).dot(b.sub(p))));
}
point trunc(double r)
{
double l=len();
if (!dblcmp(l))return *this;
r/=l;
return point(x*r,y*r);
}
point rotleft()
{
return point(-y,x);
}
point rotright()
{
return point(y,-x);
}
point rotate(point p,double angle)//绕点p逆时针旋转angle角度
{
point v=this->sub(p);
double c=cos(angle),s=sin(angle);
return point(p.x+v.x*c-v.y*s,p.y+v.x*s+v.y*c);
}
};
struct line
{
point a,b;
line(){}
line(point _a,point _b)
{
a=_a;
b=_b;
}
bool operator==(line v)
{
return (a==v.a)&&(b==v.b);
}
//倾斜角angle
line(point p,double angle)
{
a=p;
if (dblcmp(angle-pi/)==)
{
b=a.add(point(,));
}
else
{
b=a.add(point(,tan(angle)));
}
}
//ax+by+c=0
line(double _a,double _b,double _c)
{
if (dblcmp(_a)==)
{
a=point(,-_c/_b);
b=point(,-_c/_b);
}
else if (dblcmp(_b)==)
{
a=point(-_c/_a,);
b=point(-_c/_a,);
}
else
{
a=point(,-_c/_b);
b=point(,(-_c-_a)/_b);
}
}
void input()
{
a.input();
b.input();
}
void adjust()
{
if (b<a)swap(a,b);
}
double length()
{
return a.distance(b);
}
double angle()//直线倾斜角 0<=angle<180
{
double k=atan2(b.y-a.y,b.x-a.x);
if (dblcmp(k)<)k+=pi;
if (dblcmp(k-pi)==)k-=pi;
return k;
}
//点和线段关系
//1 在逆时针
//2 在顺时针
//3 平行
int relation(point p)
{
int c=dblcmp(p.sub(a).det(b.sub(a)));
if (c<)return ;
if (c>)return ;
return ;
}
bool pointonseg(point p)
{
return dblcmp(p.sub(a).det(b.sub(a)))==&&dblcmp(p.sub(a).dot(p.sub(b)))<=;
}
bool parallel(line v)
{
return dblcmp(b.sub(a).det(v.b.sub(v.a)))==;
}
//2 规范相交
//1 非规范相交
//0 不相交
int segcrossseg(line v)
{
int d1=dblcmp(b.sub(a).det(v.a.sub(a)));
int d2=dblcmp(b.sub(a).det(v.b.sub(a)));
int d3=dblcmp(v.b.sub(v.a).det(a.sub(v.a)));
int d4=dblcmp(v.b.sub(v.a).det(b.sub(v.a)));
if ((d1^d2)==-&&(d3^d4)==-)return ;
return (d1==&&dblcmp(v.a.sub(a).dot(v.a.sub(b)))<=||
d2==&&dblcmp(v.b.sub(a).dot(v.b.sub(b)))<=||
d3==&&dblcmp(a.sub(v.a).dot(a.sub(v.b)))<=||
d4==&&dblcmp(b.sub(v.a).dot(b.sub(v.b)))<=);
}
int linecrossseg(line v)//*this seg v line
{
int d1=dblcmp(b.sub(a).det(v.a.sub(a)));
int d2=dblcmp(b.sub(a).det(v.b.sub(a)));
if ((d1^d2)==-)return ;
return (d1==||d2==);
}
//0 平行
//1 重合
//2 相交
int linecrossline(line v)
{
if ((*this).parallel(v))
{
return v.relation(a)==;
}
return ;
}
point crosspoint(line v)
{
double a1=v.b.sub(v.a).det(a.sub(v.a));
double a2=v.b.sub(v.a).det(b.sub(v.a));
return point((a.x*a2-b.x*a1)/(a2-a1),(a.y*a2-b.y*a1)/(a2-a1));
}
double dispointtoline(point p)
{
return fabs(p.sub(a).det(b.sub(a)))/length();
}
double dispointtoseg(point p)
{
if (dblcmp(p.sub(b).dot(a.sub(b)))<||dblcmp(p.sub(a).dot(b.sub(a)))<)
{
return min(p.distance(a),p.distance(b));
}
return dispointtoline(p);
}
point lineprog(point p)
{
return a.add(b.sub(a).mul(b.sub(a).dot(p.sub(a))/b.sub(a).len2()));
}
point symmetrypoint(point p)
{
point q=lineprog(p);
return point(*q.x-p.x,*q.y-p.y);
}
}; struct Vector:public point
{
Vector(){}
Vector(double a,double b)
{
x=a; y=b;
}
Vector(point _a,point _b) //a->b
{
double dx=_b.x-_a.x;
double dy=_b.y-_a.y;
x=dx; y=dy;
}
Vector(line v)
{
double dx=v.b.x-v.a.x;
double dy=v.b.y-v.a.y;
x=dx; y=dy;
}
double length()
{
return (sqrt(x*x+y*y));
}
Vector Normal()
{
double L=sqrt(x*x+y*y);
Vector Vans=Vector(-y/L,x/L);
return Vans;
}
}; struct halfplane:public line //半平面
{
double angle;
halfplane(){}
//表示向量 a->b逆时针(左侧)的半平面
halfplane(point _a,point _b)
{
a=_a;
b=_b;
}
halfplane(line v)
{
a=v.a;
b=v.b;
}
void calcangle()
{
angle=atan2(b.y-a.y,b.x-a.x);
}
bool operator<(const halfplane &b)const
{
return angle<b.angle;
}
};
struct halfplanes //半平面交
{
int n;
halfplane hp[maxp];
point p[maxp];
int que[maxp];
int st,ed;
void push(halfplane tmp)
{
hp[n++]=tmp;
}
void unique()
{
int m=,i;
for (i=;i<n;i++)
{
if (dblcmp(hp[i].angle-hp[i-].angle))hp[m++]=hp[i];
else if (dblcmp(hp[m-].b.sub(hp[m-].a).det(hp[i].a.sub(hp[m-].a))>))hp[m-]=hp[i];
}
n=m;
}
bool halfplaneinsert()
{
int i;
for (i=;i<n;i++)hp[i].calcangle();
sort(hp,hp+n);
unique();
que[st=]=;
que[ed=]=;
p[]=hp[].crosspoint(hp[]);
for (i=;i<n;i++)
{
while (st<ed&&dblcmp((hp[i].b.sub(hp[i].a).det(p[ed].sub(hp[i].a))))<)ed--;
while (st<ed&&dblcmp((hp[i].b.sub(hp[i].a).det(p[st+].sub(hp[i].a))))<)st++;
que[++ed]=i;
if (hp[i].parallel(hp[que[ed-]]))return false;
p[ed]=hp[i].crosspoint(hp[que[ed-]]);
}
while (st<ed&&dblcmp(hp[que[st]].b.sub(hp[que[st]].a).det(p[ed].sub(hp[que[st]].a)))<)ed--;
while (st<ed&&dblcmp(hp[que[ed]].b.sub(hp[que[ed]].a).det(p[st+].sub(hp[que[ed]].a)))<)st++;
if (st+>=ed)return false;
return true;
}
/*
void getconvex(polygon &con)
{
p[st]=hp[que[st]].crosspoint(hp[que[ed]]);
con.n=ed-st+1;
int j=st,i=0;
for (;j<=ed;i++,j++)
{
con.p[i]=p[j];
}
}*/
}; point p[];
halfplanes TH;
int n,T; int main()
{
//freopen("in.txt","r",stdin); cin>>T;
while (T--)
{
cin>>n;
for (int i=n-;i>=;i--)
p[i].input();
//p[i]->p[i+1] TH.n=;
for (int i=;i<=n-;i++)
TH.push(halfplane(p[i],p[(i+)%n])); if (TH.halfplaneinsert())
cout<<"YES"<<endl;
else cout<<"NO"<<endl;
} return ;
}