Monotone chain convex hull.cpp

// Implementation of Monotone Chain Convex Hull algorithm. using namespace std;
 * 1) include
 * 2) include

typedef long long CoordType;

struct Point { CoordType x, y;

bool operator <(const Point &p) const { return x < p.x || (x == p.x && y < p.y); } };

// 2D cross product. // Return a positive value, if OAB makes a counter-clockwise turn, // negative for clockwise turn, and zero if the points are collinear. CoordType cross(const Point &O, const Point &A, const Point &B) {	return (A.x - O.x) * (B.y - O.y) - (A.y - O.y) * (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 convexHull(vector P) { int n = P.size, k = 0; vector 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; }