package algs91; // section 9.8
import stdlib.*;
import java.util.Arrays;
import algs12.Point2D;
import algs13.Stack;
/* ***********************************************************************
 *  Compilation:  javac GrahamScan.java
 *  Execution:    java GrahamScan < input.txt
 *  Dependencies: Point2D.java
 *
 *  Create points from standard input and compute the convex hull using
 *  Graham scan algorithm.
 *
 *  May be floating-point issues if x- and y-coordinates are not integers.
 *
 *  % java GrahamScan < rs1423.txt
 *  (24690.0, 216.0)
 *  (32420.0, 756.0)
 *  (32706.0, 20013.0)
 *  (32373.0, 20274.0)
 *  (31776.0, 20523.0)
 *  (13443.0, 28086.0)
 *  (9252.0, 27747.0)
 *  (8286.0, 27555.0)
 *  (798.0, 22215.0)
 *  (954.0, 11163.0)
 *  (1833.0, 6300.0)
 *  (3804.0, 1017.0)
 *  (11196.0, 504.0)
 *
 *************************************************************************/

public class GrahamScan {
  private final Stack<Point2D> hull = new Stack<>();

  public GrahamScan(Point2D[] pts) {

    // defensive copy
    int N = pts.length;
    Point2D[] points = new Point2D[N];
    for (int i = 0; i < N; i++)
      points[i] = pts[i];

    // preprocess so that points[0] has lowest y-coordinate; break ties by x-coordinate
    // points[0] is an extreme point of the convex hull
    // (alternatively, could do easily in linear time)
    Arrays.sort(points);

    // sort by polar angle with respect to base point points[0],
    // breaking ties by distance to points[0]
    Arrays.sort(points, 1, N, points[0].POLAR_ORDER);

    hull.push(points[0]);       // p[0] is first extreme point

    // find index k1 of first point not equal to points[0]
    int k1;
    for (k1 = 1; k1 < N; k1++)
      if (!points[0].equals(points[k1])) break;
    if (k1 == N) return;        // all points equal

    // find index k2 of first point not collinear with points[0] and points[k1]
    int k2;
    for (k2 = k1 + 1; k2 < N; k2++)
      if (Point2D.ccw(points[0], points[k1], points[k2]) != 0) break;
    hull.push(points[k2-1]);    // points[k2-1] is second extreme point

    // Graham scan; note that points[N-1] is extreme point different from points[0]
    for (int i = k2; i < N; i++) {
      Point2D top = hull.pop();
      while (Point2D.ccw(hull.peek(), top, points[i]) <= 0) {
        top = hull.pop();
      }
      hull.push(top);
      hull.push(points[i]);
    }

    assert isConvex();
  }

  // return extreme points on convex hull in counterclockwise order as an Iterable
  public Iterable<Point2D> hull() {
    Stack<Point2D> s = new Stack<>();
    for (Point2D p : hull) s.push(p);
    return s;
  }

  // check that boundary of hull is strictly convex
  private boolean isConvex() {
    int N = hull.size();
    if (N <= 2) return true;

    Point2D[] points = new Point2D[N];
    int n = 0;
    for (Point2D p : hull()) {
      points[n++] = p;
    }

    for (int i = 0; i < N; i++) {
      if (Point2D.ccw(points[i], points[(i+1) % N], points[(i+2) % N]) <= 0) {
        return false;
      }
    }
    return true;
  }

  // test client
  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);
    }
    GrahamScan graham = new GrahamScan(points);
    for (Point2D p : graham.hull())
      StdOut.println(p);
  }

}