Convex Hull

#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <cstdio>
#include <vector>
#include <cmath>
#include <string>
#include <algorithm>
#include <string>
#include <deque>
#include <iomanip>
#include <cstddef>

#define F first
#define S second

using namespace std;

struct point
{
    double x, y;
    point():x(0.0), y(0.0){}
    point(double _x, double _y):x(_x), y(_y){}
};

point operator+(point a, point b)
{
    return point(a.x + b.x, a.y + b.y);
}

point operator-(point a, point b)
{
    return point(a.x - b.x, a.y - b.y);
}

point operator*(point a, double k)
{
    return point(a.x * k, b.y * k);
}

point operator/(point a, double k)
{
    return point(a.x / k, b.y / k);
}

double vect(point a, point b)
{
    return a.x * b.y - a.y * b.x;
}

const long double eps = 0.000000005;
const long double pi = 3.1415926535897932;
const long long inf = 1e9;

vector <point> all, up, down;

bool comp(const point& a, const point& b)
{
    return (a.x < b.x) || (a.x == b.x && a.y < b.y);
}

int main()
{
    ios_base::sync_with_stdio(0);
    //freopen("input.txt", "r", stdin);freopen("output.txt", "w", stdout);
    // freopen("slalom.in", "r", stdin);freopen("slalom.out", "w", stdout);

    int n;
    cin >> n;
    double x, y;
    for (int i = 0; i < n; i++)
    {
        cin >> x >> y;
        all.push_back(point(x, y));
    }

    sort(all.begin(), all.end(), comp);

    point b = all[0], e = all.back();

    up.push_back(b);
    down.push_back(b);

    for (int i = 1; i < all.size(); i++)
    {
        point t = all[i];
        if (vect(e - b, t - b) > eps || i == all.size() - 1)
        {
            while (up.size() > 1 && vect(t - up.back(), up[up.size() - 2] - up.back()) > -eps)
                up.pop_back();
            up.push_back(t);
        }
        if (vect(e - b, t - b) < -eps || i == all.size() - 1)
        {
            while (down.size() > 1 && vect(t - down.back(), down[down.size() - 1] - down.back()) < eps)
                down.pop_back();
            down.push_back(t);
        }
    }

    return 0;
}