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

// Copyright (C) 2001, 2002, 2003, 2004, 2005, 2006
// 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, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
// 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 _TREE_H
#define _TREE_H 1

#include <bits/stl_algobase.h>
#include <bits/allocator.h>
#include <bits/stl_construct.h>
#include <bits/stl_function.h>
#include <bits/cpp_type_traits.h>

_GLIBCXX_BEGIN_NAMESPACE(std)

  // 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.

  enum _Rb_tree_color { _S_red = false, _S_black = true };

  struct _Rb_tree_node_base
  {
    typedef _Rb_tree_node_base* _Base_ptr;
    typedef const _Rb_tree_node_base* _Const_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 _Const_Base_ptr
    _S_minimum(_Const_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;
    }

    static _Const_Base_ptr
    _S_maximum(_Const_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;
    };

  _Rb_tree_node_base*
  _Rb_tree_increment(_Rb_tree_node_base* __x);

  const _Rb_tree_node_base*
  _Rb_tree_increment(const _Rb_tree_node_base* __x);

  _Rb_tree_node_base*
  _Rb_tree_decrement(_Rb_tree_node_base* __x);

  const _Rb_tree_node_base*
  _Rb_tree_decrement(const _Rb_tree_node_base* __x);

  template<typename _Tp>
    struct _Rb_tree_iterator
    {
      typedef _Tp  value_type;
      typedef _Tp& reference;
      typedef _Tp* pointer;

      typedef bidirectional_iterator_tag iterator_category;
      typedef ptrdiff_t                  difference_type;

      typedef _Rb_tree_iterator<_Tp>        _Self;
      typedef _Rb_tree_node_base::_Base_ptr _Base_ptr;
      typedef _Rb_tree_node<_Tp>*           _Link_type;

      _Rb_tree_iterator()
      : _M_node() { }

      explicit
      _Rb_tree_iterator(_Link_type __x)
      : _M_node(__x) { }

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

      pointer
      operator->() const
      { return &static_cast<_Link_type>(_M_node)->_M_value_field; }

      _Self&
      operator++()
      {
	_M_node = _Rb_tree_increment(_M_node);
	return *this;
      }

      _Self
      operator++(int)
      {
	_Self __tmp = *this;
	_M_node = _Rb_tree_increment(_M_node);
	return __tmp;
      }

      _Self&
      operator--()
      {
	_M_node = _Rb_tree_decrement(_M_node);
	return *this;
      }

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

      bool
      operator==(const _Self& __x) const
      { return _M_node == __x._M_node; }

      bool
      operator!=(const _Self& __x) const
      { return _M_node != __x._M_node; }

      _Base_ptr _M_node;
  };

  template<typename _Tp>
    struct _Rb_tree_const_iterator
    {
      typedef _Tp        value_type;
      typedef const _Tp& reference;
      typedef const _Tp* pointer;

      typedef _Rb_tree_iterator<_Tp> iterator;

      typedef bidirectional_iterator_tag iterator_category;
      typedef ptrdiff_t                  difference_type;

      typedef _Rb_tree_const_iterator<_Tp>        _Self;
      typedef _Rb_tree_node_base::_Const_Base_ptr _Base_ptr;
      typedef const _Rb_tree_node<_Tp>*           _Link_type;

      _Rb_tree_const_iterator()
      : _M_node() { }

      explicit
      _Rb_tree_const_iterator(_Link_type __x)
      : _M_node(__x) { }

      _Rb_tree_const_iterator(const iterator& __it)
      : _M_node(__it._M_node) { }

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

      pointer
      operator->() const
      { return &static_cast<_Link_type>(_M_node)->_M_value_field; }

      _Self&
      operator++()
      {
	_M_node = _Rb_tree_increment(_M_node);
	return *this;
      }

      _Self
      operator++(int)
      {
	_Self __tmp = *this;
	_M_node = _Rb_tree_increment(_M_node);
	return __tmp;
      }

      _Self&
      operator--()
      {
	_M_node = _Rb_tree_decrement(_M_node);
	return *this;
      }

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

      bool
      operator==(const _Self& __x) const
      { return _M_node == __x._M_node; }

      bool
      operator!=(const _Self& __x) const
      { return _M_node != __x._M_node; }

      _Base_ptr _M_node;
    };

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

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

  void
  _Rb_tree_rotate_left(_Rb_tree_node_base* const __x,
                       _Rb_tree_node_base*& __root);

  void
  _Rb_tree_rotate_right(_Rb_tree_node_base* const __x,
                        _Rb_tree_node_base*& __root);

  void
  _Rb_tree_insert_and_rebalance(const bool __insert_left,
                                _Rb_tree_node_base* __x,
                                _Rb_tree_node_base* __p,
                                _Rb_tree_node_base& __header);

  _Rb_tree_node_base*
  _Rb_tree_rebalance_for_erase(_Rb_tree_node_base* const __z,
			       _Rb_tree_node_base& __header);


  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc = allocator<_Val> >
    class _Rb_tree
    {
      typedef typename _Alloc::template rebind<_Rb_tree_node<_Val> >::other
              _Node_allocator;

    protected:
      typedef _Rb_tree_node_base* _Base_ptr;
      typedef const _Rb_tree_node_base* _Const_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 const _Rb_tree_node* _Const_Link_type;
      typedef size_t size_type;
      typedef ptrdiff_t difference_type;
      typedef _Alloc allocator_type;

      _Node_allocator&
      _M_get_Node_allocator()
      { return *static_cast<_Node_allocator*>(&this->_M_impl); }
      
      const _Node_allocator&
      _M_get_Node_allocator() const
      { return *static_cast<const _Node_allocator*>(&this->_M_impl); }

      allocator_type
      get_allocator() const
      { return allocator_type(_M_get_Node_allocator()); }

    protected:
      _Rb_tree_node*
      _M_get_node()
      { return _M_impl._Node_allocator::allocate(1); }

      void
      _M_put_node(_Rb_tree_node* __p)
      { _M_impl._Node_allocator::deallocate(__p, 1); }

      _Link_type
      _M_create_node(const value_type& __x)
      {
	_Link_type __tmp = _M_get_node();
	try
	  { get_allocator().construct(&__tmp->_M_value_field, __x); }
	catch(...)
	  {
	    _M_put_node(__tmp);
	    __throw_exception_again;
	  }
	return __tmp;
      }

      _Link_type
      _M_clone_node(_Const_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
      _M_destroy_node(_Link_type __p)
      {
	get_allocator().destroy(&__p->_M_value_field);
	_M_put_node(__p);
      }

    protected:
      template<typename _Key_compare, 
	       bool _Is_pod_comparator = std::__is_pod<_Key_compare>::__value>
        struct _Rb_tree_impl : public _Node_allocator
        {
	  _Key_compare		_M_key_compare;
	  _Rb_tree_node_base 	_M_header;
	  size_type 		_M_node_count; // Keeps track of size of tree.

          // LLVM LOCAL begin mainline 129013
	  _Rb_tree_impl()
	  : _Node_allocator(), _M_key_compare(), _M_header(),
	    _M_node_count(0)
	  { _M_initialize(); }

	  _Rb_tree_impl(const _Key_compare& __comp, const _Node_allocator& __a)
	  : _Node_allocator(__a), _M_key_compare(__comp), _M_header(),
	    _M_node_count(0)
	  { _M_initialize(); }

	private:
	  void
	  _M_initialize()
          // LLVM LOCAL end mainline 129013
	  {
	    this->_M_header._M_color = _S_red;
	    this->_M_header._M_parent = 0;
	    this->_M_header._M_left = &this->_M_header;
	    this->_M_header._M_right = &this->_M_header;
	  }
	};

      // Specialization for _Comparison types that are not capable of
      // being base classes / super classes.
      template<typename _Key_compare>
        struct _Rb_tree_impl<_Key_compare, true> : public _Node_allocator 
	{
	  _Key_compare 		_M_key_compare;
	  _Rb_tree_node_base 	_M_header;
	  size_type 		_M_node_count; // Keeps track of size of tree.

          // LLVM LOCAL begin mainline 129013
	  _Rb_tree_impl()
	  : _Node_allocator(), _M_key_compare(), _M_header(),
	    _M_node_count(0)
	  { _M_initialize(); }

	  _Rb_tree_impl(const _Key_compare& __comp, const _Node_allocator& __a)
	  : _Node_allocator(__a), _M_key_compare(__comp), _M_header(),
	    _M_node_count(0)
	  { _M_initialize(); }

	private:
	  void
	  _M_initialize()
          // LLVM LOCAL end mainline 129013
	  {
	    this->_M_header._M_color = _S_red;
	    this->_M_header._M_parent = 0;
	    this->_M_header._M_left = &this->_M_header;
	    this->_M_header._M_right = &this->_M_header;
	  }
	};

      _Rb_tree_impl<_Compare> _M_impl;

    protected:
      _Base_ptr&
      _M_root()
      { return this->_M_impl._M_header._M_parent; }

      _Const_Base_ptr
      _M_root() const
      { return this->_M_impl._M_header._M_parent; }

      _Base_ptr&
      _M_leftmost()
      { return this->_M_impl._M_header._M_left; }

      _Const_Base_ptr
      _M_leftmost() const
      { return this->_M_impl._M_header._M_left; }

      _Base_ptr&
      _M_rightmost()
      { return this->_M_impl._M_header._M_right; }

      _Const_Base_ptr
      _M_rightmost() const
      { return this->_M_impl._M_header._M_right; }

      _Link_type
      _M_begin()
      { return static_cast<_Link_type>(this->_M_impl._M_header._M_parent); }

      _Const_Link_type
      _M_begin() const
      {
	return static_cast<_Const_Link_type>
	  (this->_M_impl._M_header._M_parent);
      }

      _Link_type
      _M_end()
      { return static_cast<_Link_type>(&this->_M_impl._M_header); }

      _Const_Link_type
      _M_end() const
      { return static_cast<_Const_Link_type>(&this->_M_impl._M_header); }

      static const_reference
      _S_value(_Const_Link_type __x)
      { return __x->_M_value_field; }

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

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

      static _Const_Link_type
      _S_left(_Const_Base_ptr __x)
      { return static_cast<_Const_Link_type>(__x->_M_left); }

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

      static _Const_Link_type
      _S_right(_Const_Base_ptr __x)
      { return static_cast<_Const_Link_type>(__x->_M_right); }

      static const_reference
      _S_value(_Const_Base_ptr __x)
      { return static_cast<_Const_Link_type>(__x)->_M_value_field; }

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

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

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

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

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

    public:
      typedef _Rb_tree_iterator<value_type>       iterator;
      typedef _Rb_tree_const_iterator<value_type> const_iterator;

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

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

      // _GLIBCXX_RESOLVE_LIB_DEFECTS
      // 233. Insertion hints in associative containers.
      iterator
      _M_insert_lower(_Base_ptr __x, _Base_ptr __y, const value_type& __v);

      const_iterator
      _M_insert(_Const_Base_ptr __x, _Const_Base_ptr __y,
		const value_type& __v);

      _Link_type
      _M_copy(_Const_Link_type __x, _Link_type __p);

      void
      _M_erase(_Link_type __x);

    public:
      // allocation/deallocation
      _Rb_tree()
      { }

      // LLVM LOCAL begin mainline 129013
      _Rb_tree(const _Compare& __comp,
	       const allocator_type& __a = allocator_type())
      : _M_impl(__comp, __a)
      { }

      _Rb_tree(const _Rb_tree& __x)
      : _M_impl(__x._M_impl._M_key_compare, __x._M_get_Node_allocator())
      // LLVM LOCAL end mainline 129013
      {
	if (__x._M_root() != 0)
	  {
	    _M_root() = _M_copy(__x._M_begin(), _M_end());
	    _M_leftmost() = _S_minimum(_M_root());
	    _M_rightmost() = _S_maximum(_M_root());
	    _M_impl._M_node_count = __x._M_impl._M_node_count;
	  }
      }

      ~_Rb_tree()
      { _M_erase(_M_begin()); }

      // LLVM LOCAL begin mainline 129013
      _Rb_tree&
      operator=(const _Rb_tree& __x);
      // LLVM LOCAL end mainline 129013

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

      iterator
      begin()
      { 
	return iterator(static_cast<_Link_type>
			(this->_M_impl._M_header._M_left));
      }

      const_iterator
      begin() const
      { 
	return const_iterator(static_cast<_Const_Link_type>
			      (this->_M_impl._M_header._M_left));
      }

      iterator
      end()
      { return iterator(static_cast<_Link_type>(&this->_M_impl._M_header)); }

      const_iterator
      end() const
      { 
	return const_iterator(static_cast<_Const_Link_type>
			      (&this->_M_impl._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_impl._M_node_count == 0; }

      size_type
      size() const
      { return _M_impl._M_node_count; }

      size_type
      max_size() const
      { return get_allocator().max_size(); }

      // LLVM LOCAL begin mainline 129013
      void
      swap(_Rb_tree& __t);
      // LLVM LOCAL end mainline 129013

      // Insert/erase.
      pair<iterator, bool>
      _M_insert_unique(const value_type& __x);

      iterator
      _M_insert_equal(const value_type& __x);

      // _GLIBCXX_RESOLVE_LIB_DEFECTS
      // 233. Insertion hints in associative containers.
      iterator
      _M_insert_equal_lower(const value_type& __x);

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

      const_iterator
      _M_insert_unique(const_iterator __position, const value_type& __x);

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

      const_iterator
      _M_insert_equal(const_iterator __position, const value_type& __x);

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

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

      void
      erase(iterator __position);

      void
      erase(const_iterator __position);

      size_type
      erase(const key_type& __x);

      void
      erase(iterator __first, iterator __last);

      void
      erase(const_iterator __first, const_iterator __last);

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

      void
      clear()
      {
        _M_erase(_M_begin());
        _M_leftmost() = _M_end();
        _M_root() = 0;
        _M_rightmost() = _M_end();
        _M_impl._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()
	     && std::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 std::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_impl._M_key_compare = __x._M_impl._M_key_compare;
	  if (__x._M_root() != 0)
	    {
	      _M_root() = _M_copy(__x._M_begin(), _M_end());
	      _M_leftmost() = _S_minimum(_M_root());
	      _M_rightmost() = _S_maximum(_M_root());
	      _M_impl._M_node_count = __x._M_impl._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 __p, const _Val& __v)
    {
      bool __insert_left = (__x != 0 || __p == _M_end()
			    || _M_impl._M_key_compare(_KeyOfValue()(__v), 
						      _S_key(__p)));

      _Link_type __z = _M_create_node(__v);

      _Rb_tree_insert_and_rebalance(__insert_left, __z, __p,  
				    this->_M_impl._M_header);
      ++_M_impl._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>::
    _M_insert_lower(_Base_ptr __x, _Base_ptr __p, const _Val& __v)
    {
      bool __insert_left = (__x != 0 || __p == _M_end()
			    || !_M_impl._M_key_compare(_S_key(__p),
						       _KeyOfValue()(__v)));

      _Link_type __z = _M_create_node(__v);

      _Rb_tree_insert_and_rebalance(__insert_left, __z, __p,  
				    this->_M_impl._M_header);
      ++_M_impl._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>::const_iterator
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_insert(_Const_Base_ptr __x, _Const_Base_ptr __p, const _Val& __v)
    {
      bool __insert_left = (__x != 0 || __p == _M_end()
			    || _M_impl._M_key_compare(_KeyOfValue()(__v), 
						      _S_key(__p)));

      _Link_type __z = _M_create_node(__v);

      _Rb_tree_insert_and_rebalance(__insert_left, __z,
				    const_cast<_Base_ptr>(__p),  
				    this->_M_impl._M_header);
      ++_M_impl._M_node_count;
      return const_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>::
    _M_insert_equal(const _Val& __v)
    {
      _Link_type __x = _M_begin();
      _Link_type __y = _M_end();
      while (__x != 0)
	{
	  __y = __x;
	  __x = _M_impl._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>
    typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_insert_equal_lower(const _Val& __v)
    {
      _Link_type __x = _M_begin();
      _Link_type __y = _M_end();
      while (__x != 0)
	{
	  __y = __x;
	  __x = !_M_impl._M_key_compare(_S_key(__x), _KeyOfValue()(__v)) ?
	        _S_left(__x) : _S_right(__x);
	}
      return _M_insert_lower(__x, __y, __v);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    void
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    swap(_Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __t)
    {
      if (_M_root() == 0)
	{
	  if (__t._M_root() != 0)
	    {
	      _M_root() = __t._M_root();
	      _M_leftmost() = __t._M_leftmost();
	      _M_rightmost() = __t._M_rightmost();
	      _M_root()->_M_parent = _M_end();
	      
	      __t._M_root() = 0;
	      __t._M_leftmost() = __t._M_end();
	      __t._M_rightmost() = __t._M_end();
	    }
	}
      else if (__t._M_root() == 0)
	{
	  __t._M_root() = _M_root();
	  __t._M_leftmost() = _M_leftmost();
	  __t._M_rightmost() = _M_rightmost();
	  __t._M_root()->_M_parent = __t._M_end();
	  
	  _M_root() = 0;
	  _M_leftmost() = _M_end();
	  _M_rightmost() = _M_end();
	}
      else
	{
	  std::swap(_M_root(),__t._M_root());
	  std::swap(_M_leftmost(),__t._M_leftmost());
	  std::swap(_M_rightmost(),__t._M_rightmost());
	  
	  _M_root()->_M_parent = _M_end();
	  __t._M_root()->_M_parent = __t._M_end();
	}
      // No need to swap header's color as it does not change.
      std::swap(this->_M_impl._M_node_count, __t._M_impl._M_node_count);
      std::swap(this->_M_impl._M_key_compare, __t._M_impl._M_key_compare);
      
      // _GLIBCXX_RESOLVE_LIB_DEFECTS
      // 431. Swapping containers with unequal allocators.
      std::__alloc_swap<_Node_allocator>::
	_S_do_it(_M_get_Node_allocator(), __t._M_get_Node_allocator());
    }

  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>::
    _M_insert_unique(const _Val& __v)
    {
      _Link_type __x = _M_begin();
      _Link_type __y = _M_end();
      bool __comp = true;
      while (__x != 0)
	{
	  __y = __x;
	  __comp = _M_impl._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_impl._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>::
    _M_insert_unique(iterator __position, const _Val& __v)
    {
      // end()
      if (__position._M_node == _M_end())
	{
	  if (size() > 0
	      && _M_impl._M_key_compare(_S_key(_M_rightmost()), 
					_KeyOfValue()(__v)))
	    return _M_insert(0, _M_rightmost(), __v);
	  else
	    return _M_insert_unique(__v).first;
	}
      else if (_M_impl._M_key_compare(_KeyOfValue()(__v),
				      _S_key(__position._M_node)))
	{
	  // First, try before...
	  iterator __before = __position;
	  if (__position._M_node == _M_leftmost()) // begin()
	    return _M_insert(_M_leftmost(), _M_leftmost(), __v);
	  else if (_M_impl._M_key_compare(_S_key((--__before)._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);
	    }
	  else
	    return _M_insert_unique(__v).first;
	}
      else if (_M_impl._M_key_compare(_S_key(__position._M_node),
				      _KeyOfValue()(__v)))
	{
	  // ... then try after.
	  iterator __after = __position;
	  if (__position._M_node == _M_rightmost())
	    return _M_insert(0, _M_rightmost(), __v);
	  else if (_M_impl._M_key_compare(_KeyOfValue()(__v),
					  _S_key((++__after)._M_node)))
	    {
	      if (_S_right(__position._M_node) == 0)
		return _M_insert(0, __position._M_node, __v);
	      else
		return _M_insert(__after._M_node, __after._M_node, __v);
	    }
	  else
	    return _M_insert_unique(__v).first;
	}
      else
	return __position; // Equivalent keys.
    }

  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>::
    _M_insert_unique(const_iterator __position, const _Val& __v)
    {
      // end()
      if (__position._M_node == _M_end())
	{
	  if (size() > 0
	      && _M_impl._M_key_compare(_S_key(_M_rightmost()), 
					_KeyOfValue()(__v)))
	    return _M_insert(0, _M_rightmost(), __v);
	  else
	    return const_iterator(_M_insert_unique(__v).first);
	}
      else if (_M_impl._M_key_compare(_KeyOfValue()(__v),
				      _S_key(__position._M_node)))
	{
	  // First, try before...
	  const_iterator __before = __position;
	  if (__position._M_node == _M_leftmost()) // begin()
	    return _M_insert(_M_leftmost(), _M_leftmost(), __v);
	  else if (_M_impl._M_key_compare(_S_key((--__before)._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);
	    }
	  else
	    return const_iterator(_M_insert_unique(__v).first);
	}
      else if (_M_impl._M_key_compare(_S_key(__position._M_node),
				      _KeyOfValue()(__v)))
	{
	  // ... then try after.
	  const_iterator __after = __position;
	  if (__position._M_node == _M_rightmost())
	    return _M_insert(0, _M_rightmost(), __v);
	  else if (_M_impl._M_key_compare(_KeyOfValue()(__v),
					  _S_key((++__after)._M_node)))
	    {
	      if (_S_right(__position._M_node) == 0)
		return _M_insert(0, __position._M_node, __v);
	      else
		return _M_insert(__after._M_node, __after._M_node, __v);
	    }
	  else
	    return const_iterator(_M_insert_unique(__v).first);
	}
      else
	return __position; // Equivalent keys.
    }

  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_equal(iterator __position, const _Val& __v)
    {
      // end()
      if (__position._M_node == _M_end())
	{
	  if (size() > 0
	      && !_M_impl._M_key_compare(_KeyOfValue()(__v),
					 _S_key(_M_rightmost())))
	    return _M_insert(0, _M_rightmost(), __v);
	  else
	    return _M_insert_equal(__v);
	}
      else if (!_M_impl._M_key_compare(_S_key(__position._M_node),
				       _KeyOfValue()(__v)))
	{
	  // First, try before...
	  iterator __before = __position;
	  if (__position._M_node == _M_leftmost()) // begin()
	    return _M_insert(_M_leftmost(), _M_leftmost(), __v);
	  else if (!_M_impl._M_key_compare(_KeyOfValue()(__v),
					   _S_key((--__before)._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);
	    }
	  else
	    return _M_insert_equal(__v);
	}
      else
	{
	  // ... then try after.  
	  iterator __after = __position;
	  if (__position._M_node == _M_rightmost())
	    return _M_insert(0, _M_rightmost(), __v);
	  else if (!_M_impl._M_key_compare(_S_key((++__after)._M_node),
					   _KeyOfValue()(__v)))
	    {
	      if (_S_right(__position._M_node) == 0)
		return _M_insert(0, __position._M_node, __v);
	      else
		return _M_insert(__after._M_node, __after._M_node, __v);
	    }
	  else
	    return _M_insert_equal_lower(__v);
	}
    }

  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>::
    _M_insert_equal(const_iterator __position, const _Val& __v)
    {
      // end()
      if (__position._M_node == _M_end())
	{
	  if (size() > 0
	      && !_M_impl._M_key_compare(_KeyOfValue()(__v),
					 _S_key(_M_rightmost())))
	    return _M_insert(0, _M_rightmost(), __v);
	  else
	    return const_iterator(_M_insert_equal(__v));
	}
      else if (!_M_impl._M_key_compare(_S_key(__position._M_node),
				       _KeyOfValue()(__v)))
	{
	  // First, try before...
	  const_iterator __before = __position;
	  if (__position._M_node == _M_leftmost()) // begin()
	    return _M_insert(_M_leftmost(), _M_leftmost(), __v);
	  else if (!_M_impl._M_key_compare(_KeyOfValue()(__v),
					   _S_key((--__before)._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);
	    }
	  else
	    return const_iterator(_M_insert_equal(__v));
	}
      else
	{
	  // ... then try after.  
	  const_iterator __after = __position;
	  if (__position._M_node == _M_rightmost())
	    return _M_insert(0, _M_rightmost(), __v);
	  else if (!_M_impl._M_key_compare(_S_key((++__after)._M_node),
					   _KeyOfValue()(__v)))
	    {
	      if (_S_right(__position._M_node) == 0)
		return _M_insert(0, __position._M_node, __v);
	      else
		return _M_insert(__after._M_node, __after._M_node, __v);
	    }
	  else
	    return const_iterator(_M_insert_equal_lower(__v));
	}
    }

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

  template<typename _Key, typename _Val, typename _KoV,
           typename _Cmp, typename _Alloc>
    template<class _II>
      void
      _Rb_tree<_Key, _Val, _KoV, _Cmp, _Alloc>::
      _M_insert_unique(_II __first, _II __last)
      {
	for (; __first != __last; ++__first)
	  _M_insert_unique(end(), *__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 =
	static_cast<_Link_type>(_Rb_tree_rebalance_for_erase
				(__position._M_node,
				 this->_M_impl._M_header));
      _M_destroy_node(__y);
      --_M_impl._M_node_count;
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    inline void
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    erase(const_iterator __position)
    {
      _Link_type __y =
	static_cast<_Link_type>(_Rb_tree_rebalance_for_erase
				(const_cast<_Base_ptr>(__position._M_node),
				 this->_M_impl._M_header));
      _M_destroy_node(__y);
      --_M_impl._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);
      const size_type __old_size = size();
      erase(__p.first, __p.second);
      return __old_size - size();
    }

  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(_Const_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);
	  _M_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_iterator __first, const_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 __x = _M_begin(); // Current node.
      _Link_type __y = _M_end(); // Last node which is not less than __k.

      while (__x != 0)
	if (!_M_impl._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_impl._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
    {
      _Const_Link_type __x = _M_begin(); // Current node.
      _Const_Link_type __y = _M_end(); // Last node which is not less than __k.

     while (__x != 0)
       {
	 if (!_M_impl._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_impl._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);
      const size_type __n = std::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 __x = _M_begin(); // Current node.
      _Link_type __y = _M_end(); // Last node which is not less than __k.

      while (__x != 0)
	if (!_M_impl._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
    {
      _Const_Link_type __x = _M_begin(); // Current node.
      _Const_Link_type __y = _M_end(); // Last node which is not less than __k.

      while (__x != 0)
	if (!_M_impl._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 __x = _M_begin(); // Current node.
      _Link_type __y = _M_end(); // Last node which is greater than __k.

      while (__x != 0)
	if (_M_impl._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
    {
      _Const_Link_type __x = _M_begin(); // Current node.
      _Const_Link_type __y = _M_end(); // Last node which is greater than __k.

      while (__x != 0)
	if (_M_impl._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)); }

  unsigned int
  _Rb_tree_black_count(const _Rb_tree_node_base* __node,
                       const _Rb_tree_node_base* __root);

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    bool
    _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::__rb_verify() const
    {
      if (_M_impl._M_node_count == 0 || begin() == end())
	return _M_impl._M_node_count == 0 && begin() == end()
	       && this->_M_impl._M_header._M_left == _M_end()
	       && this->_M_impl._M_header._M_right == _M_end();

      unsigned int __len = _Rb_tree_black_count(_M_leftmost(), _M_root());
      for (const_iterator __it = begin(); __it != end(); ++__it)
	{
	  _Const_Link_type __x = static_cast<_Const_Link_type>(__it._M_node);
	  _Const_Link_type __L = _S_left(__x);
	  _Const_Link_type __R = _S_right(__x);

	  if (__x->_M_color == _S_red)
	    if ((__L && __L->_M_color == _S_red)
		|| (__R && __R->_M_color == _S_red))
	      return false;

	  if (__L && _M_impl._M_key_compare(_S_key(__x), _S_key(__L)))
	    return false;
	  if (__R && _M_impl._M_key_compare(_S_key(__R), _S_key(__x)))
	    return false;

	  if (!__L && !__R && _Rb_tree_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;
    }

_GLIBCXX_END_NAMESPACE

#endif