// Textbook fragment 06.09
  /** Constructor that creates an empty list; O(1) time */
  public NodePositionList() {
    numElts = 0;
    header = new DNode<E>(null, null, null);    // create header
    trailer = new DNode<E>(header, null, null); // create trailer
    header.setNext(trailer);    // make header and trailer point to each other
  }
  /** Checks if position is valid for this list and converts it to
    *  DNode if it is valid; O(1) time */
  protected DNode<E> checkPosition(Position<E> p)
    throws InvalidPositionException {
    if (p == null)
      throw new InvalidPositionException
        ("Null position passed to NodeList");
    if (p == header)
        throw new InvalidPositionException
          ("The header node is not a valid position");
    if (p == trailer)
        throw new InvalidPositionException
          ("The trailer node is not a valid position");
    try {
      DNode<E> temp = (DNode<E>) p;
      if ((temp.getPrev() == null) || (temp.getNext() == null))
        throw new InvalidPositionException
          ("Position does not belong to a valid NodeList");
      return temp;
    } catch (ClassCastException e) {
      throw new InvalidPositionException
        ("Position is of wrong type for this list");
    }
  }