package algs91; // section 9.8
import algs12.Point2D;
import stdlib.*;
/* ***********************************************************************
 *  Compilation:  javac FarthestPair.java
 *  Execution:    java FarthestPair < input.txt
 *  Dependencies: GrahamScan.java Point2D.java
 *
 *  Given a set of N points in the plane, find the farthest pair
 *  (equivalently, compute the diameter of the set of points).
 *
 *  Computes the convex hull of the set of points and using the
 *  rotating callipers method to find all antipodal point pairs
 *  and the farthest pair.
 *
 *  % java FarthestPair < rs1423.txt
 *  7748.838622658237 from (24690.0, 216.0) to (32420.0, 756.0)
 *************************************************************************/

public class FarthestPair {

  // farthest pair of points and distance
  private Point2D best1, best2;
  private double bestDistance = Double.NEGATIVE_INFINITY;

  public FarthestPair(Point2D[] points) {
    GrahamScan graham = new GrahamScan(points);

    // single point
    if (points.length <= 1) return;

    // number of points on the hull
    int M = 0;
    for (Point2D p : graham.hull())
      M++;

    // the hull, in counterclockwise order
    Point2D[] hull = new Point2D[M+1];
    int m = 1;
    for (Point2D p : graham.hull()) {
      hull[m++] = p;
    }

    // all points are equal
    if (M == 1) return;

    // points are collinear
    if (M == 2) {
      best1 = hull[1];
      best2 = hull[2];
      bestDistance = best1.distanceTo(best2);
      return;
    }

    // k = farthest vertex from edge from hull[1] to hull[M]
    int k = 2;
    while (Point2D.area2(hull[M], hull[k+1], hull[1]) > Point2D.area2(hull[M], hull[k], hull[1])) {
      k++;
    }

    int j = k;
    for (int i = 1; i <= k; i++) {
      // StdOut.println("hull[i] + " and " + hull[j] + " are antipodal");
      if (hull[i].distanceTo(hull[j]) > bestDistance) {
        best1 = hull[i];
        best2 = hull[j];
        bestDistance = hull[i].distanceTo(hull[j]);
      }
      while ((j < M) && Point2D.area2(hull[i], hull[j+1], hull[i+1]) > Point2D.area2(hull[i], hull[j], hull[i+1])) {
        j++;
        // StdOut.println(hull[i] + " and " + hull[j] + " are antipodal");
        double distance = hull[i].distanceTo(hull[j]);
        if (distance > bestDistance) {
          best1 = hull[i];
          best2 = hull[j];
          bestDistance = hull[i].distanceTo(hull[j]);
        }
      }
    }
  }

  public Point2D either()    { return best1;        }
  public Point2D other()     { return best2;        }
  public double distance()   { return bestDistance; }


  public static void main(String[] args) {
    StdIn.fromFile ("data/rs1423.txt");

    int N = StdIn.readInt();
    Point2D[] points = new Point2D[N];
    for (int i = 0; i < N; i++) {
      int x = StdIn.readInt();
      int y = StdIn.readInt();
      points[i] = new Point2D(x, y);
    }
    FarthestPair farthest = new FarthestPair(points);
    StdOut.println(farthest.distance() + " from " + farthest.either() + " to " + farthest.other());
  }

}