// Textbook fragment 07.18
  // Additional accessor method
  /** Return the sibling of a node */
  public Position<E> sibling(Position<E> v)
    throws InvalidPositionException, BoundaryViolationException {
      BTPosition<E> vv = checkPosition(v);
      BTPosition<E> parentPos = vv.getParent();
      if (parentPos != null) {
        BTPosition<E> sibPos;
        BTPosition<E> leftPos = parentPos.getLeft();
        if (leftPos == vv)
          sibPos = parentPos.getRight();
        else
          sibPos = parentPos.getLeft();
        if (sibPos != null)
          return sibPos;
      }
      throw new BoundaryViolationException("No sibling");
  }
  // Additional update methods
  /** Adds a root node to an empty tree */
  public Position<E> addRoot(E e) throws NonEmptyTreeException {
    if(!isEmpty())
      throw new NonEmptyTreeException("Tree already has a root");
    size = 1;
    root = createNode(e,null,null,null);
    return root;
  }
  /** Inserts a left child at a given node. */
  public Position<E>  insertLeft(Position<E> v, E e)
    throws InvalidPositionException {
    BTPosition<E> vv = checkPosition(v);
    Position<E> leftPos = vv.getLeft();
    if (leftPos != null)
      throw new InvalidPositionException("Node already has a left child");
    BTPosition<E> ww = createNode(e, vv, null, null);
    vv.setLeft(ww);
    size++;
    return ww;
  }