conter_clockwise.cpp

#include <iostream>
#include <cmath>

#define EPS (1e-10)
#define equals(a, b) (fabs(a) - (b)) < EPS)

using namespace std;

class Point {
public:
	double x, y;

	Point(double x = 0, double y = 0) :x(x), y(y) {}

	Point operator + (Point p) { return Point(x + p.x, y + p.y); }
	Point operator - (Point p) { return Point(x - p.x, y - p.y); }
	Point operator * (double s) { return Point(x * s, y * s); }
	Point operator / (double s) { return Point(x / s, y / s); }

	double abs() {
		return sqrt(norm());
	}
	double norm() {
		return x * x + y * y;
	}

	bool operator < (const Point &p) const {
		return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
	}

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

};
typedef Point Vector;

double cross(Vector a, Vector b) {
	return a.x * b.y - a.y * b.x;
}

double dot(Vector a, Vector b) {
	return a.x*b.x + a.y * b.y;
}
const int COUNTER_CLOCKWISE = 1;
const int CLOCKWISE = -1;
const int ONLINE_BACK = 2;
const int ONLINE_FRONT = -2;
const int ON_SEGMENT = 0;

// Calculate the relation of points
int ccw(Point p0, Point p1, Point p2)
{
	Vector a = p1 - p0;
	Vector b = p2 - p0;
	if (cross(a, b) > EPS) return COUNTER_CLOCKWISE;
	if (cross(a, b) < -EPS) return CLOCKWISE;
	if (dot(a, b) < -EPS) return ONLINE_BACK;
	if (a.norm() < b.norm()) return ONLINE_FRONT;
	return ON_SEGMENT;
}

int main() {
	// Input
	double x, y;
	cin >> x >> y;
	Point p0(x,y);
	cin >> x >> y;
	Point p1(x, y);
	int q;
	cin >> q;
	for (int i = 0; i < q; i++) {
		cin >> x >> y;
		Point p2(x, y);
		// CCW
		switch (ccw(p0,p1,p2))
		{
		case -1: cout << "CLOCKWISE" << endl;
			break;
		case 1: cout << "COUNTER_CLOCKWISE" << endl;
			break;
		case -2: cout << "ONLINE_FRONT" << endl;
			break;
		case 2: cout << "ONLINE_BACK" << endl;
			break;
		default:
			cout << "ON_SEGMENT" << endl;
			break;
		}
		
	}
	
	return 0;
}