Code Fragment: LinkedBinaryTree2

  // ... (utilities for LinkedBinaryTree)
  NodePtr nodePtr(const Position& v) const 		// convert to NodePtr
    { return v.node; }
  bool isExternal(NodePtr n) const 			// is node external?
    { return (n->left == NULL && n->right == NULL); }
  bool isInternal(NodePtr n) const 			// is node internal?
    { return ! isExternal(n); }
  bool isRoot(NodePtr n) const 				// is node the root?
    { return (n == theRoot); }
  void setRoot(NodePtr r)				// make r the root
    { theRoot = r;  r->parent = NULL; }
  void replaceElement(NodePtr n, const Object& o)	// replace element
    { n->element = o; }
  void swapElements(NodePtr n, NodePtr w) {		// swap elements
    Object temp = w->element;
    w->element = n->element;
    n->element = temp;	
  }
  void expandExternal(NodePtr n) {			// expand external node
    n->left   = new Node;	n->left->parent = n;
    n->right  = new Node;	n->right->parent = n;
    sz += 2;
  }
  NodePtr removeAboveExternal(NodePtr n) {		// remove n and parent
    NodePtr p = n->parent;
    NodePtr s = n->sibling();
    if (isRoot(p)) setRoot(s);				// p was root; now s is
    else {
      NodePtr g = p->parent;				// the grandparent
      if (p == g->left)	    g->left  = s;		// replace parent by sibling
      else 		    g->right = s;
      s->parent = g;
    }
    delete n; delete p;					// delete removed nodes
    sz -= 2;						// two fewer nodes
    return s;
  }