凸包稳定性判断：每条边上是否至少有三点 POJ 1228

 //凸包稳定性判断：每条边上是否至少有三点
 // POJ 1228

 #include <iostream>
 #include <cstdio>
 #include <cstdlib>
 #include <algorithm>
 #include <vector>
 #include <math.h>
 using namespace std;
 #define LL long long
 typedef pair<int,int> pii;
 const double inf = 0x3f3f3f3f;
 const LL MOD =100000000LL;
 const int N =;
 #define clc(a,b) memset(a,b,sizeof(a))
 const double eps = 1e-;
 void fre() {freopen("in.txt","r",stdin);}
 void freout() {freopen("out.txt","w",stdout);}
 inline int read() {int x=,f=;char ch=getchar();while(ch>''||ch<'') {if(ch=='-') f=-; ch=getchar();}while(ch>=''&&ch<='') {x=x*+ch-'';ch=getchar();}return x*f;}

 int sgn(double x){
     if(fabs(x) < eps)return ;
     if(x < )return -;
     else return ;
 }

 struct Point{
     double x,y;
     Point(){}
     Point(double _x,double _y){
         x = _x;y = _y;
     }
     Point operator -(const Point &b)const{
         return Point(x - b.x,y - b.y);
     }
     double operator ^(const Point &b)const{
         return x*b.y - y*b.x;
     }
     double operator *(const Point &b)const{
         return x*b.x + y*b.y;
     }
     friend bool operator<(const Point &a,const Point &b){
         if(fabs(a.y-b.y)<eps) return a.x<b.x;
         return a.y<b.y;
     }
     friend double dis2(Point a){
         return a.x*a.x+a.y*a.y;
     }
 };

 double dis(Point a,Point b){
     return sqrt(dis2(a-b));
 }

 int mult(Point a,Point b,Point o){
     return sgn((a.x-o.x)*(b.y-o.y)-(b.x-o.x)*(a.y-o.y));
 }
 //返回top个点
 int graham(Point p[],int n,Point q[]){
      int top=;
      sort(p,p+n);
      if(n==) return ;
      q[]=p[];
      if(n==) return ;
      q[]=p[];
      if(n==) return ;
      q[]=p[];
      for(int i=;i<n;i++){
          while(top&&(mult(p[i],q[top],q[top-])>)) top--;
          q[++top]=p[i];
      }
      int len=top;
      q[++top]=p[n-];
      for(int i=n-;i>=;i--){
          while(top!=len&&(mult(p[i],q[top],q[top-])>)) top--;
          q[++top]=p[i];
      }
      return top;
 }

 // 判断凸包边上是否至少有三点
 bool judge(Point p[],int m){
     p[m]=p[];
     p[m+]=p[];
     for(int i=;i<m;i++){
        if(mult(p[i-],p[i+],p[i])!=&&mult(p[i],p[i+],p[i+])!=)
         return false;
     }
     return true;
 }

 Point p[];
 Point ch[];
 int main(){
     // fre();
     int T;
     scanf("%d",&T);
     while(T--){
        int n;
        scanf("%d",&n);
        for(int i=;i<n;i++){
            double x,y;
            scanf("%lf%lf",&x,&y);
            p[i]=Point(x,y);
        }
        int m=graham(p,n,ch);
        if(n<) {
         puts("NO");
         continue;
        }
        if(judge(ch,m)) puts("YES");
        else puts("NO");
     }
     return ;
 }