stl_tree.h

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

// Copyright (C) 2001-2018 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 3, 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.

// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.

// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
// <http://www.gnu.org/licenses/>.

/*
 *
 * 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 bits/stl_tree.h
 *  This is an internal header file, included by other library headers.
 *  Do not attempt to use it directly. @headername{map,set}
 */

#ifndef _STL_TREE_H
#define _STL_TREE_H 1

#pragma GCC system_header

#include <bits/stl_algobase.h>
#include <bits/allocator.h>
#include <bits/stl_function.h>
#include <bits/cpp_type_traits.h>
#include <ext/alloc_traits.h>
#if __cplusplus >= 201103L
# include <ext/aligned_buffer.h>
#endif
#if __cplusplus > 201402L
# include <bits/node_handle.h>
#endif

namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION

#if __cplusplus > 201103L
# define __cpp_lib_generic_associative_lookup 201304
#endif

  // 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) _GLIBCXX_NOEXCEPT
    {
      while (__x->_M_left != 0) __x = __x->_M_left;
      return __x;
    }

    static _Const_Base_ptr
    _S_minimum(_Const_Base_ptr __x) _GLIBCXX_NOEXCEPT
    {
      while (__x->_M_left != 0) __x = __x->_M_left;
      return __x;
    }

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

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

  // Helper type offering value initialization guarantee on the compare functor.
  template<typename _Key_compare>
    struct _Rb_tree_key_compare
    {
      _Key_compare              _M_key_compare;

      _Rb_tree_key_compare()
      _GLIBCXX_NOEXCEPT_IF(
        is_nothrow_default_constructible<_Key_compare>::value)
      : _M_key_compare()
      { }

      _Rb_tree_key_compare(const _Key_compare& __comp)
      : _M_key_compare(__comp)
      { }

#if __cplusplus >= 201103L
      // Copy constructor added for consistency with C++98 mode.
      _Rb_tree_key_compare(const _Rb_tree_key_compare&) = default;

      _Rb_tree_key_compare(_Rb_tree_key_compare&& __x)
        noexcept(is_nothrow_copy_constructible<_Key_compare>::value)
      : _M_key_compare(__x._M_key_compare)
      { }
#endif
    };

  // Helper type to manage default initialization of node count and header.
  struct _Rb_tree_header
  {
    _Rb_tree_node_base  _M_header;
    size_t              _M_node_count; // Keeps track of size of tree.

    _Rb_tree_header() _GLIBCXX_NOEXCEPT
    {
      _M_header._M_color = _S_red;
      _M_reset();
    }

#if __cplusplus >= 201103L
    _Rb_tree_header(_Rb_tree_header&& __x) noexcept
    {
      if (__x._M_header._M_parent != nullptr)
        _M_move_data(__x);
      else
        {
          _M_header._M_color = _S_red;
          _M_reset();
        }
    }
#endif

    void
    _M_move_data(_Rb_tree_header& __from)
    {
      _M_header._M_color = __from._M_header._M_color;
      _M_header._M_parent = __from._M_header._M_parent;
      _M_header._M_left = __from._M_header._M_left;
      _M_header._M_right = __from._M_header._M_right;
      _M_header._M_parent->_M_parent = &_M_header;
      _M_node_count = __from._M_node_count;

      __from._M_reset();
    }

    void
    _M_reset()
    {
      _M_header._M_parent = 0;
      _M_header._M_left = &_M_header;
      _M_header._M_right = &_M_header;
      _M_node_count = 0;
    }
  };

  template<typename _Val>
    struct _Rb_tree_node : public _Rb_tree_node_base
    {
      typedef _Rb_tree_node<_Val>* _Link_type;

#if __cplusplus < 201103L
      _Val _M_value_field;

      _Val*
      _M_valptr()
      { return std::__addressof(_M_value_field); }

      const _Val*
      _M_valptr() const
      { return std::__addressof(_M_value_field); }
#else
      __gnu_cxx::__aligned_membuf<_Val> _M_storage;

      _Val*
      _M_valptr()
      { return _M_storage._M_ptr(); }

      const _Val*
      _M_valptr() const
      { return _M_storage._M_ptr(); }
#endif
    };

  _GLIBCXX_PURE _Rb_tree_node_base*
  _Rb_tree_increment(_Rb_tree_node_base* __x) throw ();

  _GLIBCXX_PURE const _Rb_tree_node_base*
  _Rb_tree_increment(const _Rb_tree_node_base* __x) throw ();

  _GLIBCXX_PURE _Rb_tree_node_base*
  _Rb_tree_decrement(_Rb_tree_node_base* __x) throw ();

  _GLIBCXX_PURE const _Rb_tree_node_base*
  _Rb_tree_decrement(const _Rb_tree_node_base* __x) throw ();

  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() _GLIBCXX_NOEXCEPT
      : _M_node() { }

      explicit
      _Rb_tree_iterator(_Base_ptr __x) _GLIBCXX_NOEXCEPT
      : _M_node(__x) { }

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

      pointer
      operator->() const _GLIBCXX_NOEXCEPT
      { return static_cast<_Link_type> (_M_node)->_M_valptr(); }

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

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

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

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

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

      bool
      operator!=(const _Self& __x) const _GLIBCXX_NOEXCEPT
      { 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() _GLIBCXX_NOEXCEPT
      : _M_node() { }

      explicit
      _Rb_tree_const_iterator(_Base_ptr __x) _GLIBCXX_NOEXCEPT
      : _M_node(__x) { }

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

      iterator
      _M_const_cast() const _GLIBCXX_NOEXCEPT
      { return iterator(const_cast<typename iterator::_Base_ptr>(_M_node)); }

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

      pointer
      operator->() const _GLIBCXX_NOEXCEPT
      { return static_cast<_Link_type>(_M_node)->_M_valptr(); }

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

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

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

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

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

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

  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) throw ();

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

#if __cplusplus > 201103L
  template<typename _Cmp, typename _SfinaeType, typename = __void_t<>>
    struct __has_is_transparent
    { };

  template<typename _Cmp, typename _SfinaeType>
    struct __has_is_transparent<_Cmp, _SfinaeType,
                                __void_t<typename _Cmp::is_transparent>>
    { typedef void type; };
#endif

#if __cplusplus > 201402L
  template<typename _Tree1, typename _Cmp2>
    struct _Rb_tree_merge_helper { };
#endif

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

      typedef __gnu_cxx::__alloc_traits<_Node_allocator> _Alloc_traits;

    protected:
      typedef _Rb_tree_node_base*               _Base_ptr;
      typedef const _Rb_tree_node_base*         _Const_Base_ptr;
      typedef _Rb_tree_node<_Val>*              _Link_type;
      typedef const _Rb_tree_node<_Val>*        _Const_Link_type;

    private:
      // Functor recycling a pool of nodes and using allocation once the pool
      // is empty.
      struct _Reuse_or_alloc_node
      {
        _Reuse_or_alloc_node(_Rb_tree& __t)
          : _M_root(__t._M_root()), _M_nodes(__t._M_rightmost()), _M_t(__t)
        {
          if (_M_root)
            {
              _M_root->_M_parent = 0;

              if (_M_nodes->_M_left)
                _M_nodes = _M_nodes->_M_left;
            }
          else
            _M_nodes = 0;
        }

#if __cplusplus >= 201103L
        _Reuse_or_alloc_node(const _Reuse_or_alloc_node&) = delete;
#endif

        ~_Reuse_or_alloc_node()
        { _M_t._M_erase(static_cast<_Link_type>(_M_root)); }

        template<typename _Arg>
          _Link_type
#if __cplusplus < 201103L
          operator()(const _Arg& __arg)
#else
          operator()(_Arg&& __arg)
#endif
          {
            _Link_type __node = static_cast<_Link_type>(_M_extract());
            if (__node)
              {
                _M_t._M_destroy_node(__node);
                _M_t._M_construct_node(__node, _GLIBCXX_FORWARD(_Arg, __arg));
                return __node;
              }

            return _M_t._M_create_node(_GLIBCXX_FORWARD(_Arg, __arg));
          }

      private:
        _Base_ptr
        _M_extract()
        {
          if (!_M_nodes)
            return _M_nodes;

          _Base_ptr __node = _M_nodes;
          _M_nodes = _M_nodes->_M_parent;
          if (_M_nodes)
            {
              if (_M_nodes->_M_right == __node)
                {
                  _M_nodes->_M_right = 0;

                  if (_M_nodes->_M_left)
                    {
                      _M_nodes = _M_nodes->_M_left;

                      while (_M_nodes->_M_right)
                        _M_nodes = _M_nodes->_M_right;

                      if (_M_nodes->_M_left)
                        _M_nodes = _M_nodes->_M_left;
                    }
                }
              else // __node is on the left.
                _M_nodes->_M_left = 0;
            }
          else
            _M_root = 0;

          return __node;
        }

        _Base_ptr _M_root;
        _Base_ptr _M_nodes;
        _Rb_tree& _M_t;
      };

      // Functor similar to the previous one but without any pool of nodes to
      // recycle.
      struct _Alloc_node
      {
        _Alloc_node(_Rb_tree& __t)
          : _M_t(__t) { }

        template<typename _Arg>
          _Link_type
#if __cplusplus < 201103L
          operator()(const _Arg& __arg) const
#else
          operator()(_Arg&& __arg) const
#endif
          { return _M_t._M_create_node(_GLIBCXX_FORWARD(_Arg, __arg)); }

      private:
        _Rb_tree& _M_t;
      };

    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 size_t                            size_type;
      typedef ptrdiff_t                         difference_type;
      typedef _Alloc                            allocator_type;

      _Node_allocator&
      _M_get_Node_allocator() _GLIBCXX_NOEXCEPT
      { return this->_M_impl; }

      const _Node_allocator&
      _M_get_Node_allocator() const _GLIBCXX_NOEXCEPT
      { return this->_M_impl; }

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

    protected:
      _Link_type
      _M_get_node()
      { return _Alloc_traits::allocate(_M_get_Node_allocator(), 1); }

      void
      _M_put_node(_Link_type __p) _GLIBCXX_NOEXCEPT
      { _Alloc_traits::deallocate(_M_get_Node_allocator(), __p, 1); }

#if __cplusplus < 201103L
      void
      _M_construct_node(_Link_type __node, const value_type& __x)
      {
        __try
          { get_allocator().construct(__node->_M_valptr(), __x); }
        __catch(...)
          {
            _M_put_node(__node);
            __throw_exception_again;
          }
      }

      _Link_type
      _M_create_node(const value_type& __x)
      {
        _Link_type __tmp = _M_get_node();
        _M_construct_node(__tmp, __x);
        return __tmp;
      }

      void
      _M_destroy_node(_Link_type __p)
      { get_allocator().destroy(__p->_M_valptr()); }
#else
      template<typename... _Args>
        void
        _M_construct_node(_Link_type __node, _Args&&... __args)
        {
          __try
            {
              ::new(__node) _Rb_tree_node<_Val>;
              _Alloc_traits::construct(_M_get_Node_allocator(),
                                       __node->_M_valptr(),
                                       std::forward<_Args>(__args)...);
            }
          __catch(...)
            {
              __node->~_Rb_tree_node<_Val>();
              _M_put_node(__node);
              __throw_exception_again;
            }
        }

      template<typename... _Args>
        _Link_type
        _M_create_node(_Args&&... __args)
        {
          _Link_type __tmp = _M_get_node();
          _M_construct_node(__tmp, std::forward<_Args>(__args)...);
          return __tmp;
        }

      void
      _M_destroy_node(_Link_type __p) noexcept
      {
        _Alloc_traits::destroy(_M_get_Node_allocator(), __p->_M_valptr());
        __p->~_Rb_tree_node<_Val>();
      }
#endif

      void
      _M_drop_node(_Link_type __p) _GLIBCXX_NOEXCEPT
      {
        _M_destroy_node(__p);
        _M_put_node(__p);
      }

      template<typename _NodeGen>
        _Link_type
        _M_clone_node(_Const_Link_type __x, _NodeGen& __node_gen)
        {
          _Link_type __tmp = __node_gen(*__x->_M_valptr());
          __tmp->_M_color = __x->_M_color;
          __tmp->_M_left = 0;
          __tmp->_M_right = 0;
          return __tmp;
        }

    protected:
#if _GLIBCXX_INLINE_VERSION
      template<typename _Key_compare>
#else
      // Unused _Is_pod_comparator is kept as it is part of mangled name.
      template<typename _Key_compare,
               bool /* _Is_pod_comparator */ = __is_pod(_Key_compare)>
#endif
        struct _Rb_tree_impl
        : public _Node_allocator
        , public _Rb_tree_key_compare<_Key_compare>
        , public _Rb_tree_header
        {
          typedef _Rb_tree_key_compare<_Key_compare> _Base_key_compare;

          _Rb_tree_impl()
            _GLIBCXX_NOEXCEPT_IF(
                is_nothrow_default_constructible<_Node_allocator>::value
                && is_nothrow_default_constructible<_Base_key_compare>::value )
          : _Node_allocator()
          { }

          _Rb_tree_impl(const _Rb_tree_impl& __x)
          : _Node_allocator(_Alloc_traits::_S_select_on_copy(__x))
          , _Base_key_compare(__x._M_key_compare)
          { }

#if __cplusplus < 201103L
          _Rb_tree_impl(const _Key_compare& __comp, const _Node_allocator& __a)
          : _Node_allocator(__a), _Base_key_compare(__comp)
          { }
#else
          _Rb_tree_impl(_Rb_tree_impl&&) = default;

          _Rb_tree_impl(const _Key_compare& __comp, _Node_allocator&& __a)
          : _Node_allocator(std::move(__a)), _Base_key_compare(__comp)
          { }
#endif
        };

      _Rb_tree_impl<_Compare> _M_impl;

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

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

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

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

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

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

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

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

      _Base_ptr
      _M_end() _GLIBCXX_NOEXCEPT
      { return &this->_M_impl._M_header; }

      _Const_Base_ptr
      _M_end() const _GLIBCXX_NOEXCEPT
      { return &this->_M_impl._M_header; }

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

      static const _Key&
      _S_key(_Const_Link_type __x)
      {
#if __cplusplus >= 201103L
        // If we're asking for the key we're presumably using the comparison
        // object, and so this is a good place to sanity check it.
        static_assert(__is_invocable<_Compare&, const _Key&, const _Key&>{},
                      "comparison object must be invocable "
                      "with two arguments of key type");
# if __cplusplus >= 201703L
        // _GLIBCXX_RESOLVE_LIB_DEFECTS
        // 2542. Missing const requirements for associative containers
        if constexpr (__is_invocable<_Compare&, const _Key&, const _Key&>{})
          static_assert(
              is_invocable_v<const _Compare&, const _Key&, const _Key&>,
              "comparison object must be invocable as const");
# endif // C++17
#endif // C++11

        return _KeyOfValue()(*__x->_M_valptr());
      }

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

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

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

      static _Const_Link_type
      _S_right(_Const_Base_ptr __x) _GLIBCXX_NOEXCEPT
      { 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_valptr(); }

      static const _Key&
      _S_key(_Const_Base_ptr __x)
      { return _S_key(static_cast<_Const_Link_type>(__x)); }

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

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

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

      static _Const_Base_ptr
      _S_maximum(_Const_Base_ptr __x) _GLIBCXX_NOEXCEPT
      { 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;

#if __cplusplus > 201402L
      using node_type = _Node_handle<_Key, _Val, _Node_allocator>;
      using insert_return_type = _Node_insert_return<
        conditional_t<is_same_v<_Key, _Val>, const_iterator, iterator>,
        node_type>;
#endif

      pair<_Base_ptr, _Base_ptr>
      _M_get_insert_unique_pos(const key_type& __k);

      pair<_Base_ptr, _Base_ptr>
      _M_get_insert_equal_pos(const key_type& __k);

      pair<_Base_ptr, _Base_ptr>
      _M_get_insert_hint_unique_pos(const_iterator __pos,
                                    const key_type& __k);

      pair<_Base_ptr, _Base_ptr>
      _M_get_insert_hint_equal_pos(const_iterator __pos,
                                   const key_type& __k);

    private:
#if __cplusplus >= 201103L
      template<typename _Arg, typename _NodeGen>
        iterator
        _M_insert_(_Base_ptr __x, _Base_ptr __y, _Arg&& __v, _NodeGen&);

      iterator
      _M_insert_node(_Base_ptr __x, _Base_ptr __y, _Link_type __z);

      template<typename _Arg>
        iterator
        _M_insert_lower(_Base_ptr __y, _Arg&& __v);

      template<typename _Arg>
        iterator
        _M_insert_equal_lower(_Arg&& __x);

      iterator
      _M_insert_lower_node(_Base_ptr __p, _Link_type __z);

      iterator
      _M_insert_equal_lower_node(_Link_type __z);
#else
      template<typename _NodeGen>
        iterator
        _M_insert_(_Base_ptr __x, _Base_ptr __y,
                   const value_type& __v, _NodeGen&);

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

      iterator
      _M_insert_equal_lower(const value_type& __x);
#endif

      template<typename _NodeGen>
        _Link_type
        _M_copy(_Const_Link_type __x, _Base_ptr __p, _NodeGen&);

      template<typename _NodeGen>
        _Link_type
        _M_copy(const _Rb_tree& __x, _NodeGen& __gen)
        {
          _Link_type __root = _M_copy(__x._M_begin(), _M_end(), __gen);
          _M_leftmost() = _S_minimum(__root);
          _M_rightmost() = _S_maximum(__root);
          _M_impl._M_node_count = __x._M_impl._M_node_count;
          return __root;
        }

      _Link_type
      _M_copy(const _Rb_tree& __x)
      {
        _Alloc_node __an(*this);
        return _M_copy(__x, __an);
      }

      void
      _M_erase(_Link_type __x);

      iterator
      _M_lower_bound(_Link_type __x, _Base_ptr __y,
                     const _Key& __k);

      const_iterator
      _M_lower_bound(_Const_Link_type __x, _Const_Base_ptr __y,
                     const _Key& __k) const;

      iterator
      _M_upper_bound(_Link_type __x, _Base_ptr __y,
                     const _Key& __k);

      const_iterator
      _M_upper_bound(_Const_Link_type __x, _Const_Base_ptr __y,
                     const _Key& __k) const;

    public:
      // allocation/deallocation
#if __cplusplus < 201103L
      _Rb_tree() { }
#else
      _Rb_tree() = default;
#endif

      _Rb_tree(const _Compare& __comp,
               const allocator_type& __a = allocator_type())
      : _M_impl(__comp, _Node_allocator(__a)) { }

      _Rb_tree(const _Rb_tree& __x)
      : _M_impl(__x._M_impl)
      {
        if (__x._M_root() != 0)
          _M_root() = _M_copy(__x);
      }

#if __cplusplus >= 201103L
      _Rb_tree(const allocator_type& __a)
      : _M_impl(_Compare(), _Node_allocator(__a))
      { }

      _Rb_tree(const _Rb_tree& __x, const allocator_type& __a)
      : _M_impl(__x._M_impl._M_key_compare, _Node_allocator(__a))
      {
        if (__x._M_root() != nullptr)
          _M_root() = _M_copy(__x);
      }

      _Rb_tree(_Rb_tree&&) = default;

      _Rb_tree(_Rb_tree&& __x, const allocator_type& __a)
      : _Rb_tree(std::move(__x), _Node_allocator(__a))
      { }

      _Rb_tree(_Rb_tree&& __x, _Node_allocator&& __a);
#endif

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

      _Rb_tree&
      operator=(const _Rb_tree& __x);

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

      iterator
      begin() _GLIBCXX_NOEXCEPT
      { return iterator(this->_M_impl._M_header._M_left); }

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

      iterator
      end() _GLIBCXX_NOEXCEPT
      { return iterator(&this->_M_impl._M_header); }

      const_iterator
      end() const _GLIBCXX_NOEXCEPT
      { return const_iterator(&this->_M_impl._M_header); }

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

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

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

      const_reverse_iterator
      rend() const _GLIBCXX_NOEXCEPT
      { return const_reverse_iterator(begin()); }

      bool
      empty() const _GLIBCXX_NOEXCEPT
      { return _M_impl._M_node_count == 0; }

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

      size_type
      max_size() const _GLIBCXX_NOEXCEPT
      { return _Alloc_traits::max_size(_M_get_Node_allocator()); }

      void
      swap(_Rb_tree& __t)
      _GLIBCXX_NOEXCEPT_IF(__is_nothrow_swappable<_Compare>::value);

      // Insert/erase.
#if __cplusplus >= 201103L
      template<typename _Arg>
        pair<iterator, bool>
        _M_insert_unique(_Arg&& __x);

      template<typename _Arg>
        iterator
        _M_insert_equal(_Arg&& __x);

      template<typename _Arg, typename _NodeGen>
        iterator
        _M_insert_unique_(const_iterator __pos, _Arg&& __x, _NodeGen&);

      template<typename _Arg>
        iterator
        _M_insert_unique_(const_iterator __pos, _Arg&& __x)
        {
          _Alloc_node __an(*this);
          return _M_insert_unique_(__pos, std::forward<_Arg>(__x), __an);
        }

      template<typename _Arg, typename _NodeGen>
        iterator
        _M_insert_equal_(const_iterator __pos, _Arg&& __x, _NodeGen&);

      template<typename _Arg>
        iterator
        _M_insert_equal_(const_iterator __pos, _Arg&& __x)
        {
          _Alloc_node __an(*this);
          return _M_insert_equal_(__pos, std::forward<_Arg>(__x), __an);
        }

      template<typename... _Args>
        pair<iterator, bool>
        _M_emplace_unique(_Args&&... __args);

      template<typename... _Args>
        iterator
        _M_emplace_equal(_Args&&... __args);

      template<typename... _Args>
        iterator
        _M_emplace_hint_unique(const_iterator __pos, _Args&&... __args);

      template<typename... _Args>
        iterator
        _M_emplace_hint_equal(const_iterator __pos, _Args&&... __args);
#else
      pair<iterator, bool>
      _M_insert_unique(const value_type& __x);

      iterator
      _M_insert_equal(const value_type& __x);

      template<typename _NodeGen>
        iterator
        _M_insert_unique_(const_iterator __pos, const value_type& __x,
                          _NodeGen&);

      iterator
      _M_insert_unique_(const_iterator __pos, const value_type& __x)
      {
        _Alloc_node __an(*this);
        return _M_insert_unique_(__pos, __x, __an);
      }

      template<typename _NodeGen>
        iterator
        _M_insert_equal_(const_iterator __pos, const value_type& __x,
                         _NodeGen&);
      iterator
      _M_insert_equal_(const_iterator __pos, const value_type& __x)
      {
        _Alloc_node __an(*this);
        return _M_insert_equal_(__pos, __x, __an);
      }
#endif

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

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

    private:
      void
      _M_erase_aux(const_iterator __position);

      void
      _M_erase_aux(const_iterator __first, const_iterator __last);

    public:
#if __cplusplus >= 201103L
      // _GLIBCXX_RESOLVE_LIB_DEFECTS
      // DR 130. Associative erase should return an iterator.
      _GLIBCXX_ABI_TAG_CXX11
      iterator
      erase(const_iterator __position)
      {
        __glibcxx_assert(__position != end());
        const_iterator __result = __position;
        ++__result;
        _M_erase_aux(__position);
        return __result._M_const_cast();
      }

      // LWG 2059.
      _GLIBCXX_ABI_TAG_CXX11
      iterator
      erase(iterator __position)
      {
        __glibcxx_assert(__position != end());
        iterator __result = __position;
        ++__result;
        _M_erase_aux(__position);
        return __result;
      }
#else
      void
      erase(iterator __position)
      {
        __glibcxx_assert(__position != end());
        _M_erase_aux(__position);
      }

      void
      erase(const_iterator __position)
      {
        __glibcxx_assert(__position != end());
        _M_erase_aux(__position);
      }
#endif
      size_type
      erase(const key_type& __x);

#if __cplusplus >= 201103L
      // _GLIBCXX_RESOLVE_LIB_DEFECTS
      // DR 130. Associative erase should return an iterator.
      _GLIBCXX_ABI_TAG_CXX11
      iterator
      erase(const_iterator __first, const_iterator __last)
      {
        _M_erase_aux(__first, __last);
        return __last._M_const_cast();
      }
#else
      void
      erase(iterator __first, iterator __last)
      { _M_erase_aux(__first, __last); }

      void
      erase(const_iterator __first, const_iterator __last)
      { _M_erase_aux(__first, __last); }
#endif
      void
      erase(const key_type* __first, const key_type* __last);

      void
      clear() _GLIBCXX_NOEXCEPT
      {
        _M_erase(_M_begin());
        _M_impl._M_reset();
      }

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

      const_iterator
      find(const key_type& __k) const;

      size_type
      count(const key_type& __k) const;

      iterator
      lower_bound(const key_type& __k)
      { return _M_lower_bound(_M_begin(), _M_end(), __k); }

      const_iterator
      lower_bound(const key_type& __k) const
      { return _M_lower_bound(_M_begin(), _M_end(), __k); }

      iterator
      upper_bound(const key_type& __k)
      { return _M_upper_bound(_M_begin(), _M_end(), __k); }

      const_iterator
      upper_bound(const key_type& __k) const
      { return _M_upper_bound(_M_begin(), _M_end(), __k); }

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

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

#if __cplusplus > 201103L
      template<typename _Kt,
               typename _Req =
                 typename __has_is_transparent<_Compare, _Kt>::type>
        iterator
        _M_find_tr(const _Kt& __k)
        {
          const _Rb_tree* __const_this = this;
          return __const_this->_M_find_tr(__k)._M_const_cast();
        }

      template<typename _Kt,
               typename _Req =
                 typename __has_is_transparent<_Compare, _Kt>::type>
        const_iterator
        _M_find_tr(const _Kt& __k) const
        {
          auto __j = _M_lower_bound_tr(__k);
          if (__j != end() && _M_impl._M_key_compare(__k, _S_key(__j._M_node)))
            __j = end();
          return __j;
        }

      template<typename _Kt,
               typename _Req =
                 typename __has_is_transparent<_Compare, _Kt>::type>
        size_type
        _M_count_tr(const _Kt& __k) const
        {
          auto __p = _M_equal_range_tr(__k);
          return std::distance(__p.first, __p.second);
        }

      template<typename _Kt,
               typename _Req =
                 typename __has_is_transparent<_Compare, _Kt>::type>
        iterator
        _M_lower_bound_tr(const _Kt& __k)
        {
          const _Rb_tree* __const_this = this;
          return __const_this->_M_lower_bound_tr(__k)._M_const_cast();
        }

      template<typename _Kt,
               typename _Req =
                 typename __has_is_transparent<_Compare, _Kt>::type>
        const_iterator
        _M_lower_bound_tr(const _Kt& __k) const
        {
          auto __x = _M_begin();
          auto __y = _M_end();
          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 _Kt,
               typename _Req =
                 typename __has_is_transparent<_Compare, _Kt>::type>
        iterator
        _M_upper_bound_tr(const _Kt& __k)
        {
          const _Rb_tree* __const_this = this;
          return __const_this->_M_upper_bound_tr(__k)._M_const_cast();
        }

      template<typename _Kt,
               typename _Req =
                 typename __has_is_transparent<_Compare, _Kt>::type>
        const_iterator
        _M_upper_bound_tr(const _Kt& __k) const
        {
          auto __x = _M_begin();
          auto __y = _M_end();
          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 _Kt,
               typename _Req =
                 typename __has_is_transparent<_Compare, _Kt>::type>
        pair<iterator, iterator>
        _M_equal_range_tr(const _Kt& __k)
        {
          const _Rb_tree* __const_this = this;
          auto __ret = __const_this->_M_equal_range_tr(__k);
          return { __ret.first._M_const_cast(), __ret.second._M_const_cast() };
        }

      template<typename _Kt,
               typename _Req =
                 typename __has_is_transparent<_Compare, _Kt>::type>
        pair<const_iterator, const_iterator>
        _M_equal_range_tr(const _Kt& __k) const
        {
          auto __low = _M_lower_bound_tr(__k);
          auto __high = __low;
          auto& __cmp = _M_impl._M_key_compare;
          while (__high != end() && !__cmp(__k, _S_key(__high._M_node)))
            ++__high;
          return { __low, __high };
        }
#endif

      // Debugging.
      bool
      __rb_verify() const;

#if __cplusplus >= 201103L
      _Rb_tree&
      operator=(_Rb_tree&&)
      noexcept(_Alloc_traits::_S_nothrow_move()
               && is_nothrow_move_assignable<_Compare>::value);

      template<typename _Iterator>
        void
        _M_assign_unique(_Iterator, _Iterator);

      template<typename _Iterator>
        void
        _M_assign_equal(_Iterator, _Iterator);

    private:
      // Move elements from container with equal allocator.
      void
      _M_move_data(_Rb_tree& __x, std::true_type)
      { _M_impl._M_move_data(__x._M_impl); }

      // Move elements from container with possibly non-equal allocator,
      // which might result in a copy not a move.
      void
      _M_move_data(_Rb_tree&, std::false_type);

      // Move assignment from container with equal allocator.
      void
      _M_move_assign(_Rb_tree&, std::true_type);

      // Move assignment from container with possibly non-equal allocator,
      // which might result in a copy not a move.
      void
      _M_move_assign(_Rb_tree&, std::false_type);
#endif

#if __cplusplus > 201402L
    public:
      /// Re-insert an extracted node.
      insert_return_type
      _M_reinsert_node_unique(node_type&& __nh)
      {
        insert_return_type __ret;
        if (__nh.empty())
          __ret.position = end();
        else
          {
            __glibcxx_assert(_M_get_Node_allocator() == *__nh._M_alloc);

            auto __res = _M_get_insert_unique_pos(__nh._M_key());
            if (__res.second)
              {
                __ret.position
                  = _M_insert_node(__res.first, __res.second, __nh._M_ptr);
                __nh._M_ptr = nullptr;
                __ret.inserted = true;
              }
            else
              {
                __ret.node = std::move(__nh);
                __ret.position = iterator(__res.first);
                __ret.inserted = false;
              }
          }
        return __ret;
      }

      /// Re-insert an extracted node.
      iterator
      _M_reinsert_node_equal(node_type&& __nh)
      {
        iterator __ret;
        if (__nh.empty())
          __ret = end();
        else
          {
            __glibcxx_assert(_M_get_Node_allocator() == *__nh._M_alloc);
            auto __res = _M_get_insert_equal_pos(__nh._M_key());
            if (__res.second)
              __ret = _M_insert_node(__res.first, __res.second, __nh._M_ptr);
            else
              __ret = _M_insert_equal_lower_node(__nh._M_ptr);
            __nh._M_ptr = nullptr;
          }
        return __ret;
      }

      /// Re-insert an extracted node.
      iterator
      _M_reinsert_node_hint_unique(const_iterator __hint, node_type&& __nh)
      {
        iterator __ret;
        if (__nh.empty())
          __ret = end();
        else
          {
            __glibcxx_assert(_M_get_Node_allocator() == *__nh._M_alloc);
            auto __res = _M_get_insert_hint_unique_pos(__hint, __nh._M_key());
            if (__res.second)
              {
                __ret = _M_insert_node(__res.first, __res.second, __nh._M_ptr);
                __nh._M_ptr = nullptr;
              }
            else
              __ret = iterator(__res.first);
          }
        return __ret;
      }

      /// Re-insert an extracted node.
      iterator
      _M_reinsert_node_hint_equal(const_iterator __hint, node_type&& __nh)
      {
        iterator __ret;
        if (__nh.empty())
          __ret = end();
        else
          {
            __glibcxx_assert(_M_get_Node_allocator() == *__nh._M_alloc);
            auto __res = _M_get_insert_hint_equal_pos(__hint, __nh._M_key());
            if (__res.second)
              __ret = _M_insert_node(__res.first, __res.second, __nh._M_ptr);
            else
              __ret = _M_insert_equal_lower_node(__nh._M_ptr);
            __nh._M_ptr = nullptr;
          }
        return __ret;
      }

      /// Extract a node.
      node_type
      extract(const_iterator __pos)
      {
        auto __ptr = _Rb_tree_rebalance_for_erase(
            __pos._M_const_cast()._M_node, _M_impl._M_header);
        --_M_impl._M_node_count;
        return { static_cast<_Link_type>(__ptr), _M_get_Node_allocator() };
      }

      /// Extract a node.
      node_type
      extract(const key_type& __k)
      {
        node_type __nh;
        auto __pos = find(__k);
        if (__pos != end())
          __nh = extract(const_iterator(__pos));
        return __nh;
      }

      template<typename _Compare2>
        using _Compatible_tree
          = _Rb_tree<_Key, _Val, _KeyOfValue, _Compare2, _Alloc>;

      template<typename, typename>
        friend class _Rb_tree_merge_helper;

      /// Merge from a compatible container into one with unique keys.
      template<typename _Compare2>
        void
        _M_merge_unique(_Compatible_tree<_Compare2>& __src) noexcept
        {
          using _Merge_helper = _Rb_tree_merge_helper<_Rb_tree, _Compare2>;
          for (auto __i = __src.begin(), __end = __src.end(); __i != __end;)
            {
              auto __pos = __i++;
              auto __res = _M_get_insert_unique_pos(_KeyOfValue()(*__pos));
              if (__res.second)
                {
                  auto& __src_impl = _Merge_helper::_S_get_impl(__src);
                  auto __ptr = _Rb_tree_rebalance_for_erase(
                      __pos._M_node, __src_impl._M_header);
                  --__src_impl._M_node_count;
                  _M_insert_node(__res.first, __res.second,
                                 static_cast<_Link_type>(__ptr));
                }
            }
        }

      /// Merge from a compatible container into one with equivalent keys.
      template<typename _Compare2>
        void
        _M_merge_equal(_Compatible_tree<_Compare2>& __src) noexcept
        {
          using _Merge_helper = _Rb_tree_merge_helper<_Rb_tree, _Compare2>;
          for (auto __i = __src.begin(), __end = __src.end(); __i != __end;)
            {
              auto __pos = __i++;
              auto __res = _M_get_insert_equal_pos(_KeyOfValue()(*__pos));
              if (__res.second)
                {
                  auto& __src_impl = _Merge_helper::_S_get_impl(__src);
                  auto __ptr = _Rb_tree_rebalance_for_erase(
                      __pos._M_node, __src_impl._M_header);
                  --__src_impl._M_node_count;
                  _M_insert_node(__res.first, __res.second,
                                 static_cast<_Link_type>(__ptr));
                }
            }
        }
#endif // C++17
    };

  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); }

#if __cplusplus >= 201103L
  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _Rb_tree(_Rb_tree&& __x, _Node_allocator&& __a)
    : _M_impl(__x._M_impl._M_key_compare, std::move(__a))
    {
      using __eq = typename _Alloc_traits::is_always_equal;
      if (__x._M_root() != nullptr)
        _M_move_data(__x, __eq());
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    void
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_move_data(_Rb_tree& __x, std::false_type)
    {
      if (_M_get_Node_allocator() == __x._M_get_Node_allocator())
        _M_move_data(__x, std::true_type());
      else
        {
          _Alloc_node __an(*this);
          auto __lbd =
            [&__an](const value_type& __cval)
            {
              auto& __val = const_cast<value_type&>(__cval);
              return __an(std::move_if_noexcept(__val));
            };
          _M_root() = _M_copy(__x, __lbd);
        }
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    inline void
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_move_assign(_Rb_tree& __x, true_type)
    {
      clear();
      if (__x._M_root() != nullptr)
        _M_move_data(__x, std::true_type());
      std::__alloc_on_move(_M_get_Node_allocator(),
                           __x._M_get_Node_allocator());
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    void
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_move_assign(_Rb_tree& __x, false_type)
    {
      if (_M_get_Node_allocator() == __x._M_get_Node_allocator())
        return _M_move_assign(__x, true_type{});

      // Try to move each node reusing existing nodes and copying __x nodes
      // structure.
      _Reuse_or_alloc_node __roan(*this);
      _M_impl._M_reset();
      if (__x._M_root() != nullptr)
        {
          auto __lbd =
            [&__roan](const value_type& __cval)
            {
              auto& __val = const_cast<value_type&>(__cval);
              return __roan(std::move_if_noexcept(__val));
            };
          _M_root() = _M_copy(__x, __lbd);
          __x.clear();
        }
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    inline _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>&
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    operator=(_Rb_tree&& __x)
    noexcept(_Alloc_traits::_S_nothrow_move()
             && is_nothrow_move_assignable<_Compare>::value)
    {
      _M_impl._M_key_compare = std::move(__x._M_impl._M_key_compare);
      _M_move_assign(__x, __bool_constant<_Alloc_traits::_S_nothrow_move()>());
      return *this;
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    template<typename _Iterator>
      void
      _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
      _M_assign_unique(_Iterator __first, _Iterator __last)
      {
        _Reuse_or_alloc_node __roan(*this);
        _M_impl._M_reset();
        for (; __first != __last; ++__first)
          _M_insert_unique_(end(), *__first, __roan);
      }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    template<typename _Iterator>
      void
      _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
      _M_assign_equal(_Iterator __first, _Iterator __last)
      {
        _Reuse_or_alloc_node __roan(*this);
        _M_impl._M_reset();
        for (; __first != __last; ++__first)
          _M_insert_equal_(end(), *__first, __roan);
      }
#endif

  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& __x)
    {
      if (this != &__x)
        {
          // Note that _Key may be a constant type.
#if __cplusplus >= 201103L
          if (_Alloc_traits::_S_propagate_on_copy_assign())
            {
              auto& __this_alloc = this->_M_get_Node_allocator();
              auto& __that_alloc = __x._M_get_Node_allocator();
              if (!_Alloc_traits::_S_always_equal()
                  && __this_alloc != __that_alloc)
                {
                  // Replacement allocator cannot free existing storage, we need
                  // to erase nodes first.
                  clear();
                  std::__alloc_on_copy(__this_alloc, __that_alloc);
                }
            }
#endif

          _Reuse_or_alloc_node __roan(*this);
          _M_impl._M_reset();
          _M_impl._M_key_compare = __x._M_impl._M_key_compare;
          if (__x._M_root() != 0)
            _M_root() = _M_copy(__x, __roan);
        }

      return *this;
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
#if __cplusplus >= 201103L
    template<typename _Arg, typename _NodeGen>
#else
    template<typename _NodeGen>
#endif
      typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
      _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
      _M_insert_(_Base_ptr __x, _Base_ptr __p,
#if __cplusplus >= 201103L
                 _Arg&& __v,
#else
                 const _Val& __v,
#endif
                 _NodeGen& __node_gen)
      {
        bool __insert_left = (__x != 0 || __p == _M_end()
                              || _M_impl._M_key_compare(_KeyOfValue()(__v),
                                                        _S_key(__p)));

        _Link_type __z = __node_gen(_GLIBCXX_FORWARD(_Arg, __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>
#if __cplusplus >= 201103L
    template<typename _Arg>
#endif
    typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
#if __cplusplus >= 201103L
    _M_insert_lower(_Base_ptr __p, _Arg&& __v)
#else
    _M_insert_lower(_Base_ptr __p, const _Val& __v)
#endif
    {
      bool __insert_left = (__p == _M_end()
                            || !_M_impl._M_key_compare(_S_key(__p),
                                                       _KeyOfValue()(__v)));

      _Link_type __z = _M_create_node(_GLIBCXX_FORWARD(_Arg, __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>
#if __cplusplus >= 201103L
    template<typename _Arg>
#endif
    typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
#if __cplusplus >= 201103L
    _M_insert_equal_lower(_Arg&& __v)
#else
    _M_insert_equal_lower(const _Val& __v)
#endif
    {
      _Link_type __x = _M_begin();
      _Base_ptr __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(__y, _GLIBCXX_FORWARD(_Arg, __v));
    }

  template<typename _Key, typename _Val, typename _KoV,
           typename _Compare, typename _Alloc>
    template<typename _NodeGen>
      typename _Rb_tree<_Key, _Val, _KoV, _Compare, _Alloc>::_Link_type
      _Rb_tree<_Key, _Val, _KoV, _Compare, _Alloc>::
      _M_copy(_Const_Link_type __x, _Base_ptr __p, _NodeGen& __node_gen)
      {
        // Structural copy. __x and __p must be non-null.
        _Link_type __top = _M_clone_node(__x, __node_gen);
        __top->_M_parent = __p;

        __try
          {
            if (__x->_M_right)
              __top->_M_right = _M_copy(_S_right(__x), __top, __node_gen);
            __p = __top;
            __x = _S_left(__x);

            while (__x != 0)
              {
                _Link_type __y = _M_clone_node(__x, __node_gen);
                __p->_M_left = __y;
                __y->_M_parent = __p;
                if (__x->_M_right)
                  __y->_M_right = _M_copy(_S_right(__x), __y, __node_gen);
                __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_drop_node(__x);
          __x = __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>::
    _M_lower_bound(_Link_type __x, _Base_ptr __y,
                   const _Key& __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>::
    _M_lower_bound(_Const_Link_type __x, _Const_Base_ptr __y,
                   const _Key& __k) const
    {
      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>::
    _M_upper_bound(_Link_type __x, _Base_ptr __y,
                   const _Key& __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>::
    _M_upper_bound(_Const_Link_type __x, _Const_Base_ptr __y,
                   const _Key& __k) const
    {
      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>
    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)
    {
      _Link_type __x = _M_begin();
      _Base_ptr __y = _M_end();
      while (__x != 0)
        {
          if (_M_impl._M_key_compare(_S_key(__x), __k))
            __x = _S_right(__x);
          else if (_M_impl._M_key_compare(__k, _S_key(__x)))
            __y = __x, __x = _S_left(__x);
          else
            {
              _Link_type __xu(__x);
              _Base_ptr __yu(__y);
              __y = __x, __x = _S_left(__x);
              __xu = _S_right(__xu);
              return pair<iterator,
                          iterator>(_M_lower_bound(__x, __y, __k),
                                    _M_upper_bound(__xu, __yu, __k));
            }
        }
      return pair<iterator, iterator>(iterator(__y),
                                      iterator(__y));
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    pair<typename _Rb_tree<_Key, _Val, _KeyOfValue,
                           _Compare, _Alloc>::const_iterator,
         typename _Rb_tree<_Key, _Val, _KeyOfValue,
                           _Compare, _Alloc>::const_iterator>
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    equal_range(const _Key& __k) const
    {
      _Const_Link_type __x = _M_begin();
      _Const_Base_ptr __y = _M_end();
      while (__x != 0)
        {
          if (_M_impl._M_key_compare(_S_key(__x), __k))
            __x = _S_right(__x);
          else if (_M_impl._M_key_compare(__k, _S_key(__x)))
            __y = __x, __x = _S_left(__x);
          else
            {
              _Const_Link_type __xu(__x);
              _Const_Base_ptr __yu(__y);
              __y = __x, __x = _S_left(__x);
              __xu = _S_right(__xu);
              return pair<const_iterator,
                          const_iterator>(_M_lower_bound(__x, __y, __k),
                                          _M_upper_bound(__xu, __yu, __k));
            }
        }
      return pair<const_iterator, const_iterator>(const_iterator(__y),
                                                  const_iterator(__y));
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    void
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    swap(_Rb_tree& __t)
    _GLIBCXX_NOEXCEPT_IF(__is_nothrow_swappable<_Compare>::value)
    {
      if (_M_root() == 0)
        {
          if (__t._M_root() != 0)
            _M_impl._M_move_data(__t._M_impl);
        }
      else if (__t._M_root() == 0)
        __t._M_impl._M_move_data(_M_impl);
      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();
          std::swap(this->_M_impl._M_node_count, __t._M_impl._M_node_count);
        }
      // No need to swap header's color as it does not change.
      std::swap(this->_M_impl._M_key_compare, __t._M_impl._M_key_compare);

      _Alloc_traits::_S_on_swap(_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>::_Base_ptr,
         typename _Rb_tree<_Key, _Val, _KeyOfValue,
                           _Compare, _Alloc>::_Base_ptr>
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_get_insert_unique_pos(const key_type& __k)
    {
      typedef pair<_Base_ptr, _Base_ptr> _Res;
      _Link_type __x = _M_begin();
      _Base_ptr __y = _M_end();
      bool __comp = true;
      while (__x != 0)
        {
          __y = __x;
          __comp = _M_impl._M_key_compare(__k, _S_key(__x));
          __x = __comp ? _S_left(__x) : _S_right(__x);
        }
      iterator __j = iterator(__y);
      if (__comp)
        {
          if (__j == begin())
            return _Res(__x, __y);
          else
            --__j;
        }
      if (_M_impl._M_key_compare(_S_key(__j._M_node), __k))
        return _Res(__x, __y);
      return _Res(__j._M_node, 0);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    pair<typename _Rb_tree<_Key, _Val, _KeyOfValue,
                           _Compare, _Alloc>::_Base_ptr,
         typename _Rb_tree<_Key, _Val, _KeyOfValue,
                           _Compare, _Alloc>::_Base_ptr>
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_get_insert_equal_pos(const key_type& __k)
    {
      typedef pair<_Base_ptr, _Base_ptr> _Res;
      _Link_type __x = _M_begin();
      _Base_ptr __y = _M_end();
      while (__x != 0)
        {
          __y = __x;
          __x = _M_impl._M_key_compare(__k, _S_key(__x)) ?
                _S_left(__x) : _S_right(__x);
        }
      return _Res(__x, __y);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
#if __cplusplus >= 201103L
    template<typename _Arg>
#endif
    pair<typename _Rb_tree<_Key, _Val, _KeyOfValue,
                           _Compare, _Alloc>::iterator, bool>
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
#if __cplusplus >= 201103L
    _M_insert_unique(_Arg&& __v)
#else
    _M_insert_unique(const _Val& __v)
#endif
    {
      typedef pair<iterator, bool> _Res;
      pair<_Base_ptr, _Base_ptr> __res
        = _M_get_insert_unique_pos(_KeyOfValue()(__v));

      if (__res.second)
        {
          _Alloc_node __an(*this);
          return _Res(_M_insert_(__res.first, __res.second,
                                 _GLIBCXX_FORWARD(_Arg, __v), __an),
                      true);
        }

      return _Res(iterator(__res.first), false);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
#if __cplusplus >= 201103L
    template<typename _Arg>
#endif
    typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
#if __cplusplus >= 201103L
    _M_insert_equal(_Arg&& __v)
#else
    _M_insert_equal(const _Val& __v)
#endif
    {
      pair<_Base_ptr, _Base_ptr> __res
        = _M_get_insert_equal_pos(_KeyOfValue()(__v));
      _Alloc_node __an(*this);
      return _M_insert_(__res.first, __res.second,
                        _GLIBCXX_FORWARD(_Arg, __v), __an);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    pair<typename _Rb_tree<_Key, _Val, _KeyOfValue,
                           _Compare, _Alloc>::_Base_ptr,
         typename _Rb_tree<_Key, _Val, _KeyOfValue,
                           _Compare, _Alloc>::_Base_ptr>
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_get_insert_hint_unique_pos(const_iterator __position,
                                  const key_type& __k)
    {
      iterator __pos = __position._M_const_cast();
      typedef pair<_Base_ptr, _Base_ptr> _Res;

      // end()
      if (__pos._M_node == _M_end())
        {
          if (size() > 0
              && _M_impl._M_key_compare(_S_key(_M_rightmost()), __k))
            return _Res(0, _M_rightmost());
          else
            return _M_get_insert_unique_pos(__k);
        }
      else if (_M_impl._M_key_compare(__k, _S_key(__pos._M_node)))
        {
          // First, try before...
          iterator __before = __pos;
          if (__pos._M_node == _M_leftmost()) // begin()
            return _Res(_M_leftmost(), _M_leftmost());
          else if (_M_impl._M_key_compare(_S_key((--__before)._M_node), __k))
            {
              if (_S_right(__before._M_node) == 0)
                return _Res(0, __before._M_node);
              else
                return _Res(__pos._M_node, __pos._M_node);
            }
          else
            return _M_get_insert_unique_pos(__k);
        }
      else if (_M_impl._M_key_compare(_S_key(__pos._M_node), __k))
        {
          // ... then try after.
          iterator __after = __pos;
          if (__pos._M_node == _M_rightmost())
            return _Res(0, _M_rightmost());
          else if (_M_impl._M_key_compare(__k, _S_key((++__after)._M_node)))
            {
              if (_S_right(__pos._M_node) == 0)
                return _Res(0, __pos._M_node);
              else
                return _Res(__after._M_node, __after._M_node);
            }
          else
            return _M_get_insert_unique_pos(__k);
        }
      else
        // Equivalent keys.
        return _Res(__pos._M_node, 0);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
#if __cplusplus >= 201103L
    template<typename _Arg, typename _NodeGen>
#else
    template<typename _NodeGen>
#endif
      typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
      _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
      _M_insert_unique_(const_iterator __position,
#if __cplusplus >= 201103L
                        _Arg&& __v,
#else
                        const _Val& __v,
#endif
                        _NodeGen& __node_gen)
    {
      pair<_Base_ptr, _Base_ptr> __res
        = _M_get_insert_hint_unique_pos(__position, _KeyOfValue()(__v));

      if (__res.second)
        return _M_insert_(__res.first, __res.second,
                          _GLIBCXX_FORWARD(_Arg, __v),
                          __node_gen);
      return iterator(__res.first);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    pair<typename _Rb_tree<_Key, _Val, _KeyOfValue,
                           _Compare, _Alloc>::_Base_ptr,
         typename _Rb_tree<_Key, _Val, _KeyOfValue,
                           _Compare, _Alloc>::_Base_ptr>
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_get_insert_hint_equal_pos(const_iterator __position, const key_type& __k)
    {
      iterator __pos = __position._M_const_cast();
      typedef pair<_Base_ptr, _Base_ptr> _Res;

      // end()
      if (__pos._M_node == _M_end())
        {
          if (size() > 0
              && !_M_impl._M_key_compare(__k, _S_key(_M_rightmost())))
            return _Res(0, _M_rightmost());
          else
            return _M_get_insert_equal_pos(__k);
        }
      else if (!_M_impl._M_key_compare(_S_key(__pos._M_node), __k))
        {
          // First, try before...
          iterator __before = __pos;
          if (__pos._M_node == _M_leftmost()) // begin()
            return _Res(_M_leftmost(), _M_leftmost());
          else if (!_M_impl._M_key_compare(__k, _S_key((--__before)._M_node)))
            {
              if (_S_right(__before._M_node) == 0)
                return _Res(0, __before._M_node);
              else
                return _Res(__pos._M_node, __pos._M_node);
            }
          else
            return _M_get_insert_equal_pos(__k);
        }
      else
        {
          // ... then try after.
          iterator __after = __pos;
          if (__pos._M_node == _M_rightmost())
            return _Res(0, _M_rightmost());
          else if (!_M_impl._M_key_compare(_S_key((++__after)._M_node), __k))
            {
              if (_S_right(__pos._M_node) == 0)
                return _Res(0, __pos._M_node);
              else
                return _Res(__after._M_node, __after._M_node);
            }
          else
            return _Res(0, 0);
        }
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
#if __cplusplus >= 201103L
    template<typename _Arg, typename _NodeGen>
#else
    template<typename _NodeGen>
#endif
      typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
      _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
      _M_insert_equal_(const_iterator __position,
#if __cplusplus >= 201103L
                       _Arg&& __v,
#else
                       const _Val& __v,
#endif
                       _NodeGen& __node_gen)
      {
        pair<_Base_ptr, _Base_ptr> __res
          = _M_get_insert_hint_equal_pos(__position, _KeyOfValue()(__v));

        if (__res.second)
          return _M_insert_(__res.first, __res.second,
                            _GLIBCXX_FORWARD(_Arg, __v),
                            __node_gen);

        return _M_insert_equal_lower(_GLIBCXX_FORWARD(_Arg, __v));
      }

#if __cplusplus >= 201103L
  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_node(_Base_ptr __x, _Base_ptr __p, _Link_type __z)
    {
      bool __insert_left = (__x != 0 || __p == _M_end()
                            || _M_impl._M_key_compare(_S_key(__z),
                                                      _S_key(__p)));

      _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_node(_Base_ptr __p, _Link_type __z)
    {
      bool __insert_left = (__p == _M_end()
                            || !_M_impl._M_key_compare(_S_key(__p),
                                                       _S_key(__z)));

      _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_equal_lower_node(_Link_type __z)
    {
      _Link_type __x = _M_begin();
      _Base_ptr __y = _M_end();
      while (__x != 0)
        {
          __y = __x;
          __x = !_M_impl._M_key_compare(_S_key(__x), _S_key(__z)) ?
                _S_left(__x) : _S_right(__x);
        }
      return _M_insert_lower_node(__y, __z);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    template<typename... _Args>
      pair<typename _Rb_tree<_Key, _Val, _KeyOfValue,
                             _Compare, _Alloc>::iterator, bool>
      _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
      _M_emplace_unique(_Args&&... __args)
      {
        _Link_type __z = _M_create_node(std::forward<_Args>(__args)...);

        __try
          {
            typedef pair<iterator, bool> _Res;
            auto __res = _M_get_insert_unique_pos(_S_key(__z));
            if (__res.second)
              return _Res(_M_insert_node(__res.first, __res.second, __z), true);
        
            _M_drop_node(__z);
            return _Res(iterator(__res.first), false);
          }
        __catch(...)
          {
            _M_drop_node(__z);
            __throw_exception_again;
          }
      }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    template<typename... _Args>
      typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
      _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
      _M_emplace_equal(_Args&&... __args)
      {
        _Link_type __z = _M_create_node(std::forward<_Args>(__args)...);

        __try
          {
            auto __res = _M_get_insert_equal_pos(_S_key(__z));
            return _M_insert_node(__res.first, __res.second, __z);
          }
        __catch(...)
          {
            _M_drop_node(__z);
            __throw_exception_again;
          }
      }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    template<typename... _Args>
      typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
      _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
      _M_emplace_hint_unique(const_iterator __pos, _Args&&... __args)
      {
        _Link_type __z = _M_create_node(std::forward<_Args>(__args)...);

        __try
          {
            auto __res = _M_get_insert_hint_unique_pos(__pos, _S_key(__z));

            if (__res.second)
              return _M_insert_node(__res.first, __res.second, __z);

            _M_drop_node(__z);
            return iterator(__res.first);
          }
        __catch(...)
          {
            _M_drop_node(__z);
            __throw_exception_again;
          }
      }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    template<typename... _Args>
      typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
      _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
      _M_emplace_hint_equal(const_iterator __pos, _Args&&... __args)
      {
        _Link_type __z = _M_create_node(std::forward<_Args>(__args)...);

        __try
          {
            auto __res = _M_get_insert_hint_equal_pos(__pos, _S_key(__z));

            if (__res.second)
              return _M_insert_node(__res.first, __res.second, __z);

            return _M_insert_equal_lower_node(__z);
          }
        __catch(...)
          {
            _M_drop_node(__z);
            __throw_exception_again;
          }
      }
#endif

  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)
      {
        _Alloc_node __an(*this);
        for (; __first != __last; ++__first)
          _M_insert_unique_(end(), *__first, __an);
      }

  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)
      {
        _Alloc_node __an(*this);
        for (; __first != __last; ++__first)
          _M_insert_equal_(end(), *__first, __an);
      }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    void
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_erase_aux(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_drop_node(__y);
      --_M_impl._M_node_count;
    }

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

  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();
      _M_erase_aux(__p.first, __p.second);
      return __old_size - size();
    }

  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)
    {
      iterator __j = _M_lower_bound(_M_begin(), _M_end(), __k);
      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_iterator __j = _M_lower_bound(_M_begin(), _M_end(), __k);
      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;
    }

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

  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;
    }

#if __cplusplus > 201402L
  // Allow access to internals of compatible _Rb_tree specializations.
  template<typename _Key, typename _Val, typename _Sel, typename _Cmp1,
           typename _Alloc, typename _Cmp2>
    struct _Rb_tree_merge_helper<_Rb_tree<_Key, _Val, _Sel, _Cmp1, _Alloc>,
                                 _Cmp2>
    {
    private:
      friend class _Rb_tree<_Key, _Val, _Sel, _Cmp1, _Alloc>;

      static auto&
      _S_get_impl(_Rb_tree<_Key, _Val, _Sel, _Cmp2, _Alloc>& __tree)
      { return __tree._M_impl; }
    };
#endif // C++17

_GLIBCXX_END_NAMESPACE_VERSION
} // namespace

#endif