// Each Rectangle object represents a 2D rectangle with a
// top-left x/y coordinate, width, and height.
public class Rectangle {
    private int x;
    private int y;
    private int width;
    private int height;
    
    // Constructs a new rectangle 
    public Rectangle(int initialX, int initialY, int initialWidth, int initialHeight) {
        x = initialX;
        y = initialY;
        width = initialWidth;
        height = initialHeight;
    }

    // Returns this rectangle's leftmost x coordinate.
    public int getX() {
        return x;
    }
    
    // Returns this rectangle's topmost y coordinate.
    public int getY() {
        return y;
    }
    
    // Returns this rectangle's width.
    public int getWidth() {
        return width;
    }
    
    // Returns this rectangle's height.
    public int getHeight() {
        return height;
    }
    
    // Returns the area (w x h) of this rectangle.
    public int getArea() {
        return width * height;
    }

    // Returns a text representation of this rectangle.
    public String toString() {
        return "Rectangle[x=" + getX() + ",y=" + getY() + 
               ",w=" + width + ",h=" + height + "]";
    }
    
    // Returns whether the given point is contained within this rectangle.
    public boolean contains(Point p) {
        return getX() <= p.getX() && p.getX() < (getX() + width) &&
               getY() <= p.getY() && p.getY() < (getY() + height);
    }

    // Returns whether the given rectangle is entirely contained in this rectangle.
    public boolean contains(Rectangle r) {
        return getX() <= r.getX() && r.getX() + r.getWidth() < (getX() + width) &&
               getY() <= r.getY() && r.getY() + r.getHeight() < (getY() + height);
    }

    // Turns this rectangle into the smallest area that contains itself and rect.
    public void union(Rectangle r) {
        // find the union's bounds
        int left = Math.min(getX(), r.getX());
        int top = Math.min(getY(), r.getY());
        int right = Math.max(getX() + width, r.getX() + r.getWidth());
        int bottom = Math.max(getY() + height, r.getY() + r.getHeight());
        
        x = left;
        y = top;
        width = right - left;
        height = bottom - top;
    }
}