Convex Hull

vector<Point> convex_hull(vector<Point> P)
{
	int n = P.size(), k = 0;
	vector<Point> H(2*n);

	sort(P.begin(), P.end());

	for (int i = 0; i < n; ++i) {
		while (k >= 2 && cross(H[k-2], H[k-1], P[i]) < 0) k--;
		H[k++] = P[i];
	}

	for (int i = n-2, t = k+1; i >= 0; i--) {
		while (k >= t && cross(H[k-2], H[k-1], P[i]) < 0) k--;
		H[k++] = P[i];
	}

	H.resize(k);
	return H;
}
double dist( Point a , Point b ) {
    return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y)) ;
}