HW4E

#include <iostream>
#include <stdio.h>
#include <algorithm>
#include <vector>
#include <cmath>

using namespace std;

struct point {
    double x, y;
    point operator-(point a) {
        return {x - a.x, y - a.y};
    }
    double operator^(point a) {
        return x * a.y - y * a.x;
    }
};

double perimeter(vector<point> & points) {
    point p0 = points[0];
    for (point p : points)
        if (p.x < p0.x || (p.x == p0.x && p.y < p0.y))
            p0 = p;

    for (point &x : points) {
        x.x -= p0.x;
        x.y -= p0.y;
    }

    sort(points.begin(), points.end(), [&](point a, point b){
        return (a ^ b) > 0 || (a ^ b) == 0 && a.x * a.x + a.y * a.y < b.x * b.x + b.y * b.y;
    });

    vector<point> hull;
    for (point p : points) {
        while (hull.size() >= 2 && (((p - hull.back()) ^ (hull[hull.size() - 2] - hull.back())) <= 0)) {
             hull.pop_back();
        }
        hull.push_back(p);
    }

    for (point &x : hull) {
        x.x += p0.x;
        x.y += p0.y;
    }

    double sum = 0;
    for (int i = 1; i < hull.size(); i++) {
        sum += sqrt((hull[i - 1].x - hull[i].x)*(hull[i - 1].x - hull[i].x) +
                    (hull[i - 1].y - hull[i].y)*(hull[i - 1].y - hull[i].y));
    }
    sum += sqrt((hull[hull.size() - 1].x - hull[0].x)*(hull[hull.size() - 1].x - hull[0].x) +
                (hull[hull.size() - 1].y - hull[0].y)*(hull[hull.size() - 1].y - hull[0].y));

    return sum;
}


int main()
{
    int N;
    cin >> N;
    vector <point> points (N);
    for (int i = 0; i < N; i++)
        cin >> points[i].x >> points[i].y;

    double sum = perimeter(points);
    printf("%.2f", sum);
    return 0;
}