stl_tree.h   [plain text]

// RB tree implementation -*- C++ -*-

// Copyright (C) 2001, 2002 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library.  This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 2, or (at your option)
// any later version.

// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License along
// with this library; see the file COPYING.  If not, write to the Free
// Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307,
// USA.

// As a special exception, you may use this file as part of a free software
// library without restriction.  Specifically, if other files instantiate
// templates or use macros or inline functions from this file, or you compile
// this file and link it with other files to produce an executable, this
// file does not by itself cause the resulting executable to be covered by
// the GNU General Public License.  This exception does not however
// invalidate any other reasons why the executable file might be covered by
// the GNU General Public License.

/*
 *
 * Copyright (c) 1996,1997
 * Silicon Graphics Computer Systems, Inc.
 *
 * Permission to use, copy, modify, distribute and sell this software
 * and its documentation for any purpose is hereby granted without fee,
 * provided that the above copyright notice appear in all copies and
 * that both that copyright notice and this permission notice appear
 * in supporting documentation.  Silicon Graphics makes no
 * representations about the suitability of this software for any
 * purpose.  It is provided "as is" without express or implied warranty.
 *
 *
 * Copyright (c) 1994
 * Hewlett-Packard Company
 *
 * Permission to use, copy, modify, distribute and sell this software
 * and its documentation for any purpose is hereby granted without fee,
 * provided that the above copyright notice appear in all copies and
 * that both that copyright notice and this permission notice appear
 * in supporting documentation.  Hewlett-Packard Company makes no
 * representations about the suitability of this software for any
 * purpose.  It is provided "as is" without express or implied warranty.
 *
 *
 */

/** @file stl_tree.h
 *  This is an internal header file, included by other library headers.
 *  You should not attempt to use it directly.
 */

#ifndef __GLIBCPP_INTERNAL_TREE_H
#define __GLIBCPP_INTERNAL_TREE_H

/*

Red-black tree class, designed for use in implementing STL
associative containers (set, multiset, map, and multimap). The
insertion and deletion algorithms are based on those in Cormen,
Leiserson, and Rivest, Introduction to Algorithms (MIT Press, 1990),
except that

(1) the header cell is maintained with links not only to the root
but also to the leftmost node of the tree, to enable constant time
begin(), and to the rightmost node of the tree, to enable linear time
performance when used with the generic set algorithms (set_union,
etc.);

(2) when a node being deleted has two children its successor node is
relinked into its place, rather than copied, so that the only
iterators invalidated are those referring to the deleted node.

*/

#include <bits/stl_algobase.h>
#include <bits/stl_alloc.h>
#include <bits/stl_construct.h>
#include <bits/stl_function.h>

namespace std
{ 
  enum _Rb_tree_color { _M_red = false, _M_black = true };

  struct _Rb_tree_node_base
  {
    typedef _Rb_tree_node_base* _Base_ptr;
    
    _Rb_tree_color 	_M_color; 
    _Base_ptr 		_M_parent;
    _Base_ptr 		_M_left;
    _Base_ptr 		_M_right;
    
    static _Base_ptr 
    _S_minimum(_Base_ptr __x)
    {
      while (__x->_M_left != 0) __x = __x->_M_left;
      return __x;
    }

    static _Base_ptr 
    _S_maximum(_Base_ptr __x)
    {
      while (__x->_M_right != 0) __x = __x->_M_right;
      return __x;
    }
  };

  template<typename _Val>
    struct _Rb_tree_node : public _Rb_tree_node_base
    {
      typedef _Rb_tree_node<_Val>* _Link_type;
      _Val _M_value_field;
    };
  
  struct _Rb_tree_base_iterator
  {
    typedef _Rb_tree_node_base::_Base_ptr 	_Base_ptr;
    typedef bidirectional_iterator_tag 		iterator_category;
    typedef ptrdiff_t 				difference_type;

    _Base_ptr _M_node;

    void 
    _M_increment()
    {
      if (_M_node->_M_right != 0) 
	{
	  _M_node = _M_node->_M_right;
	  while (_M_node->_M_left != 0)
	    _M_node = _M_node->_M_left;
	}
      else 
	{
	  _Base_ptr __y = _M_node->_M_parent;
	  while (_M_node == __y->_M_right) 
	    {
	      _M_node = __y;
	      __y = __y->_M_parent;
	    }
	  if (_M_node->_M_right != __y)
	    _M_node = __y;
	}
    }

    void 
    _M_decrement()
    {
      if (_M_node->_M_color == _M_red 
	  && _M_node->_M_parent->_M_parent == _M_node)
	_M_node = _M_node->_M_right;
      else if (_M_node->_M_left != 0) 
	{
	  _Base_ptr __y = _M_node->_M_left;
	  while (__y->_M_right != 0)
	    __y = __y->_M_right;
	  _M_node = __y;
	}
      else 
	{
	  _Base_ptr __y = _M_node->_M_parent;
	  while (_M_node == __y->_M_left) 
	    {
	      _M_node = __y;
	      __y = __y->_M_parent;
	    }
	  _M_node = __y;
	}
    }
  };

  template<typename _Val, typename _Ref, typename _Ptr>
    struct _Rb_tree_iterator : public _Rb_tree_base_iterator
    {
      typedef _Val value_type;
      typedef _Ref reference;
      typedef _Ptr pointer;
      typedef _Rb_tree_iterator<_Val, _Val&, _Val*> iterator;
      typedef _Rb_tree_iterator<_Val, const _Val&, const _Val*> 
      const_iterator;
      typedef _Rb_tree_iterator<_Val, _Ref, _Ptr> _Self;
      typedef _Rb_tree_node<_Val>* _Link_type;
      
      _Rb_tree_iterator() {}
      _Rb_tree_iterator(_Link_type __x) { _M_node = __x; }
      _Rb_tree_iterator(const iterator& __it) { _M_node = __it._M_node; }

      reference 
      operator*() const { return _Link_type(_M_node)->_M_value_field; }

      pointer 
      operator->() const { return &(operator*()); }

      _Self& 
      operator++() 
      { 
	_M_increment(); 
	return *this; 
      }

      _Self 
      operator++(int) 
      {
	_Self __tmp = *this;
	_M_increment();
	return __tmp;
      }
    
      _Self& 
      operator--() { _M_decrement(); return *this; }

      _Self 
      operator--(int) 
      {
	_Self __tmp = *this;
	_M_decrement();
	return __tmp;
      }
  };

  template<typename _Val, typename _Ref, typename _Ptr>
    inline bool 
    operator==(const _Rb_tree_iterator<_Val, _Ref, _Ptr>& __x,
	       const _Rb_tree_iterator<_Val, _Ref, _Ptr>& __y) 
    { return __x._M_node == __y._M_node; }

  template<typename _Val>
    inline bool 
    operator==(const _Rb_tree_iterator<_Val, const _Val&, const _Val*>& __x,
	       const _Rb_tree_iterator<_Val, _Val&, _Val*>& __y) 
    { return __x._M_node == __y._M_node; }

  template<typename _Val>
    inline bool 
    operator==(const _Rb_tree_iterator<_Val, _Val&, _Val*>& __x,
	       const _Rb_tree_iterator<_Val, const _Val&, const _Val*>& __y) 
    { return __x._M_node == __y._M_node; }

  template<typename _Val, typename _Ref, typename _Ptr>
    inline bool 
    operator!=(const _Rb_tree_iterator<_Val, _Ref, _Ptr>& __x,
	       const _Rb_tree_iterator<_Val, _Ref, _Ptr>& __y) 
    { return __x._M_node != __y._M_node; }

  template<typename _Val>
    inline bool 
    operator!=(const _Rb_tree_iterator<_Val, const _Val&, const _Val*>& __x,
	       const _Rb_tree_iterator<_Val, _Val&, _Val*>& __y) 
    { return __x._M_node != __y._M_node; }

  template<typename _Val>
    inline bool 
    operator!=(const _Rb_tree_iterator<_Val, _Val&, _Val*>& __x,
	       const _Rb_tree_iterator<_Val, const _Val&, const _Val*>& __y) 
    { return __x._M_node != __y._M_node; }

  inline void 
  _Rb_tree_rotate_left(_Rb_tree_node_base* __x, _Rb_tree_node_base*& __root)
  {
    _Rb_tree_node_base* __y = __x->_M_right;
    __x->_M_right = __y->_M_left;
    if (__y->_M_left !=0)
      __y->_M_left->_M_parent = __x;
    __y->_M_parent = __x->_M_parent;
    
    if (__x == __root)
      __root = __y;
    else if (__x == __x->_M_parent->_M_left)
      __x->_M_parent->_M_left = __y;
    else
      __x->_M_parent->_M_right = __y;
    __y->_M_left = __x;
    __x->_M_parent = __y;
  }

  inline void 
  _Rb_tree_rotate_right(_Rb_tree_node_base* __x, _Rb_tree_node_base*& __root)
  {
    _Rb_tree_node_base* __y = __x->_M_left;
    __x->_M_left = __y->_M_right;
    if (__y->_M_right != 0)
      __y->_M_right->_M_parent = __x;
    __y->_M_parent = __x->_M_parent;

    if (__x == __root)
      __root = __y;
    else if (__x == __x->_M_parent->_M_right)
      __x->_M_parent->_M_right = __y;
    else
      __x->_M_parent->_M_left = __y;
    __y->_M_right = __x;
    __x->_M_parent = __y;
  }

  inline void 
  _Rb_tree_rebalance(_Rb_tree_node_base* __x, _Rb_tree_node_base*& __root)
  {
    __x->_M_color = _M_red;
    while (__x != __root 
	   && __x->_M_parent->_M_color == _M_red) 
      {
	if (__x->_M_parent == __x->_M_parent->_M_parent->_M_left) 
	  {
	    _Rb_tree_node_base* __y = __x->_M_parent->_M_parent->_M_right;
	    if (__y && __y->_M_color == _M_red) 
	      {
		__x->_M_parent->_M_color = _M_black;
		__y->_M_color = _M_black;
		__x->_M_parent->_M_parent->_M_color = _M_red;
		__x = __x->_M_parent->_M_parent;
	      }
	    else 
	      {
		if (__x == __x->_M_parent->_M_right) 
		  {
		    __x = __x->_M_parent;
		    _Rb_tree_rotate_left(__x, __root);
		  }
		__x->_M_parent->_M_color = _M_black;
		__x->_M_parent->_M_parent->_M_color = _M_red;
		_Rb_tree_rotate_right(__x->_M_parent->_M_parent, __root);
	      }
	  }
	else 
	  {
	    _Rb_tree_node_base* __y = __x->_M_parent->_M_parent->_M_left;
	    if (__y && __y->_M_color == _M_red) 
	      {
		__x->_M_parent->_M_color = _M_black;
		__y->_M_color = _M_black;
		__x->_M_parent->_M_parent->_M_color = _M_red;
		__x = __x->_M_parent->_M_parent;
	      }
	    else 
	      {
		if (__x == __x->_M_parent->_M_left) 
		  {
		    __x = __x->_M_parent;
		    _Rb_tree_rotate_right(__x, __root);
		  }
		__x->_M_parent->_M_color = _M_black;
		__x->_M_parent->_M_parent->_M_color = _M_red;
		_Rb_tree_rotate_left(__x->_M_parent->_M_parent, __root);
	      }
	  }
      }
    __root->_M_color = _M_black;
  }

  inline _Rb_tree_node_base*
  _Rb_tree_rebalance_for_erase(_Rb_tree_node_base* __z, 
			       _Rb_tree_node_base*& __root,
			       _Rb_tree_node_base*& __leftmost,
			       _Rb_tree_node_base*& __rightmost)
  {
    _Rb_tree_node_base* __y = __z;
    _Rb_tree_node_base* __x = 0;
    _Rb_tree_node_base* __x_parent = 0;
    if (__y->_M_left == 0)     // __z has at most one non-null child. y == z.
      __x = __y->_M_right;     // __x might be null.
    else
      if (__y->_M_right == 0)  // __z has exactly one non-null child. y == z.
	__x = __y->_M_left;    // __x is not null.
      else 
	{
	  // __z has two non-null children.  Set __y to
	  __y = __y->_M_right;   //   __z's successor.  __x might be null.
	  while (__y->_M_left != 0)
	    __y = __y->_M_left;
	  __x = __y->_M_right;
	}
    if (__y != __z) 
      {
	// relink y in place of z.  y is z's successor
	__z->_M_left->_M_parent = __y; 
	__y->_M_left = __z->_M_left;
	if (__y != __z->_M_right) 
	  {
	    __x_parent = __y->_M_parent;
	    if (__x) __x->_M_parent = __y->_M_parent;
	    __y->_M_parent->_M_left = __x;   // __y must be a child of _M_left
	    __y->_M_right = __z->_M_right;
	    __z->_M_right->_M_parent = __y;
	  }
	else
	  __x_parent = __y;  
	if (__root == __z)
	  __root = __y;
	else if (__z->_M_parent->_M_left == __z)
	  __z->_M_parent->_M_left = __y;
	else 
	  __z->_M_parent->_M_right = __y;
	__y->_M_parent = __z->_M_parent;
	std::swap(__y->_M_color, __z->_M_color);
	__y = __z;
	// __y now points to node to be actually deleted
      }
    else 
      {                        // __y == __z
	__x_parent = __y->_M_parent;
	if (__x) 
	  __x->_M_parent = __y->_M_parent;   
	if (__root == __z)
	  __root = __x;
	else 
	  if (__z->_M_parent->_M_left == __z)
	    __z->_M_parent->_M_left = __x;
	  else
	    __z->_M_parent->_M_right = __x;
	if (__leftmost == __z) 
	  if (__z->_M_right == 0)        // __z->_M_left must be null also
	    __leftmost = __z->_M_parent;
	// makes __leftmost == _M_header if __z == __root
	  else
	    __leftmost = _Rb_tree_node_base::_S_minimum(__x);
	if (__rightmost == __z)  
	  if (__z->_M_left == 0)         // __z->_M_right must be null also
	    __rightmost = __z->_M_parent;  
	// makes __rightmost == _M_header if __z == __root
	  else                      // __x == __z->_M_left
	    __rightmost = _Rb_tree_node_base::_S_maximum(__x);
      }
    if (__y->_M_color != _M_red) 
      { 
	while (__x != __root && (__x == 0 || __x->_M_color == _M_black))
	  if (__x == __x_parent->_M_left) 
	    {
	      _Rb_tree_node_base* __w = __x_parent->_M_right;
	      if (__w->_M_color == _M_red) 
		{
		  __w->_M_color = _M_black;
		  __x_parent->_M_color = _M_red;
		  _Rb_tree_rotate_left(__x_parent, __root);
		  __w = __x_parent->_M_right;
		}
	      if ((__w->_M_left == 0 || 
		   __w->_M_left->_M_color == _M_black) &&
		  (__w->_M_right == 0 || 
		   __w->_M_right->_M_color == _M_black)) 
		{
		  __w->_M_color = _M_red;
		  __x = __x_parent;
		  __x_parent = __x_parent->_M_parent;
		} 
	      else 
		{
		  if (__w->_M_right == 0 
		      || __w->_M_right->_M_color == _M_black) 
		    {
		      if (__w->_M_left) __w->_M_left->_M_color = _M_black;
		      __w->_M_color = _M_red;
		      _Rb_tree_rotate_right(__w, __root);
		      __w = __x_parent->_M_right;
		    }
		  __w->_M_color = __x_parent->_M_color;
		  __x_parent->_M_color = _M_black;
		  if (__w->_M_right) 
		    __w->_M_right->_M_color = _M_black;
		  _Rb_tree_rotate_left(__x_parent, __root);
		  break;
		}
	    } 
	  else 
	    {   
	      // same as above, with _M_right <-> _M_left.
	      _Rb_tree_node_base* __w = __x_parent->_M_left;
	      if (__w->_M_color == _M_red) 
		{
		  __w->_M_color = _M_black;
		  __x_parent->_M_color = _M_red;
		  _Rb_tree_rotate_right(__x_parent, __root);
		  __w = __x_parent->_M_left;
		}
	      if ((__w->_M_right == 0 || 
		   __w->_M_right->_M_color == _M_black) &&
		  (__w->_M_left == 0 || 
		   __w->_M_left->_M_color == _M_black)) 
		{
		  __w->_M_color = _M_red;
		  __x = __x_parent;
		  __x_parent = __x_parent->_M_parent;
		} 
	      else 
		{
		  if (__w->_M_left == 0 || __w->_M_left->_M_color == _M_black) 
		    {
		      if (__w->_M_right) __w->_M_right->_M_color = _M_black;
		      __w->_M_color = _M_red;
		      _Rb_tree_rotate_left(__w, __root);
		      __w = __x_parent->_M_left;
		    }
		  __w->_M_color = __x_parent->_M_color;
		  __x_parent->_M_color = _M_black;
		  if (__w->_M_left) 
		    __w->_M_left->_M_color = _M_black;
		  _Rb_tree_rotate_right(__x_parent, __root);
		  break;
		}
	    }
	if (__x) __x->_M_color = _M_black;
      }
    return __y;
  }

  // Base class to encapsulate the differences between old SGI-style
  // allocators and standard-conforming allocators.  In order to avoid
  // having an empty base class, we arbitrarily move one of rb_tree's
  // data members into the base class.

  // _Base for general standard-conforming allocators.
  template<typename _Tp, typename _Alloc, bool _S_instanceless>
    class _Rb_tree_alloc_base 
    {
    public:
    typedef typename _Alloc_traits<_Tp, _Alloc>::allocator_type allocator_type;

      allocator_type 
      get_allocator() const { return _M_node_allocator; }

      _Rb_tree_alloc_base(const allocator_type& __a)
      : _M_node_allocator(__a), _M_header(0) {}

    protected:
      typename _Alloc_traits<_Rb_tree_node<_Tp>, _Alloc>::allocator_type
      _M_node_allocator;

      _Rb_tree_node<_Tp>* _M_header;
      
      _Rb_tree_node<_Tp>* 
      _M_get_node()  { return _M_node_allocator.allocate(1); }

      void 
      _M_put_node(_Rb_tree_node<_Tp>* __p) 
      { _M_node_allocator.deallocate(__p, 1); }
    };

  // Specialization for instanceless allocators.
  template<typename _Tp, typename _Alloc>
    class _Rb_tree_alloc_base<_Tp, _Alloc, true> 
    {
    public:
    typedef typename _Alloc_traits<_Tp, _Alloc>::allocator_type allocator_type;
      allocator_type get_allocator() const { return allocator_type(); }

      _Rb_tree_alloc_base(const allocator_type&) : _M_header(0) {}

    protected:
      _Rb_tree_node<_Tp>* _M_header;
      
      typedef typename _Alloc_traits<_Rb_tree_node<_Tp>, _Alloc>::_Alloc_type
      _Alloc_type;
      
      _Rb_tree_node<_Tp>* 
      _M_get_node() { return _Alloc_type::allocate(1); }

      void 
      _M_put_node(_Rb_tree_node<_Tp>* __p) { _Alloc_type::deallocate(__p, 1); }
    };
  
  template<typename _Tp, typename _Alloc>
    struct _Rb_tree_base : public _Rb_tree_alloc_base<_Tp, _Alloc, 
                                  _Alloc_traits<_Tp, _Alloc>::_S_instanceless>
    {
      typedef _Rb_tree_alloc_base<_Tp, 
	_Alloc, _Alloc_traits<_Tp, _Alloc>::_S_instanceless> _Base;
      typedef typename _Base::allocator_type allocator_type;

      _Rb_tree_base(const allocator_type& __a) 
      : _Base(__a) { _M_header = _M_get_node(); }
      ~_Rb_tree_base() { _M_put_node(_M_header); }
    };


  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc = allocator<_Val> >
    class _Rb_tree : protected _Rb_tree_base<_Val, _Alloc> 
    {
      typedef _Rb_tree_base<_Val, _Alloc> _Base;
      
    protected:
      typedef _Rb_tree_node_base* _Base_ptr;
      typedef _Rb_tree_node<_Val> _Rb_tree_node;
      
    public:
      typedef _Key key_type;
      typedef _Val value_type;
      typedef value_type* pointer;
      typedef const value_type* const_pointer;
      typedef value_type& reference;
      typedef const value_type& const_reference;
      typedef _Rb_tree_node* _Link_type;
      typedef size_t size_type;
      typedef ptrdiff_t difference_type;
      
      typedef typename _Base::allocator_type allocator_type;
      allocator_type get_allocator() const { return _Base::get_allocator(); }
      
    protected:
      using _Base::_M_get_node;
      using _Base::_M_put_node;
      using _Base::_M_header;
      
      _Link_type
      _M_create_node(const value_type& __x)
      {
	_Link_type __tmp = _M_get_node();
	try 
	  { _Construct(&__tmp->_M_value_field, __x); }
	catch(...)
	  {
	  _M_put_node(__tmp);
	  __throw_exception_again; 
	  }
	return __tmp;
      }
      
      _Link_type 
      _M_clone_node(_Link_type __x)
      {
	_Link_type __tmp = _M_create_node(__x->_M_value_field);
	__tmp->_M_color = __x->_M_color;
	__tmp->_M_left = 0;
	__tmp->_M_right = 0;
	return __tmp;
      }

      void
      destroy_node(_Link_type __p)
      {
	_Destroy(&__p->_M_value_field);
	_M_put_node(__p);
      }

      size_type _M_node_count; // keeps track of size of tree
      _Compare _M_key_compare;

      _Link_type& 
      _M_root() const { return (_Link_type&) _M_header->_M_parent; }

      _Link_type& 
      _M_leftmost() const { return (_Link_type&) _M_header->_M_left; }

      _Link_type& 
      _M_rightmost() const { return (_Link_type&) _M_header->_M_right; }

      static _Link_type& 
      _S_left(_Link_type __x) { return (_Link_type&)(__x->_M_left); }

      static _Link_type& 
      _S_right(_Link_type __x) { return (_Link_type&)(__x->_M_right); }

      static _Link_type& 
      _S_parent(_Link_type __x) { return (_Link_type&)(__x->_M_parent); }

      static reference 
      _S_value(_Link_type __x) { return __x->_M_value_field; }

      static const _Key& 
      _S_key(_Link_type __x) { return _KeyOfValue()(_S_value(__x)); }

      static _Rb_tree_color& 
      _S_color(_Link_type __x) { return __x->_M_color; }

      static _Link_type& 
      _S_left(_Base_ptr __x) { return (_Link_type&)(__x->_M_left); }

      static _Link_type& 
      _S_right(_Base_ptr __x) { return (_Link_type&)(__x->_M_right); }

      static _Link_type& 
      _S_parent(_Base_ptr __x) { return (_Link_type&)(__x->_M_parent); }

      static reference 
      _S_value(_Base_ptr __x) { return ((_Link_type)__x)->_M_value_field; }

      static const _Key& 
      _S_key(_Base_ptr __x) { return _KeyOfValue()(_S_value(_Link_type(__x)));} 

      static _Rb_tree_color&
      _S_color(_Base_ptr __x) { return (_Link_type(__x)->_M_color); }

      static _Link_type 
      _S_minimum(_Link_type __x) 
      { return (_Link_type)  _Rb_tree_node_base::_S_minimum(__x); }

      static _Link_type 
      _S_maximum(_Link_type __x)
      { return (_Link_type) _Rb_tree_node_base::_S_maximum(__x); }

    public:
      typedef _Rb_tree_iterator<value_type, reference, pointer> iterator;
      typedef _Rb_tree_iterator<value_type, const_reference, const_pointer> 
      const_iterator;

      typedef reverse_iterator<const_iterator> const_reverse_iterator;
      typedef reverse_iterator<iterator> reverse_iterator;

    private:
      iterator 
      _M_insert(_Base_ptr __x, _Base_ptr __y, const value_type& __v);

      _Link_type 
      _M_copy(_Link_type __x, _Link_type __p);

      void 
      _M_erase(_Link_type __x);

    public:
      // allocation/deallocation
      _Rb_tree()
	: _Base(allocator_type()), _M_node_count(0), _M_key_compare()
      { _M_empty_initialize(); }

      _Rb_tree(const _Compare& __comp)
	: _Base(allocator_type()), _M_node_count(0), _M_key_compare(__comp) 
      { _M_empty_initialize(); }

      _Rb_tree(const _Compare& __comp, const allocator_type& __a)
	: _Base(__a), _M_node_count(0), _M_key_compare(__comp) 
      { _M_empty_initialize(); }

      _Rb_tree(const _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& __x) 
	: _Base(__x.get_allocator()), _M_node_count(0), 
		 _M_key_compare(__x._M_key_compare)
      { 
	if (__x._M_root() == 0)
	  _M_empty_initialize();
	else 
	  {
	    _S_color(_M_header) = _M_red;
	    _M_root() = _M_copy(__x._M_root(), _M_header);
	    _M_leftmost() = _S_minimum(_M_root());
	    _M_rightmost() = _S_maximum(_M_root());
	  }
	_M_node_count = __x._M_node_count;
      }

      ~_Rb_tree() { clear(); }

      _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& 
      operator=(const _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& __x);

    private:
      void _M_empty_initialize() 
      {
	_S_color(_M_header) = _M_red; // used to distinguish header from 
	// __root, in iterator.operator++
	_M_root() = 0;
	_M_leftmost() = _M_header;
	_M_rightmost() = _M_header;
      }

    public:    
      // Accessors.
      _Compare 
      key_comp() const { return _M_key_compare; }

      iterator 
      begin() { return _M_leftmost(); }

      const_iterator 
      begin() const { return _M_leftmost(); }

      iterator 
      end() { return _M_header; }

      const_iterator 
      end() const { return _M_header; }

      reverse_iterator 
      rbegin() { return reverse_iterator(end()); }

      const_reverse_iterator 
      rbegin() const { return const_reverse_iterator(end()); }

      reverse_iterator 
      rend() { return reverse_iterator(begin()); }

      const_reverse_iterator 
      rend() const { return const_reverse_iterator(begin()); }
 
      bool 
      empty() const { return _M_node_count == 0; }

      size_type 
      size() const { return _M_node_count; }

      size_type 
      max_size() const { return size_type(-1); }

      void 
      swap(_Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& __t) 
      {
	std::swap(_M_header, __t._M_header);
	std::swap(_M_node_count, __t._M_node_count);
	std::swap(_M_key_compare, __t._M_key_compare);
      }
    
      // Insert/erase.
      pair<iterator,bool> 
      insert_unique(const value_type& __x);

      iterator 
      insert_equal(const value_type& __x);

      iterator 
      insert_unique(iterator __position, const value_type& __x);

      iterator 
      insert_equal(iterator __position, const value_type& __x);

      template<typename _InputIterator>
      void 
      insert_unique(_InputIterator __first, _InputIterator __last);

      template<typename _InputIterator>
      void 
      insert_equal(_InputIterator __first, _InputIterator __last);

      void 
      erase(iterator __position);

      size_type 
      erase(const key_type& __x);

      void 
      erase(iterator __first, iterator __last);

      void 
      erase(const key_type* __first, const key_type* __last);

      void 
      clear() 
      {
	if (_M_node_count != 0) 
	  {
	    _M_erase(_M_root());
	    _M_leftmost() = _M_header;
	    _M_root() = 0;
	    _M_rightmost() = _M_header;
	    _M_node_count = 0;
	  }
      }      

      // Set operations.
      iterator 
      find(const key_type& __x);

      const_iterator 
      find(const key_type& __x) const;

      size_type 
      count(const key_type& __x) const;

      iterator 
      lower_bound(const key_type& __x);

      const_iterator 
      lower_bound(const key_type& __x) const;

      iterator 
      upper_bound(const key_type& __x);

      const_iterator 
      upper_bound(const key_type& __x) const;

      pair<iterator,iterator> 
      equal_range(const key_type& __x);

      pair<const_iterator, const_iterator> 
      equal_range(const key_type& __x) const;

      // Debugging.
      bool 
      __rb_verify() const;
    };

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    inline bool 
    operator==(const _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& __x, 
	       const _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& __y)
    {
      return __x.size() == __y.size() && 
	equal(__x.begin(), __x.end(), __y.begin());
    }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    inline bool 
    operator<(const _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& __x, 
	      const _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& __y)
    {
      return lexicographical_compare(__x.begin(), __x.end(),
				     __y.begin(), __y.end());
    }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    inline bool 
    operator!=(const _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& __x, 
	       const _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& __y) 
    { return !(__x == __y); }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    inline bool 
    operator>(const _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& __x, 
	      const _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& __y) 
    { return __y < __x; }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    inline bool 
    operator<=(const _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& __x, 
	       const _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& __y) 
  { return !(__y < __x); }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    inline bool 
    operator>=(const _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& __x, 
	       const _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& __y) 
  { return !(__x < __y); }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    inline void 
    swap(_Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& __x, 
	 _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& __y)
    { __x.swap(__y); }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& 
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::
    operator=(const _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>& __x)
    {
      if (this != &__x) 
	{
	  // Note that _Key may be a constant type.
	  clear();
	  _M_node_count = 0;
	  _M_key_compare = __x._M_key_compare;        
	  if (__x._M_root() == 0) 
	    {
	      _M_root() = 0;
	      _M_leftmost() = _M_header;
	      _M_rightmost() = _M_header;
	    }
	  else 
	    {
	      _M_root() = _M_copy(__x._M_root(), _M_header);
	      _M_leftmost() = _S_minimum(_M_root());
	      _M_rightmost() = _S_maximum(_M_root());
	      _M_node_count = __x._M_node_count;
	    }
	}
      return *this;
    }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::iterator
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::
    _M_insert(_Base_ptr __x_, _Base_ptr __y_, const _Val& __v)
    {
      _Link_type __x = (_Link_type) __x_;
      _Link_type __y = (_Link_type) __y_;
      _Link_type __z;
      
      if (__y == _M_header || __x != 0 || 
	  _M_key_compare(_KeyOfValue()(__v), _S_key(__y))) 
	{
	  __z = _M_create_node(__v);
	  _S_left(__y) = __z;               // also makes _M_leftmost() = __z 
	  //    when __y == _M_header
	  if (__y == _M_header) 
	    {
	      _M_root() = __z;
	      _M_rightmost() = __z;
	    }
	  else if (__y == _M_leftmost())
	    _M_leftmost() = __z; // maintain _M_leftmost() pointing to min node
	}
      else 
	{
	  __z = _M_create_node(__v);
	  _S_right(__y) = __z;
	  // Maintain _M_rightmost() pointing to max node.
	  if (__y == _M_rightmost())
	    _M_rightmost() = __z; 
	}
      _S_parent(__z) = __y;
      _S_left(__z) = 0;
      _S_right(__z) = 0;
      _Rb_tree_rebalance(__z, _M_header->_M_parent);
      ++_M_node_count;
      return iterator(__z);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::iterator
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::
    insert_equal(const _Val& __v)
    {
      _Link_type __y = _M_header;
      _Link_type __x = _M_root();
      while (__x != 0) 
	{
	  __y = __x;
	  __x = _M_key_compare(_KeyOfValue()(__v), _S_key(__x)) ? 
	    _S_left(__x) : _S_right(__x);
	}
      return _M_insert(__x, __y, __v);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    pair<typename _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::iterator, 
    bool>
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::
    insert_unique(const _Val& __v)
    {
      _Link_type __y = _M_header;
      _Link_type __x = _M_root();
      bool __comp = true;
      while (__x != 0) 
	{
	  __y = __x;
	  __comp = _M_key_compare(_KeyOfValue()(__v), _S_key(__x));
	  __x = __comp ? _S_left(__x) : _S_right(__x);
	}
      iterator __j = iterator(__y);   
      if (__comp)
	if (__j == begin())     
	  return pair<iterator,bool>(_M_insert(__x, __y, __v), true);
	else
	  --__j;
      if (_M_key_compare(_S_key(__j._M_node), _KeyOfValue()(__v)))
	return pair<iterator,bool>(_M_insert(__x, __y, __v), true);
      return pair<iterator,bool>(__j, false);
    }
  

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator 
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    insert_unique(iterator __position, const _Val& __v)
    {
      if (__position._M_node == _M_header->_M_left) 
	{ 
	  // begin()
	  if (size() > 0 && 
	      _M_key_compare(_KeyOfValue()(__v), _S_key(__position._M_node)))
	    return _M_insert(__position._M_node, __position._M_node, __v);
	  // first argument just needs to be non-null 
	  else
	    return insert_unique(__v).first;
	} 
      else if (__position._M_node == _M_header) 
	{ 
	  // end()
	  if (_M_key_compare(_S_key(_M_rightmost()), _KeyOfValue()(__v)))
	    return _M_insert(0, _M_rightmost(), __v);
	  else
	    return insert_unique(__v).first;
	} 
      else 
	{
	  iterator __before = __position;
	  --__before;
	  if (_M_key_compare(_S_key(__before._M_node), _KeyOfValue()(__v)) 
	      && _M_key_compare(_KeyOfValue()(__v),_S_key(__position._M_node)))
	    {
	      if (_S_right(__before._M_node) == 0)
		return _M_insert(0, __before._M_node, __v); 
	      else
		return _M_insert(__position._M_node, __position._M_node, __v);
	      // first argument just needs to be non-null 
	    } 
	  else
	    return insert_unique(__v).first;
	}
    }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::iterator 
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::
    insert_equal(iterator __position, const _Val& __v)
    {
      if (__position._M_node == _M_header->_M_left) 
	{ 
	  // begin()
	  if (size() > 0 && 
	      !_M_key_compare(_S_key(__position._M_node), _KeyOfValue()(__v)))
	    return _M_insert(__position._M_node, __position._M_node, __v);
	  // first argument just needs to be non-null 
	  else
	    return insert_equal(__v);
	} 
      else if (__position._M_node == _M_header) 
	{
	  // end()
	  if (!_M_key_compare(_KeyOfValue()(__v), _S_key(_M_rightmost())))
	    return _M_insert(0, _M_rightmost(), __v);
	  else
	    return insert_equal(__v);
	} 
      else 
	{
	  iterator __before = __position;
	  --__before;
	  if (!_M_key_compare(_KeyOfValue()(__v), _S_key(__before._M_node))
	      && !_M_key_compare(_S_key(__position._M_node),
				 _KeyOfValue()(__v))) 
	    {
	      if (_S_right(__before._M_node) == 0)
		return _M_insert(0, __before._M_node, __v); 
	      else
		return _M_insert(__position._M_node, __position._M_node, __v);
	      // first argument just needs to be non-null 
	    } 
	  else
	    return insert_equal(__v);
	}
    }

  template<typename _Key, typename _Val, typename _KoV, 
           typename _Cmp, typename _Alloc>
    template<class _II>
      void 
      _Rb_tree<_Key,_Val,_KoV,_Cmp,_Alloc>::
      insert_equal(_II __first, _II __last)
      {
	for ( ; __first != __last; ++__first)
	  insert_equal(*__first);
      }

  template<typename _Key, typename _Val, typename _KoV, 
           typename _Cmp, typename _Alloc> 
    template<class _II>
    void 
    _Rb_tree<_Key,_Val,_KoV,_Cmp,_Alloc>::
    insert_unique(_II __first, _II __last) 
    {
      for ( ; __first != __last; ++__first)
	insert_unique(*__first);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    inline void 
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::erase(iterator __position)
    {
      _Link_type __y = 
	(_Link_type) _Rb_tree_rebalance_for_erase(__position._M_node,
						  _M_header->_M_parent,
						  _M_header->_M_left,
						  _M_header->_M_right);
      destroy_node(__y);
      --_M_node_count;
    }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::size_type 
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::erase(const _Key& __x)
    {
      pair<iterator,iterator> __p = equal_range(__x);
      size_type __n = distance(__p.first, __p.second);
      erase(__p.first, __p.second);
      return __n;
    }

  template<typename _Key, typename _Val, typename _KoV, 
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key, _Val, _KoV, _Compare, _Alloc>::_Link_type 
    _Rb_tree<_Key,_Val,_KoV,_Compare,_Alloc>::
    _M_copy(_Link_type __x, _Link_type __p)
    {
      // Structural copy.  __x and __p must be non-null.
      _Link_type __top = _M_clone_node(__x);
      __top->_M_parent = __p;
      
      try 
	{
	  if (__x->_M_right)
	    __top->_M_right = _M_copy(_S_right(__x), __top);
	  __p = __top;
	  __x = _S_left(__x);
	  
	  while (__x != 0) 
	    {
	      _Link_type __y = _M_clone_node(__x);
	      __p->_M_left = __y;
	      __y->_M_parent = __p;
	      if (__x->_M_right)
		__y->_M_right = _M_copy(_S_right(__x), __y);
	      __p = __y;
	      __x = _S_left(__x);
	    }
	}
      catch(...)
	{
	  _M_erase(__top);
	  __throw_exception_again; 
	}
      return __top;
    }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    void 
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::_M_erase(_Link_type __x)
    {
      // Erase without rebalancing.
      while (__x != 0) 
	{
	  _M_erase(_S_right(__x));
	  _Link_type __y = _S_left(__x);
	  destroy_node(__x);
	  __x = __y;
	}
    }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    void 
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::
    erase(iterator __first, iterator __last)
    {
      if (__first == begin() && __last == end())
	clear();
      else
	while (__first != __last) erase(__first++);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    void 
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::
    erase(const _Key* __first, const _Key* __last) 
    { 
      while (__first != __last) 
	erase(*__first++); 
    }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::iterator 
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::find(const _Key& __k)
    {
      _Link_type __y = _M_header;  // Last node which is not less than __k. 
      _Link_type __x = _M_root();  // Current node. 
      
      while (__x != 0) 
	if (!_M_key_compare(_S_key(__x), __k))
	  __y = __x, __x = _S_left(__x);
	else
	  __x = _S_right(__x);
      
      iterator __j = iterator(__y);   
      return (__j == end() || _M_key_compare(__k, _S_key(__j._M_node))) ? 
	end() : __j;
    }
  
  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::const_iterator 
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::
    find(const _Key& __k) const
    {
      _Link_type __y = _M_header; // Last node which is not less than __k. 
      _Link_type __x = _M_root(); // Current node. 
 
     while (__x != 0) 
       {
	 if (!_M_key_compare(_S_key(__x), __k))
	   __y = __x, __x = _S_left(__x);
	 else
	   __x = _S_right(__x);
       } 
     const_iterator __j = const_iterator(__y);   
     return (__j == end() || _M_key_compare(__k, _S_key(__j._M_node))) ?
       end() : __j;
    }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::size_type 
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::
    count(const _Key& __k) const
    {
      pair<const_iterator, const_iterator> __p = equal_range(__k);
      size_type __n = distance(__p.first, __p.second);
      return __n;
    }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::iterator 
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::
    lower_bound(const _Key& __k)
    {
      _Link_type __y = _M_header; /* Last node which is not less than __k. */
      _Link_type __x = _M_root(); /* Current node. */
      
      while (__x != 0) 
	if (!_M_key_compare(_S_key(__x), __k))
	  __y = __x, __x = _S_left(__x);
	else
	  __x = _S_right(__x);
      
      return iterator(__y);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::const_iterator 
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::
    lower_bound(const _Key& __k) const
    {
      _Link_type __y = _M_header; /* Last node which is not less than __k. */
      _Link_type __x = _M_root(); /* Current node. */
      
      while (__x != 0) 
	if (!_M_key_compare(_S_key(__x), __k))
	  __y = __x, __x = _S_left(__x);
	else
	  __x = _S_right(__x);
      
      return const_iterator(__y);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::iterator 
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::
    upper_bound(const _Key& __k)
    {
      _Link_type __y = _M_header; /* Last node which is greater than __k. */
      _Link_type __x = _M_root(); /* Current node. */
      
      while (__x != 0) 
	if (_M_key_compare(__k, _S_key(__x)))
	  __y = __x, __x = _S_left(__x);
	else
	  __x = _S_right(__x);
      
      return iterator(__y);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::const_iterator 
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::
    upper_bound(const _Key& __k) const
    {
      _Link_type __y = _M_header; /* Last node which is greater than __k. */
      _Link_type __x = _M_root(); /* Current node. */
      
      while (__x != 0) 
	if (_M_key_compare(__k, _S_key(__x)))
	  __y = __x, __x = _S_left(__x);
	else
	  __x = _S_right(__x);
      
      return const_iterator(__y);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    inline 
    pair<typename _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::iterator,
								   typename _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::iterator>
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::
    equal_range(const _Key& __k)
    { return pair<iterator, iterator>(lower_bound(__k), upper_bound(__k)); }

  template<typename _Key, typename _Val, typename _KoV, 
           typename _Compare, typename _Alloc>
  inline 
  pair<typename _Rb_tree<_Key, _Val, _KoV, _Compare, _Alloc>::const_iterator,
								typename _Rb_tree<_Key, _Val, _KoV, _Compare, _Alloc>::const_iterator>
  _Rb_tree<_Key, _Val, _KoV, _Compare, _Alloc>
  ::equal_range(const _Key& __k) const
  {
    return pair<const_iterator,const_iterator>(lower_bound(__k),
					       upper_bound(__k));
  }

  inline int
  __black_count(_Rb_tree_node_base* __node, _Rb_tree_node_base* __root)
  {
    if (__node == 0)
      return 0;
    int __sum = 0;
    do 
      {
	if (__node->_M_color == _M_black) 
	  ++__sum;
	if (__node == __root) 
	  break;
	__node = __node->_M_parent;
      } 
    while (1);
    return __sum;
  }

  template<typename _Key, typename _Val, typename _KeyOfValue, 
           typename _Compare, typename _Alloc>
    bool 
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::__rb_verify() const
    {
    if (_M_node_count == 0 || begin() == end())
      return _M_node_count == 0 && begin() == end() &&
	_M_header->_M_left == _M_header && _M_header->_M_right == _M_header;
  
    int __len = __black_count(_M_leftmost(), _M_root());
    for (const_iterator __it = begin(); __it != end(); ++__it) 
      {
	_Link_type __x = (_Link_type) __it._M_node;
	_Link_type __L = _S_left(__x);
	_Link_type __R = _S_right(__x);
	
	if (__x->_M_color == _M_red)
	  if ((__L && __L->_M_color == _M_red) 
	      || (__R && __R->_M_color == _M_red))
	    return false;
	
	if (__L && _M_key_compare(_S_key(__x), _S_key(__L)))
	  return false;
	if (__R && _M_key_compare(_S_key(__R), _S_key(__x)))
	  return false;

	if (!__L && !__R && __black_count(__x, _M_root()) != __len)
	  return false;
      }
    
    if (_M_leftmost() != _Rb_tree_node_base::_S_minimum(_M_root()))
      return false;
    if (_M_rightmost() != _Rb_tree_node_base::_S_maximum(_M_root()))
      return false;
    return true;
    }
} // namespace std 

#endif