Monotone Chain Convex Hull.cpp

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This is an implementation of Monotone Chain Convex Hull in C++.

// Implementation of Andrew's monotone chain 2D convex hull algorithm.
#include <algorithm>
#include <vector>
using namespace std;
 
typedef int coord_t;         // coordinate type
typedef long long coord2_t;  // must be big enough to hold 2*max(|coordinate|)^2
 
struct Point {
	coord_t x, y;
 
	bool operator <(const Point &p) const {
		return x < p.x || (x == p.x && y < p.y);
	}
};
 
// 2D cross product of OA and OB vectors, i.e. z-component of their 3D cross product.
// Returns a positive value, if OAB makes a counter-clockwise turn,
// negative for clockwise turn, and zero if the points are collinear.
coord2_t cross(const Point &O, const Point &A, const Point &B)
{
	return (A.x - O.x) * (coord2_t)(B.y - O.y) - (A.y - O.y) * (coord2_t)(B.x - O.x);
}
 
// Returns a list of points on the convex hull in counter-clockwise order.
// Note: the last point in the returned list is the same as the first one.
vector<Point> convex_hull(vector<Point> P)
{
	int n = P.size(), k = 0;
	vector<Point> H(2*n);
 
	// Sort points lexicographically
	sort(P.begin(), P.end());
 
	// Build lower hull
	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];
	}
 
	// Build upper hull
	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;
}