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

public class Polygon
{

    int ncorners = 0;
    Point[] points;
   /**
      Constructs a Polygon object with no corners
   */
   public Polygon()
   {
       points = new Point[0];
   }

   /**
      Adds a point to the list.
      @param p the point to add
   */
   public void add(Point p)
   {
       points = addToArray(points, p);
       ncorners++;
   }

   /**
      Computes the area of a polygon.
      @return area of a polygon
   */
   public double getArea()
   {
      if (ncorners < 3) return 0;
      if (ncorners == 3) {
          return getTriangleSize(points);
      }else {

          Arrays.sort(points, new Comparator<Point>() {
              public int compare(Point a, Point b) {
                  if(a.getX() > b.getX()) {
                      return 1;
                  }else if(a.getX() < b.getX()) {
                      return -1;
                  }else {
                      return 0;
                  }
              }
          });

          Point[] triangle = new Point[]{points[points.length -1], points[points.length -2], points[points.length -3]};

          Polygon p = new Polygon();
          for(int i = 0; i < (points.length - 1); i++) {
              p.add(points[i]);
          }

          return getTriangleSize(triangle) + p.getArea();

      }
   }

   private double getTriangleSize(Point[] pointArray) {

       //Just making the triangle calculation algorithm easier to type.
       double x1 = pointArray[0].getX();
       double y1 = pointArray[0].getY();
       double x2 = pointArray[1].getX();
       double y2 = pointArray[1].getY();
       double x3 = pointArray[2].getX();
       double y3 = pointArray[2].getY();

       //Algorithm provided by assignment.
       return ((x1*y2) + (x2*y3) + (x3*y1) - (y1*x2) - (y2*x3) - (y3*x1)) / 2;
   }

   private Point[] addToArray(Point[] array, Point newPoint) {
       Point[] point = new Point[array.length + 1];
       for(int i = 0 ; i < array.length; i++) {
           point[i] = array[i];
       }
       point[point.length-1] = newPoint;
       return point;
   }

}