Выпуклая оболочка

#include <iostream>
#include <bits/stdc++.h>
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")

#define mp make_pair
#define pb push_back
#define eb emplace_back
#define x first
#define y second
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define FOR(i,a,b) for (int i = (a); i < (b); i++)
#define RFOR(i,b,a) for (int i = (b) - 1; i >= (a); i--)

using namespace std;

typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pi;
typedef pair<ld, ld> pld;
typedef pair<ll, ll> pl;
typedef vector<int> veci;
typedef vector<bool> vecb;
typedef vector<vector<int>> vvi;
typedef vector<vector<bool>> vvb;

const int INF_I = 1e9;
const ll INF_LL = 1e18;
const int MOD = 1000000007;
const double eps = 1e-6;

pld m(pld a, pld b){
    return {b.x - a.x, b.y - a.y};
}

ld vec(pld a, pld b){
    return a.x * b.y - a.y * b.x;
}

ld l(pld a, pld b){
    return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
}

int main() {

    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);

    int n;
    cin >> n;
    vector<pi> a(n);
    pi mn = {INF_I, INF_I};
    for (int i = 0; i < n; i++) {
        cin >> a[i].x >> a[i].y;
        mn = min(mn, a[i]);
    }
    for (int i = 0; i < n; i++) {
        a[i] = {a[i].x - mn.x, a[i].y - mn.y};
    }
    a.erase(find(all(a), mp(0, 0)));
    sort(all(a), [](pi a1, pi a2){
        return atan2(a1.y, a1.x) < atan2(a2.y, a2.x);
    });
    a.eb(mp(0, 0));
    for (int i = n-1; i >= 1; i--)
        swap(a[i], a[i-1]);
    veci b;
    b.reserve(n);
    b.eb(0), b.eb(1);
    for (int i = 2; i < n; i++){
        pld v1 = m(a[b[sz(b)-2]], a[i]);
        pld v2 = m(a[b[sz(b)-2]], a[b[sz(b)-1]]);
        while (sz(b) >= 2 && vec(v2, v1) < 0) {
            b.pop_back();
            v1 = m(a[b[sz(b)-2]], a[i]);
            v2 = m(a[b[sz(b)-2]], a[b[sz(b)-1]]);
        }
        b.eb(i);
    }
    ld P = 0;
    ld S = 0;
    for (int i = 0; i < sz(b); i++) {
        S += vec(a[b[i]], a[b[(i + 1) % sz(b)]]) * 0.5;
        P += l(a[b[i]], a[b[(i + 1) % sz(b)]]);
    }
    cout << fixed << P << " " << fabs(S) << "\n";

    return 0;
}