Алгоритм Грэхема

#include <algorithm>
#include <iostream>
#include <vector>
 
using namespace std;
 
struct pt {
    double x, y;
};
 
bool cmp (pt a, pt b) {
    return a.x < b.x || a.x == b.x && a.y < b.y;
}
 
bool cw (pt a, pt b, pt c) {
    return a.x*(b.y-c.y)+b.x*(c.y-a.y)+c.x*(a.y-b.y) < 0;
}
 
bool ccw (pt a, pt b, pt c) {
    return a.x*(b.y-c.y)+b.x*(c.y-a.y)+c.x*(a.y-b.y) > 0;
}
 
void convex_hull (vector<pt> & a) {
    if (a.size() == 1)  return;
    sort (a.begin(), a.end(), &cmp);
    pt p1 = a[0],  p2 = a.back();
    vector<pt> up, down;
    up.push_back (p1);
    down.push_back (p1);
    for (size_t i=1; i<a.size(); ++i) {
        if (i==a.size()-1 || cw (p1, a[i], p2)) {
            while (up.size()>=2 && !cw (up[up.size()-2], up[up.size()-1], a[i]))
                up.pop_back();
            up.push_back (a[i]);
        }
        if (i==a.size()-1 || ccw (p1, a[i], p2)) {
            while (down.size()>=2 && !ccw (down[down.size()-2], down[down.size()-1], a[i]))
                down.pop_back();
            down.push_back (a[i]);
        }
    }
    a.clear();
    for (size_t i=0; i<up.size(); ++i)
        a.push_back (up[i]);
    for (size_t i=down.size()-2; i>0; --i)
        a.push_back (down[i]);
}
 
int main() {
    std::vector<pt> a = {
        {2, 2},
        {3, 4},
        {1, 4},
        {2, 7},
        {4, 7},
        {5, 4},
        {5, 1},
        {7, 4}
    };
 
    convex_hull(a);
    for (const auto& pt : a) {
        std::cout << pt.x << " " << pt.y << std::endl;
    }
}

for (std::vector<pt>::iterator it = a.begin(); it != a.end(); ++it) {
    std::cout << it->x << " " << it->y << std::endl;
}