// 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
{ 
  typedef bool _Rb_tree_Color_type;
  extern const _Rb_tree_Color_type _S_rb_tree_red; // false
  extern const _Rb_tree_Color_type _S_rb_tree_black; // true

struct _Rb_tree_node_base
{
  typedef _Rb_tree_Color_type _Color_type;
  typedef _Rb_tree_node_base* _Base_ptr;

  _Color_type _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 <class _Value>
struct _Rb_tree_node : public _Rb_tree_node_base
{
  typedef _Rb_tree_node<_Value>* _Link_type;
  _Value _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 == _S_rb_tree_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 <class _Value, class _Ref, class _Ptr>
struct _Rb_tree_iterator : public _Rb_tree_base_iterator
{
  typedef _Value value_type;
  typedef _Ref reference;
  typedef _Ptr pointer;
  typedef _Rb_tree_iterator<_Value, _Value&, _Value*>             
    iterator;
  typedef _Rb_tree_iterator<_Value, const _Value&, const _Value*> 
    const_iterator;
  typedef _Rb_tree_iterator<_Value, _Ref, _Ptr>                   
    _Self;
  typedef _Rb_tree_node<_Value>* _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 <class _Value, class _Ref, class _Ptr>
inline bool operator==(const _Rb_tree_iterator<_Value, _Ref, _Ptr>& __x,
		       const _Rb_tree_iterator<_Value, _Ref, _Ptr>& __y) {
  return __x._M_node == __y._M_node;
}

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

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

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

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

template <class _Value>
inline bool operator!=(const _Rb_tree_iterator<_Value, _Value&, _Value*>& __x,
		       const _Rb_tree_iterator<_Value, const _Value&, const _Value*>& __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 = _S_rb_tree_red;
  while (__x != __root && __x->_M_parent->_M_color == _S_rb_tree_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 == _S_rb_tree_red) {
        __x->_M_parent->_M_color = _S_rb_tree_black;
        __y->_M_color = _S_rb_tree_black;
        __x->_M_parent->_M_parent->_M_color = _S_rb_tree_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 = _S_rb_tree_black;
        __x->_M_parent->_M_parent->_M_color = _S_rb_tree_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 == _S_rb_tree_red) {
        __x->_M_parent->_M_color = _S_rb_tree_black;
        __y->_M_color = _S_rb_tree_black;
        __x->_M_parent->_M_parent->_M_color = _S_rb_tree_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 = _S_rb_tree_black;
        __x->_M_parent->_M_parent->_M_color = _S_rb_tree_red;
        _Rb_tree_rotate_left(__x->_M_parent->_M_parent, __root);
      }
    }
  }
  __root->_M_color = _S_rb_tree_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 != _S_rb_tree_red) { 
    while (__x != __root && (__x == 0 || __x->_M_color == _S_rb_tree_black))
      if (__x == __x_parent->_M_left) {
        _Rb_tree_node_base* __w = __x_parent->_M_right;
        if (__w->_M_color == _S_rb_tree_red) {
          __w->_M_color = _S_rb_tree_black;
          __x_parent->_M_color = _S_rb_tree_red;
          _Rb_tree_rotate_left(__x_parent, __root);
          __w = __x_parent->_M_right;
        }
        if ((__w->_M_left == 0 || 
             __w->_M_left->_M_color == _S_rb_tree_black) &&
            (__w->_M_right == 0 || 
             __w->_M_right->_M_color == _S_rb_tree_black)) {
          __w->_M_color = _S_rb_tree_red;
          __x = __x_parent;
          __x_parent = __x_parent->_M_parent;
        } else {
          if (__w->_M_right == 0 || 
              __w->_M_right->_M_color == _S_rb_tree_black) {
            if (__w->_M_left) __w->_M_left->_M_color = _S_rb_tree_black;
            __w->_M_color = _S_rb_tree_red;
            _Rb_tree_rotate_right(__w, __root);
            __w = __x_parent->_M_right;
          }
          __w->_M_color = __x_parent->_M_color;
          __x_parent->_M_color = _S_rb_tree_black;
          if (__w->_M_right) __w->_M_right->_M_color = _S_rb_tree_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 == _S_rb_tree_red) {
          __w->_M_color = _S_rb_tree_black;
          __x_parent->_M_color = _S_rb_tree_red;
          _Rb_tree_rotate_right(__x_parent, __root);
          __w = __x_parent->_M_left;
        }
        if ((__w->_M_right == 0 || 
             __w->_M_right->_M_color == _S_rb_tree_black) &&
            (__w->_M_left == 0 || 
             __w->_M_left->_M_color == _S_rb_tree_black)) {
          __w->_M_color = _S_rb_tree_red;
          __x = __x_parent;
          __x_parent = __x_parent->_M_parent;
        } else {
          if (__w->_M_left == 0 || 
              __w->_M_left->_M_color == _S_rb_tree_black) {
            if (__w->_M_right) __w->_M_right->_M_color = _S_rb_tree_black;
            __w->_M_color = _S_rb_tree_red;
            _Rb_tree_rotate_left(__w, __root);
            __w = __x_parent->_M_left;
          }
          __w->_M_color = __x_parent->_M_color;
          __x_parent->_M_color = _S_rb_tree_black;
          if (__w->_M_left) __w->_M_left->_M_color = _S_rb_tree_black;
          _Rb_tree_rotate_right(__x_parent, __root);
          break;
        }
      }
    if (__x) __x->_M_color = _S_rb_tree_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 <class _Tp, class _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 <class _Tp, class _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 <class _Tp, class _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 <class _Key, class _Value, class _KeyOfValue, class _Compare,
          class _Alloc = allocator<_Value> >
class _Rb_tree : protected _Rb_tree_base<_Value, _Alloc> {
  typedef _Rb_tree_base<_Value, _Alloc> _Base;
protected:
  typedef _Rb_tree_node_base* _Base_ptr;
  typedef _Rb_tree_node<_Value> _Rb_tree_node;
  typedef _Rb_tree_Color_type _Color_type;
public:
  typedef _Key key_type;
  typedef _Value 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;

protected:

  _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);
  }

protected:
  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 _Color_type& _S_color(_Link_type __x)
    { return (_Color_type&)(__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 _Color_type& _S_color(_Base_ptr __x)
    { return (_Color_type&)(_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,_Value,_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) = _S_rb_tree_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,_Value,_KeyOfValue,_Compare,_Alloc>& 
  operator=(const _Rb_tree<_Key,_Value,_KeyOfValue,_Compare,_Alloc>& __x);

private:
  void _M_empty_initialize() {
    _S_color(_M_header) = _S_rb_tree_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,_Value,_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);
  }
    
public:
                                // 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 <class _InputIterator>
  void insert_unique(_InputIterator __first, _InputIterator __last);
  template <class _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;
    }
  }      

public:
                                // 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;

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

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

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

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

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

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

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


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


template <class _Key, class _Value, class _KeyOfValue, 
          class _Compare, class _Alloc>
_Rb_tree<_Key,_Value,_KeyOfValue,_Compare,_Alloc>& 
_Rb_tree<_Key,_Value,_KeyOfValue,_Compare,_Alloc>
  ::operator=(const _Rb_tree<_Key,_Value,_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 <class _Key, class _Value, class _KeyOfValue, 
          class _Compare, class _Alloc>
typename _Rb_tree<_Key,_Value,_KeyOfValue,_Compare,_Alloc>::iterator
_Rb_tree<_Key,_Value,_KeyOfValue,_Compare,_Alloc>
  ::_M_insert(_Base_ptr __x_, _Base_ptr __y_, const _Value& __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;
    if (__y == _M_rightmost())
      _M_rightmost() = __z;  // maintain _M_rightmost() pointing to max node
  }
  _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 <class _Key, class _Value, class _KeyOfValue, 
          class _Compare, class _Alloc>
typename _Rb_tree<_Key,_Value,_KeyOfValue,_Compare,_Alloc>::iterator
_Rb_tree<_Key,_Value,_KeyOfValue,_Compare,_Alloc>
  ::insert_equal(const _Value& __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 <class _Key, class _Value, class _KeyOfValue, 
          class _Compare, class _Alloc>
pair<typename _Rb_tree<_Key,_Value,_KeyOfValue,_Compare,_Alloc>::iterator, 
     bool>
_Rb_tree<_Key,_Value,_KeyOfValue,_Compare,_Alloc>
  ::insert_unique(const _Value& __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 <class _Key, class _Val, class _KeyOfValue, 
          class _Compare, class _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 <class _Key, class _Val, class _KeyOfValue, 
          class _Compare, class _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 <class _Key, class _Val, class _KoV, class _Cmp, class _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 <class _Key, class _Val, class _KoV, class _Cmp, class _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 <class _Key, class _Value, class _KeyOfValue, 
          class _Compare, class _Alloc>
inline void _Rb_tree<_Key,_Value,_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 <class _Key, class _Value, class _KeyOfValue, 
          class _Compare, class _Alloc>
typename _Rb_tree<_Key,_Value,_KeyOfValue,_Compare,_Alloc>::size_type 
_Rb_tree<_Key,_Value,_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 <class _Key, class _Val, class _KoV, class _Compare, class _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 <class _Key, class _Value, class _KeyOfValue, 
          class _Compare, class _Alloc>
void _Rb_tree<_Key,_Value,_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 <class _Key, class _Value, class _KeyOfValue, 
          class _Compare, class _Alloc>
void _Rb_tree<_Key,_Value,_KeyOfValue,_Compare,_Alloc>
  ::erase(iterator __first, iterator __last)
{
  if (__first == begin() && __last == end())
    clear();
  else
    while (__first != __last) erase(__first++);
}

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

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

template <class _Key, class _Value, class _KoV, class _Compare, class _Alloc>
inline 
pair<typename _Rb_tree<_Key, _Value, _KoV, _Compare, _Alloc>::const_iterator,
     typename _Rb_tree<_Key, _Value, _KoV, _Compare, _Alloc>::const_iterator>
_Rb_tree<_Key, _Value, _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 == _S_rb_tree_black) 
      ++__sum;
    if (__node == __root) 
      break;
    __node = __node->_M_parent;
  } while (1);
  return __sum;
}

template <class _Key, class _Value, class _KeyOfValue, 
          class _Compare, class _Alloc>
bool _Rb_tree<_Key,_Value,_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 == _S_rb_tree_red)
      if ((__L && __L->_M_color == _S_rb_tree_red) ||
          (__R && __R->_M_color == _S_rb_tree_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 /* __GLIBCPP_INTERNAL_TREE_H */

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