Выпуклая оболочка

#include <bits/stdc++.h>
 
using namespace std;
 
struct point
{
    long long x, y;
};
 
point operator-(const point& a, const point& b)
{
    return {a.x-b.x, a.y-b.y};
}
 
bool operator<(const point& a, const point& b)
{
    return a.x < b.x || a.x == b.x && a.y < b.y;
}
 
long long operator^(const point& a, const point& b)
{
    return a.x*b.y - a.y*b.x;
}
 
int rotation(const point& a, const point& b, const point& c)
{
    long long cross = (b-a)^(c-b);
    if (cross < 0)
        return -1;
    if (cross > 0)
        return 1;
    return 0;
}
 
void convex_hull(vector<point>& points)
{
    sort(points.begin(), points.end());
    int n = points.size();
    vector<point> top = {points[0]}, bottom = {points[0]};
    for (int i = 1; i < n; i ++)
    {
        if (rotation(points[0], points[n-1], points[i]) >= 0)
        {
            while (top.size() > 1 && rotation(top[top.size()-2], top[top.size()-1], points[i]) >= 0)
                top.pop_back();
            top.push_back(points[i]);
        }
        else
        {
            while (bottom.size() > 1 && rotation(bottom[bottom.size()-2], bottom[bottom.size()-1], points[i]) <= 0)
                bottom.pop_back();
            bottom.push_back(points[i]);
        }
    }
    reverse(bottom.begin(), bottom.end());
    bottom.pop_back();
    cout << top.size() + bottom.size() << "\n";
 
 
    for(int i = 0; i < top.size() ; i ++)
    {
        cout << top[i].x << " " << top[i].y << "\n";
    }
    for(int i = 0; i < bottom.size() ; i ++)
    {
        cout << bottom[i].x << " " << bottom[i].y << "\n";
    }
 
}
 
int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    int n, x, y;
    cin >> n;
    vector < point > points;
    for (int i = 0 ; i < n; i ++)
    {
        cin >> x >> y;
        points.push_back({x, y});
    }
    convex_hull(points);
}

struct point
{
    long long x, y;
};
 
point operator-(const point& a, const point& b)
{
    return {a.x-b.x, a.y-b.y};
}
 
bool operator<(const point& a, const point& b)
{
    return a.x < b.x || a.x == b.x && a.y < b.y;
}
 
long long operator^(const point& a, const point& b)
{
    return a.x*b.y - a.y*b.x;
}
 
int rotation(const point& a, const point& b, const point& c)
{
    long long cross = (b-a)^(c-b);
    if (cross < 0) return -1;
    if (cross > 0) return 1;
    return 0;
}
 
vector < point > convex_hull(vector<point>& points)
{
    sort(points.begin(), points.end());
    int n = points.size();
    vector<point> top = {points[0]}, bottom = {points[0]};
    for (int i = 1; i < n; i ++)
    {
        if (rotation(points[0], points[n-1], points[i]) >= 0)
        {
            while (top.size() > 1 && rotation(top[top.size()-2], top[top.size()-1], points[i]) >= 0)
                top.pop_back();
            top.push_back(points[i]);
        }
        else
        {
            while (bottom.size() > 1 && rotation(bottom[bottom.size()-2], bottom[bottom.size()-1], points[i]) <= 0)
                bottom.pop_back();
            bottom.push_back(points[i]);
        }
 
    }
 
    while (bottom.size() > 1 && rotation(bottom[bottom.size()-2], bottom[bottom.size()-1], points[n-1]) <= 0)
        bottom.pop_back();
 
    reverse(bottom.begin(), bottom.end());
 
    for (point u:bottom)
        top.push_back(u);
    top.pop_back();
    return top;
}