/******************************************************************************
 *  Compilation:  javac Point.java
 *  Execution:    java Point
 *
 *  Implementation of 2D point using rectangular coordinates.
 *
 ******************************************************************************/

public class Point { 
    public final int x;
    public final int y; 

    // create and initialize a point with given (x, y)
    public Point(int x, int y) {
        this.x = x;
        this.y = y;
    }
  
    // return Euclidean distance between this point and that point
    public double distanceTo(Point that) {
        if (that == null) return Double.POSITIVE_INFINITY;
        double dx = this.x - that.x;
        double dy = this.y - that.y;
        return Math.hypot(dx, dy);
    }

    // draw point
    public void draw() {
        StdDraw.point(x, y);
    }

    // draw line segment between this point and that point
    public void drawTo(Point that) {
        StdDraw.line(this.x, this.y, that.x, that.y);
    }

    // is a->b->c a counter-clockwise turn?
    // +1 if counter-clockwise, -1 if clockwise, 0 if collinear
    public static int ccw(Point a, Point b, Point c) {
        // return a.x*b.y - a.y*b.x + a.y*c.x - a.x*c.y + b.x*c.y - b.y*c.x;
        double area2 = (b.x - a.x) * (c.y - a.y) - (c.x - a.x) * (b.y - a.y);
        if      (area2 < 0) return -1;
        else if (area2 > 0) return +1;
        else                return  0;
    }

    // is a-b-c collinear?
    public static boolean collinear(Point a, Point b, Point c) {
        return ccw(a, b, c) == 0;
    }

    // is c between a and b?
    // Reference: O' Rourke p. 32
    public static boolean between(Point a, Point b, Point c) {
        if (ccw(a, b, c) != 0) return false;
        if (a.x == b.x && a.y == b.y) {
            return a.x == c.x && a.y == c.y;
        }
        else if (a.x != b.x) {
            // ab not vertical
            return (a.x <= c.x && c.x <= b.x) || (a.x >= c.x && c.x >= b.x);
        }
        else {
            // ab not horizontal
            return (a.y <= c.y && c.y <= b.y) || (a.y >= c.y && c.y >= b.y);
        }
    }


    // return string representation of this point
    public String toString() {
        return "(" + x + ", " + y + ")";
    }


    // test client
    public static void main(String[] args) {
        Point p = new Point(5, 6);
        StdOut.println("p  = " + p);
        Point q = new Point(2, 2);
        StdOut.println("q  = " + q);
        StdOut.println("dist(p, q) = " + p.distanceTo(q) + " = " + q.distanceTo(p));
    }
}