/*************************************************************************
 *  Compilation:  javac Point2D.java
 *
 *  Immutable point data type for points in the plane.
 *
 *************************************************************************/

import java.util.Arrays;
import java.util.Comparator;

import edu.princeton.cs.introcs.StdDraw;
import edu.princeton.cs.introcs.StdRandom;


/**
 *  The  Point  class is an immutable data type to encapsulate a
 *  two-dimensional point with real-value coordinates.
 *   
 *  Note: in order to deal with the difference behavior of double and 
 *  Double with respect to -0.0 and +0.0, the Point2D constructor converts
 *  any coordinates that are -0.0 to +0.0.
 *  
 *  For additional documentation, see <a href="/algs4/12oop">Section 1.2</a> of
 *   Algorithms, 4th Edition  by Robert Sedgewick and Kevin Wayne.
 *
 *  @author Robert Sedgewick
 *  @author Kevin Wayne
 */
public class Point2D implements Comparable<Point2D> {

    /**
     * Compares two points by x-coordinate.
     */
    public static final Comparator<Point2D> X_ORDER = new XOrder();

    /**
     * Compares two points by y-coordinate.
     */
    public static final Comparator<Point2D> Y_ORDER = new YOrder();

    /**
     * Compares two points by polar radius.
     */
    public static final Comparator<Point2D> R_ORDER = new ROrder();

    /**
     * Compares two points by polar angle (between 0 and 2pi) with respect to this point.
     */
    public final Comparator<Point2D> POLAR_ORDER = new PolarOrder();

    /**
     * Compares two points by atan2() angle (between -pi and pi) with respect to this point.
     */
    public final Comparator<Point2D> ATAN2_ORDER = new Atan2Order();

    /**
     * Compares two points by distance to this point.
     */
    public final Comparator<Point2D> DISTANCE_TO_ORDER = new DistanceToOrder();

    private final double x;    // x coordinate
    private final double y;    // y coordinate

    /**
     * Initializes a new point (x, y).
     * @param x the x-coordinate
     * @param y the y-coordinate
     * @throws IllegalArgumentException if either  x  or  y 
     *    is  Double.NaN ,  Double.POSITIVE_INFINITY  or
     *     Double.NEGATIVE_INFINITY 
     */
    public Point2D(double x, double y) {
        if (Double.isInfinite(x) || Double.isInfinite(y))
            throw new IllegalArgumentException("Coordinates must be finite");
        if (Double.isNaN(x) || Double.isNaN(y))
            throw new IllegalArgumentException("Coordinates cannot be NaN");
        if (x == 0.0) x = 0.0;  // convert -0.0 to +0.0
        if (y == 0.0) y = 0.0;  // convert -0.0 to +0.0
        this.x = x;
        this.y = y;
    }

    /**
     * Returns the x-coordinate.
     * @return the x-coordinate
     */
    public double x() {
        return x;
    }

    /**
     * Returns the y-coordinate.
     * @return the y-coordinate
     */
    public double y() {
        return y;
    }

    /**
     * Returns the polar radius of this point.
     * @return the polar radius of this point in polar coordiantes: sqrt(x*x + y*y)
     */
    public double r() {
        return Math.sqrt(x*x + y*y);
    }

    /**
     * Returns the angle of this point in polar coordinates.
     * @return the angle (in radians) of this point in polar coordiantes (between -pi/2 and pi/2)
     */
    public double theta() {
        return Math.atan2(y, x);
    }

    /**
     * Returns the angle between this point and that point.
     * @return the angle in radians (between -pi and pi) between this point and that point (0 if equal)
     */
    private double angleTo(Point2D that) {
        double dx = that.x - this.x;
        double dy = that.y - this.y;
        return Math.atan2(dy, dx);
    }

    /**
     * Is a->b->c a counterclockwise turn?
     * @param a first point
     * @param b second point
     * @param c third point
     * @return { -1, 0, +1 } if a->b->c is a { clockwise, collinear; counterclocwise } turn.
     */
    public static int ccw(Point2D a, Point2D b, Point2D c) {
        double area2 = (b.x-a.x)*(c.y-a.y) - (b.y-a.y)*(c.x-a.x);
        if      (area2 < 0) return -1;
        else if (area2 > 0) return +1;
        else                return  0;
    }

    /**
     * Returns twice the signed area of the triangle a-b-c.
     * @param a first point
     * @param b second point
     * @param c third point
     * @return twice the signed area of the triangle a-b-c
     */
    public static double area2(Point2D a, Point2D b, Point2D c) {
        return (b.x-a.x)*(c.y-a.y) - (b.y-a.y)*(c.x-a.x);
    }

    /**
     * Returns the Euclidean distance between this point and that point.
     * @param that the other point
     * @return the Euclidean distance between this point and that point
     */
    public double distanceTo(Point2D that) {
        double dx = this.x - that.x;
        double dy = this.y - that.y;
        return Math.sqrt(dx*dx + dy*dy);
    }

    /**
     * Returns the square of the Euclidean distance between this point and that point.
     * @param that the other point
     * @return the square of the Euclidean distance between this point and that point
     */
    public double distanceSquaredTo(Point2D that) {
        double dx = this.x - that.x;
        double dy = this.y - that.y;
        return dx*dx + dy*dy;
    }

    /**
     * Compares this point to that point by y-coordinate, breaking ties by x-coordinate.
     * @param that the other point
     * @return { a negative integer, zero, a positive integer } if this point is
     *    { less than, equal to, greater than } that point
     */
    public int compareTo(Point2D that) {
        if (this.y < that.y) return -1;
        if (this.y > that.y) return +1;
        if (this.x < that.x) return -1;
        if (this.x > that.x) return +1;
        return 0;
    }

    // compare points according to their x-coordinate
    private static class XOrder implements Comparator<Point2D> {
        public int compare(Point2D p, Point2D q) {
            if (p.x < q.x) return -1;
            if (p.x > q.x) return +1;
            return 0;
        }
    }

    // compare points according to their y-coordinate
    private static class YOrder implements Comparator<Point2D> {
        public int compare(Point2D p, Point2D q) {
            if (p.y < q.y) return -1;
            if (p.y > q.y) return +1;
            return 0;
        }
    }

    // compare points according to their polar radius
    private static class ROrder implements Comparator<Point2D> {
        public int compare(Point2D p, Point2D q) {
            double delta = (p.x*p.x + p.y*p.y) - (q.x*q.x + q.y*q.y);
            if (delta < 0) return -1;
            if (delta > 0) return +1;
            return 0;
        }
    }
 
    // compare other points relative to atan2 angle (bewteen -pi/2 and pi/2) they make with this Point
    private class Atan2Order implements Comparator<Point2D> {
        public int compare(Point2D q1, Point2D q2) {
            double angle1 = angleTo(q1);
            double angle2 = angleTo(q2);
            if      (angle1 < angle2) return -1;
            else if (angle1 > angle2) return +1;
            else                      return  0;
        }
    }

    // compare other points relative to polar angle (between 0 and 2pi) they make with this Point
    private class PolarOrder implements Comparator<Point2D> {
        public int compare(Point2D q1, Point2D q2) {
            double dx1 = q1.x - x;
            double dy1 = q1.y - y;
            double dx2 = q2.x - x;
            double dy2 = q2.y - y;

            if      (dy1 >= 0 && dy2 < 0) return -1;    // q1 above; q2 below
            else if (dy2 >= 0 && dy1 < 0) return +1;    // q1 below; q2 above
            else if (dy1 == 0 && dy2 == 0) {            // 3-collinear and horizontal
                if      (dx1 >= 0 && dx2 < 0) return -1;
                else if (dx2 >= 0 && dx1 < 0) return +1;
                else                          return  0;
            }
            else return -ccw(Point2D.this, q1, q2);     // both above or below

            // Note: ccw() recomputes dx1, dy1, dx2, and dy2
        }
    }

    // compare points according to their distance to this point
    private class DistanceToOrder implements Comparator<Point2D> {
        public int compare(Point2D p, Point2D q) {
            double dist1 = distanceSquaredTo(p);
            double dist2 = distanceSquaredTo(q);
            if      (dist1 < dist2) return -1;
            else if (dist1 > dist2) return +1;
            else                    return  0;
        }
    }


    /**
     * Does this point equal y?
     * @param other the other point
     * @return true if this point equals the other point; false otherwise
     */
    @Override
    public boolean equals(Object other) {
        if (other == this) return true;
        if (other == null) return false;
        if (other.getClass() != this.getClass()) return false;
        Point2D that = (Point2D) other;
        return this.x == that.x && this.y == that.y;
    }

    /**
     * Return a string representation of this point.
     * @return a string representation of this point in the format (x, y)
     */
    @Override
    public String toString() {
        return "(" + x + ", " + y + ")";
    }

    /**
     * Returns an integer hash code for this point.
     * @return an integer hash code for this point
     */
    @Override
    public int hashCode() {
        int hashX = ((Double) x).hashCode();
        int hashY = ((Double) y).hashCode();
        return 31*hashX + hashY;
    }

    /**
     * Plot this point using standard draw.
     */
    public void draw() {
        StdDraw.point(x, y);
    }

    /**
     * Plot a line from this point to that point using standard draw.
     * @param that the other point
     */
    public void drawTo(Point2D that) {
        StdDraw.line(this.x, this.y, that.x, that.y);
    }


    /**
     * Unit tests the point data type.
     */
    public static void main(String[] args) {
        int x0 = Integer.parseInt(args[0]);
        int y0 = Integer.parseInt(args[1]);
        int N = Integer.parseInt(args[2]);

        StdDraw.setCanvasSize(800, 800);
        StdDraw.setXscale(0, 100);
        StdDraw.setYscale(0, 100);
        StdDraw.setPenRadius(.005);
        Point2D[] points = new Point2D[N];
        for (int i = 0; i < N; i++) {
            int x = StdRandom.uniform(100);
            int y = StdRandom.uniform(100);
            points[i] = new Point2D(x, y);
            points[i].draw();
        }

        // draw p = (x0, x1) in red
        Point2D p = new Point2D(x0, y0);
        StdDraw.setPenColor(StdDraw.RED);
        StdDraw.setPenRadius(.02);
        p.draw();


        // draw line segments from p to each point, one at a time, in polar order
        StdDraw.setPenRadius();
        StdDraw.setPenColor(StdDraw.BLUE);
        Arrays.sort(points, p.POLAR_ORDER);
        for (int i = 0; i < N; i++) {
            p.drawTo(points[i]);
            StdDraw.show(100);
        }
    }
}