稳定凸包
即每条边上至少有3个点即可。。

#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <queue>
using namespace std;
const int MAXN = 1e3 + 5;
const double EPS = 1e-6;
const int INF = 0x7fffffff;
struct Point
{
    Point() {}
    Point(double _x, double _y): x(_x), y(_y) {}

    double getDis(Point rhs)
    {
        double xx = rhs.x - x;
        double yy = rhs.y - y;
        return sqrt(xx * xx + yy * yy);
    }

    void input()
    {
        scanf("%lf%lf", &x, &y);
    }
    double x, y;
};

Point operator -(Point lhs, Point rhs)
{
    Point ret = Point(rhs.x - lhs.x, rhs.y - lhs.y);
    return ret;
}

double operator ^(Point lhs, Point rhs)
{
    double ret = lhs.x * rhs.y - lhs.y * rhs.x;
    return ret;
}

Point point[MAXN];
Point src;
int n;

bool cmp(Point &a, Point &b)
{
    double temp = (a - src) ^ (b - src);
    if(fabs(temp) <= EPS) return src.getDis(a) < src.getDis(b);
    return temp > -EPS;
}
bool cmp2(Point &a, Point &b)
{
    return src.getDis(a) > src.getDis(b);
}

bool convex()
{
    sort(point, point + n, cmp);
    int j = n - 1;
    while(j > 0 && fabs((point[j] - src) ^ (point[j - 1] - src)) < EPS)
    {
        --j;
    }
    if(j > 0) sort(point + j, point + n, cmp2);
    else return false;

    int now = 0, nxt;
    for(int i = 1; i < n; ++i)
    {
        nxt = (i + 1) % n;
        double temp = (point[i] - point[now]) ^ (point[nxt] - point[now]);
        if(fabs(temp) < EPS)
        {
            //nothing to do
        }
        else
        {
            if(i - now <= 1) return false;
            else now = i;
        }
    }
    return true;
}

int main()
{
    // freopen("in.txt", "r", stdin);
    int T;
    scanf("%d", &T);
    while(T--)
    {
        src = Point(INF, INF);
        scanf("%d", &n);
        for(int i = 0; i < n; ++i)
        {
            point[i].input();
            if(point[i].x < src.x || (fabs(point[i].x - src.x) < EPS && point[i].y < src.y))
            {
                src = point[i];
            }
        }
        if(n < 6)
        {
            puts("NO");
            continue;
        }
        if(convex()) puts("YES");
        else puts("NO");
    }
}