Monotone Chain Convex Hull.cpp

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;
}