Convex hull trigonometric + coliniare

#include <bits/stdc++.h>
#define INF 0x3f3f3f3f
#define pi pair<int,int>
#define mp make_pair
#define x first
#define y second
#define sqr(x) (x) * (x)
#define sz(x) static_cast<int>((x).size())

using namespace std;

ifstream fin("infasuratoareconvexa.in");
ofstream fout("infasuratoareconvexa.out");

int det(pi O, pi A, pi B) {
    return (A.x - O.x) * (B.y - O.y) - (B.x - O.x) * (A.y - O.y);
}

int fcmp(const pi &a, const pi &b) {
    int d = det(mp(0, 0), a, b);
    if(d != 0)
        return d > 0;
    return sqr(a.x) + sqr(a.y) > sqr(b.x) + sqr(b.y);
}

int main() {
    int N;
    fin >> N;
    vector<pi> a(N + 1);
    a[0] = mp(INF, INF);
    int first = 0;
    for(int i = 1; i <= N; ++i) {
        fin >> a[i].x >> a[i].y;
        if(a[i].y < a[first].y || (a[i].y == a[first].y && a[i].x < a[first].x))
            first = i;
    }
    a[0] = a[first];
    a[first] = a[1];
    a[1] = a[0];
    for(int i = 1; i <= N; ++i) {
        a[i].x -= a[0].x;
        a[i].y -= a[0].y;
    }
    sort(a.begin() + 2, a.end(), fcmp);
    int j;
    for(j = 3; j <= N; ++j)
        if(det(a[1], a[2], a[j]))
            break;
    int i = 2;
    --j;
    while(i < j) {
        swap(a[i], a[j]);
        ++i, --j;
    }
    vector<pi> S;
    S.emplace_back(a[1]), S.emplace_back(a[2]);
    for(int i = 3; i <= N; ++i) {
        while(sz(S) > 1 && det(S[sz(S) - 2], S.back(), a[i]) < 0)
            S.pop_back();
       S.emplace_back(a[i]);
    }
    fout << sz(S) << '\n';
    for(const pi &x : S)
        fout << x.x + a[0].x << ' ' << x.y + a[0].y << '\n';
}