pat_trie_base.hpp

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// -*- C++ -*-

// Copyright (C) 2005-2018 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) 2004 Ami Tavory and Vladimir Dreizin, IBM-HRL.

// Permission to use, copy, modify, sell, and distribute this software
// is hereby granted without fee, provided that the above copyright
// notice appears in all copies, and that both that copyright notice
// and this permission notice appear in supporting documentation. None
// of the above authors, nor IBM Haifa Research Laboratories, make any
// representation about the suitability of this software for any
// purpose. It is provided "as is" without express or implied
// warranty.

/**
 * @file pat_trie_/pat_trie_base.hpp
 * Contains the base class for a patricia tree.
 */

#ifndef PB_DS_PAT_TRIE_BASE
#define PB_DS_PAT_TRIE_BASE

#include <debug/debug.h>

namespace __gnu_pbds
{
  namespace detail
  {
    /// Base type for PATRICIA trees.
    struct pat_trie_base
    {
      /**
       *  @brief  Three types of nodes.
       *
       *  i_node is used by _Inode, leaf_node by _Leaf, and head_node by _Head.
       */
      enum node_type
        {
          i_node,
          leaf_node,
          head_node
        };

      /// Metadata base primary template.
      template<typename Metadata, typename _Alloc>
        struct _Metadata
        {
          typedef Metadata                                      metadata_type;
          typedef _Alloc                                        allocator_type;
          typedef typename _Alloc::template rebind<Metadata>    __rebind_m;
          typedef typename __rebind_m::other::const_reference  const_reference;

          const_reference
          get_metadata() const
          { return m_metadata; }

          metadata_type                                         m_metadata;
        };

      /// Specialization for null metadata.
      template<typename _Alloc>
        struct _Metadata<null_type, _Alloc>
        {
          typedef null_type                                     metadata_type;
          typedef _Alloc                                        allocator_type;
        };


      /// Node base.
      template<typename _ATraits, typename Metadata>
      struct _Node_base
      : public Metadata
      {
      private:
        typedef typename Metadata::allocator_type               _Alloc;

      public:
        typedef _Alloc                                          allocator_type;
        typedef _ATraits                                        access_traits;
        typedef typename _ATraits::type_traits                  type_traits;
        typedef typename _Alloc::template rebind<_Node_base>    __rebind_n;
        typedef typename __rebind_n::other::pointer             node_pointer;

        node_pointer                                            m_p_parent;
        const node_type                                         m_type;

        _Node_base(node_type type) : m_type(type)
        { }

        typedef typename _Alloc::template rebind<_ATraits>    __rebind_at;
        typedef typename __rebind_at::other::const_pointer    a_const_pointer;
        typedef typename _ATraits::const_iterator             a_const_iterator;

#ifdef _GLIBCXX_DEBUG
        typedef std::pair<a_const_iterator, a_const_iterator> node_debug_info;

        void
        assert_valid(a_const_pointer p_traits,
                     const char* __file, int __line) const
        { assert_valid_imp(p_traits, __file, __line); }

        virtual node_debug_info
        assert_valid_imp(a_const_pointer, const char*, int) const = 0;
#endif
      };


    /// Head node for PATRICIA tree.
    template<typename _ATraits, typename Metadata>
    struct _Head
    : public _Node_base<_ATraits, Metadata>
    {
      typedef _Node_base<_ATraits, Metadata>                    base_type;
      typedef typename base_type::type_traits                   type_traits;
      typedef typename base_type::node_pointer                  node_pointer;

      node_pointer                                              m_p_min;
      node_pointer                                              m_p_max;

      _Head() : base_type(head_node) { }

#ifdef _GLIBCXX_DEBUG
      typedef typename base_type::node_debug_info              node_debug_info;
      typedef typename base_type::a_const_pointer              a_const_pointer;

      virtual node_debug_info
      assert_valid_imp(a_const_pointer, const char* __file, int __line) const
      {
        _GLIBCXX_DEBUG_VERIFY_AT(false,
                                 _M_message("Assertion from %1;:%2;")
                                 ._M_string(__FILE__)._M_integer(__LINE__),
                                 __file, __line);
        return node_debug_info();
      }
#endif
    };


    /// Leaf node for PATRICIA tree.
    template<typename _ATraits, typename Metadata>
    struct _Leaf
    : public _Node_base<_ATraits, Metadata>
    {
      typedef _Node_base<_ATraits, Metadata>                    base_type;
      typedef typename base_type::type_traits                   type_traits;
      typedef typename type_traits::value_type                  value_type;
      typedef typename type_traits::reference                   reference;
      typedef typename type_traits::const_reference             const_reference;

    private:
      value_type                                                m_value;

      _Leaf(const _Leaf&);

    public:
      _Leaf(const_reference other)
      : base_type(leaf_node), m_value(other) { }

      reference
      value()
      { return m_value; }

      const_reference
      value() const
      { return m_value; }

#ifdef _GLIBCXX_DEBUG
      typedef typename base_type::node_debug_info               node_debug_info;
      typedef typename base_type::a_const_pointer               a_const_pointer;

      virtual node_debug_info
      assert_valid_imp(a_const_pointer p_traits,
                       const char* __file, int __line) const
      {
        PB_DS_DEBUG_VERIFY(base_type::m_type == leaf_node);
        node_debug_info ret;
        const_reference r_val = value();
        return std::make_pair(p_traits->begin(p_traits->extract_key(r_val)),
                              p_traits->end(p_traits->extract_key(r_val)));
      }

      virtual
      ~_Leaf() { }
#endif
    };


    /// Internal node type, PATRICIA tree.
    template<typename _ATraits, typename Metadata>
    struct _Inode
    : public _Node_base<_ATraits, Metadata>
    {
      typedef _Node_base<_ATraits, Metadata>                    base_type;
      typedef typename base_type::type_traits                   type_traits;
      typedef typename base_type::access_traits                 access_traits;
      typedef typename type_traits::value_type                  value_type;
      typedef typename base_type::allocator_type                _Alloc;
      typedef _Alloc                                            allocator_type;
      typedef typename _Alloc::size_type                        size_type;

    private:
      typedef typename base_type::a_const_pointer              a_const_pointer;
      typedef typename base_type::a_const_iterator            a_const_iterator;

      typedef typename base_type::node_pointer                  node_pointer;
      typedef typename _Alloc::template rebind<base_type>       __rebind_n;
      typedef typename __rebind_n::other::const_pointer      node_const_pointer;

      typedef _Leaf<_ATraits, Metadata>                         leaf;
      typedef typename _Alloc::template rebind<leaf>::other     __rebind_l;
      typedef typename __rebind_l::pointer                      leaf_pointer;
      typedef typename __rebind_l::const_pointer            leaf_const_pointer;

      typedef typename _Alloc::template rebind<_Inode>::other   __rebind_in;
      typedef typename __rebind_in::pointer                     inode_pointer;
      typedef typename __rebind_in::const_pointer           inode_const_pointer;

      inline size_type
      get_pref_pos(a_const_iterator, a_const_iterator, a_const_pointer) const;

    public:
      typedef typename _Alloc::template rebind<node_pointer>::other __rebind_np;
      typedef typename __rebind_np::pointer             node_pointer_pointer;
      typedef typename __rebind_np::reference           node_pointer_reference;

      enum
        {
          arr_size = _ATraits::max_size + 1
        };
      PB_DS_STATIC_ASSERT(min_arr_size, arr_size >= 2);


      /// Constant child iterator.
      struct const_iterator
      {
        node_pointer_pointer                            m_p_p_cur;
        node_pointer_pointer                            m_p_p_end;

        typedef std::forward_iterator_tag               iterator_category;
        typedef typename _Alloc::difference_type        difference_type;
        typedef node_pointer                            value_type;
        typedef node_pointer_pointer                    pointer;
        typedef node_pointer_reference                  reference;

        const_iterator(node_pointer_pointer p_p_cur = 0,
                       node_pointer_pointer p_p_end = 0)
        : m_p_p_cur(p_p_cur), m_p_p_end(p_p_end)
        { }

        bool
        operator==(const const_iterator& other) const
        { return m_p_p_cur == other.m_p_p_cur; }

        bool
        operator!=(const const_iterator& other) const
        { return m_p_p_cur != other.m_p_p_cur; }

        const_iterator&
        operator++()
        {
          do
            ++m_p_p_cur;
          while (m_p_p_cur != m_p_p_end && *m_p_p_cur == 0);
          return *this;
        }

        const_iterator
        operator++(int)
        {
          const_iterator ret_it(*this);
          operator++();
          return ret_it;
        }

        const node_pointer_pointer
        operator->() const
        {
          _GLIBCXX_DEBUG_ONLY(assert_referencible();)
          return m_p_p_cur;
        }

        node_const_pointer
        operator*() const
        {
          _GLIBCXX_DEBUG_ONLY(assert_referencible();)
          return *m_p_p_cur;
        }

      protected:
#ifdef _GLIBCXX_DEBUG
        void
        assert_referencible() const
        { _GLIBCXX_DEBUG_ASSERT(m_p_p_cur != m_p_p_end && *m_p_p_cur != 0); }
#endif
      };


      /// Child iterator.
      struct iterator : public const_iterator
      {
      public:
        typedef std::forward_iterator_tag               iterator_category;
        typedef typename _Alloc::difference_type        difference_type;
        typedef node_pointer                            value_type;
        typedef node_pointer_pointer                    pointer;
        typedef node_pointer_reference                  reference;

        inline
        iterator(node_pointer_pointer p_p_cur = 0,
                 node_pointer_pointer p_p_end = 0)
        : const_iterator(p_p_cur, p_p_end) { }

        bool
        operator==(const iterator& other) const
        { return const_iterator::m_p_p_cur == other.m_p_p_cur; }

        bool
        operator!=(const iterator& other) const
        { return const_iterator::m_p_p_cur != other.m_p_p_cur; }

        iterator&
        operator++()
        {
          const_iterator::operator++();
          return *this;
        }

        iterator
        operator++(int)
        {
          iterator ret_it(*this);
          operator++();
          return ret_it;
        }

        node_pointer_pointer
        operator->()
        {
          _GLIBCXX_DEBUG_ONLY(const_iterator::assert_referencible();)
          return const_iterator::m_p_p_cur;
        }

        node_pointer
        operator*()
        {
          _GLIBCXX_DEBUG_ONLY(const_iterator::assert_referencible();)
          return *const_iterator::m_p_p_cur;
        }
      };


      _Inode(size_type, const a_const_iterator);

      void
      update_prefixes(a_const_pointer);

      const_iterator
      begin() const;

      iterator
      begin();

      const_iterator
      end() const;

      iterator
      end();

      inline node_pointer
      get_child_node(a_const_iterator, a_const_iterator, a_const_pointer);

      inline node_const_pointer
      get_child_node(a_const_iterator, a_const_iterator, a_const_pointer) const;

      inline iterator
      get_child_it(a_const_iterator, a_const_iterator, a_const_pointer);

      inline node_pointer
      get_lower_bound_child_node(a_const_iterator, a_const_iterator,
                                 size_type, a_const_pointer);

      inline node_pointer
      add_child(node_pointer, a_const_iterator, a_const_iterator,
                a_const_pointer);

      inline node_const_pointer
      get_join_child(node_const_pointer, a_const_pointer) const;

      inline node_pointer
      get_join_child(node_pointer, a_const_pointer);

      void
      remove_child(node_pointer);

      void
      remove_child(iterator);

      void
      replace_child(node_pointer, a_const_iterator, a_const_iterator,
                    a_const_pointer);

      inline a_const_iterator
      pref_b_it() const;

      inline a_const_iterator
      pref_e_it() const;

      bool
      should_be_mine(a_const_iterator, a_const_iterator, size_type,
                     a_const_pointer) const;

      leaf_pointer
      leftmost_descendant();

      leaf_const_pointer
      leftmost_descendant() const;

      leaf_pointer
      rightmost_descendant();

      leaf_const_pointer
      rightmost_descendant() const;

#ifdef _GLIBCXX_DEBUG
      typedef typename base_type::node_debug_info              node_debug_info;

      virtual node_debug_info
      assert_valid_imp(a_const_pointer, const char*, int) const;
#endif

      size_type
      get_e_ind() const
      { return m_e_ind; }

    private:
      _Inode(const _Inode&);

      size_type
      get_begin_pos() const;

      static __rebind_l                 s_leaf_alloc;
      static __rebind_in                s_inode_alloc;

      const size_type                   m_e_ind;
      a_const_iterator                  m_pref_b_it;
      a_const_iterator                  m_pref_e_it;
      node_pointer                      m_a_p_children[arr_size];
    };

#define PB_DS_CONST_IT_C_DEC \
    _CIter<Node, Leaf, Head, Inode, Is_Forward_Iterator>

#define PB_DS_CONST_ODIR_IT_C_DEC \
    _CIter<Node, Leaf, Head, Inode, !Is_Forward_Iterator>

#define PB_DS_IT_C_DEC \
    _Iter<Node, Leaf, Head, Inode, Is_Forward_Iterator>

#define PB_DS_ODIR_IT_C_DEC \
    _Iter<Node, Leaf, Head, Inode, !Is_Forward_Iterator>


    /// Const iterator.
    template<typename Node, typename Leaf, typename Head, typename Inode,
             bool Is_Forward_Iterator>
    class _CIter
    {
    public:
      // These types are all the same for the first four template arguments.
      typedef typename Node::allocator_type             allocator_type;
      typedef typename Node::type_traits                type_traits;

      typedef std::bidirectional_iterator_tag           iterator_category;
      typedef typename allocator_type::difference_type  difference_type;
      typedef typename type_traits::value_type          value_type;
      typedef typename type_traits::pointer             pointer;
      typedef typename type_traits::reference           reference;
      typedef typename type_traits::const_pointer       const_pointer;
      typedef typename type_traits::const_reference     const_reference;

      typedef allocator_type                            _Alloc;
      typedef typename _Alloc::template rebind<Node>    __rebind_n;
      typedef typename __rebind_n::other::pointer       node_pointer;
      typedef typename _Alloc::template rebind<Leaf>    __rebind_l;
      typedef typename __rebind_l::other::pointer       leaf_pointer;
      typedef typename __rebind_l::other::const_pointer leaf_const_pointer;
      typedef typename _Alloc::template rebind<Head>    __rebind_h;
      typedef typename __rebind_h::other::pointer       head_pointer;

      typedef typename _Alloc::template rebind<Inode> __rebind_in;
      typedef typename __rebind_in::other::pointer      inode_pointer;
      typedef typename Inode::iterator                  inode_iterator;

      node_pointer                                      m_p_nd;

      _CIter(node_pointer p_nd = 0) : m_p_nd(p_nd)
      { }

      _CIter(const PB_DS_CONST_ODIR_IT_C_DEC& other)
      : m_p_nd(other.m_p_nd)
      { }

      _CIter&
      operator=(const _CIter& other)
      {
        m_p_nd = other.m_p_nd;
        return *this;
      }

      _CIter&
      operator=(const PB_DS_CONST_ODIR_IT_C_DEC& other)
      {
        m_p_nd = other.m_p_nd;
        return *this;
      }

      const_pointer
      operator->() const
      {
        _GLIBCXX_DEBUG_ASSERT(m_p_nd->m_type == leaf_node);
        return &static_cast<leaf_pointer>(m_p_nd)->value();
      }

      const_reference
      operator*() const
      {
        _GLIBCXX_DEBUG_ASSERT(m_p_nd->m_type == leaf_node);
        return static_cast<leaf_pointer>(m_p_nd)->value();
      }

      bool
      operator==(const _CIter& other) const
      { return m_p_nd == other.m_p_nd; }

      bool
      operator==(const PB_DS_CONST_ODIR_IT_C_DEC& other) const
      { return m_p_nd == other.m_p_nd; }

      bool
      operator!=(const _CIter& other) const
      { return m_p_nd != other.m_p_nd; }

      bool
      operator!=(const PB_DS_CONST_ODIR_IT_C_DEC& other) const
      { return m_p_nd != other.m_p_nd; }

      _CIter&
      operator++()
      {
        inc(integral_constant<int, Is_Forward_Iterator>());
        return *this;
      }

      _CIter
      operator++(int)
      {
        _CIter ret_it(m_p_nd);
        operator++();
        return ret_it;
      }

      _CIter&
      operator--()
      {
        dec(integral_constant<int, Is_Forward_Iterator>());
        return *this;
      }

      _CIter
      operator--(int)
      {
        _CIter ret_it(m_p_nd);
        operator--();
        return ret_it;
      }

    protected:
      void
      inc(false_type)
      { dec(true_type()); }

      void
      inc(true_type)
      {
        if (m_p_nd->m_type == head_node)
          {
            m_p_nd = static_cast<head_pointer>(m_p_nd)->m_p_min;
            return;
          }

        node_pointer p_y = m_p_nd->m_p_parent;
        while (p_y->m_type != head_node && get_larger_sibling(m_p_nd) == 0)
          {
            m_p_nd = p_y;
            p_y = p_y->m_p_parent;
          }

        if (p_y->m_type == head_node)
          {
            m_p_nd = p_y;
            return;
          }
        m_p_nd = leftmost_descendant(get_larger_sibling(m_p_nd));
      }

      void
      dec(false_type)
      { inc(true_type()); }

      void
      dec(true_type)
      {
        if (m_p_nd->m_type == head_node)
          {
            m_p_nd = static_cast<head_pointer>(m_p_nd)->m_p_max;
            return;
          }

        node_pointer p_y = m_p_nd->m_p_parent;
        while (p_y->m_type != head_node && get_smaller_sibling(m_p_nd) == 0)
          {
            m_p_nd = p_y;
            p_y = p_y->m_p_parent;
          }

        if (p_y->m_type == head_node)
          {
            m_p_nd = p_y;
            return;
          }
        m_p_nd = rightmost_descendant(get_smaller_sibling(m_p_nd));
      }

      static node_pointer
      get_larger_sibling(node_pointer p_nd)
      {
        inode_pointer p_parent = static_cast<inode_pointer>(p_nd->m_p_parent);

        inode_iterator it = p_parent->begin();
        while (*it != p_nd)
          ++it;

        inode_iterator next_it = it;
        ++next_it;
        return (next_it == p_parent->end())? 0 : *next_it;
      }

      static node_pointer
      get_smaller_sibling(node_pointer p_nd)
      {
        inode_pointer p_parent = static_cast<inode_pointer>(p_nd->m_p_parent);

        inode_iterator it = p_parent->begin();
        if (*it == p_nd)
          return 0;

        inode_iterator prev_it;
        do
          {
            prev_it = it;
            ++it;
            if (*it == p_nd)
              return *prev_it;
          }
        while (true);

        _GLIBCXX_DEBUG_ASSERT(false);
        return 0;
      }

      static leaf_pointer
      leftmost_descendant(node_pointer p_nd)
      {
        if (p_nd->m_type == leaf_node)
          return static_cast<leaf_pointer>(p_nd);
        return static_cast<inode_pointer>(p_nd)->leftmost_descendant();
      }

      static leaf_pointer
      rightmost_descendant(node_pointer p_nd)
      {
        if (p_nd->m_type == leaf_node)
          return static_cast<leaf_pointer>(p_nd);
        return static_cast<inode_pointer>(p_nd)->rightmost_descendant();
      }
    };


    /// Iterator.
    template<typename Node, typename Leaf, typename Head, typename Inode,
             bool Is_Forward_Iterator>
    class _Iter
    : public _CIter<Node, Leaf, Head, Inode, Is_Forward_Iterator>
    {
    public:
      typedef _CIter<Node, Leaf, Head, Inode, Is_Forward_Iterator>
                                                        base_type;
      typedef typename base_type::allocator_type        allocator_type;
      typedef typename base_type::type_traits           type_traits;
      typedef typename type_traits::value_type          value_type;
      typedef typename type_traits::pointer             pointer;
      typedef typename type_traits::reference           reference;

      typedef typename base_type::node_pointer          node_pointer;
      typedef typename base_type::leaf_pointer          leaf_pointer;
      typedef typename base_type::leaf_const_pointer    leaf_const_pointer;
      typedef typename base_type::head_pointer          head_pointer;
      typedef typename base_type::inode_pointer         inode_pointer;

      _Iter(node_pointer p_nd = 0)
      : base_type(p_nd) { }

      _Iter(const PB_DS_ODIR_IT_C_DEC& other)
      : base_type(other.m_p_nd) { }

      _Iter&
      operator=(const _Iter& other)
      {
        base_type::m_p_nd = other.m_p_nd;
        return *this;
      }

      _Iter&
      operator=(const PB_DS_ODIR_IT_C_DEC& other)
      {
        base_type::m_p_nd = other.m_p_nd;
        return *this;
      }

      pointer
      operator->() const
      {
        _GLIBCXX_DEBUG_ASSERT(base_type::m_p_nd->m_type == leaf_node);
        return &static_cast<leaf_pointer>(base_type::m_p_nd)->value();
      }

      reference
      operator*() const
      {
        _GLIBCXX_DEBUG_ASSERT(base_type::m_p_nd->m_type == leaf_node);
        return static_cast<leaf_pointer>(base_type::m_p_nd)->value();
      }

      _Iter&
      operator++()
      {
        base_type::operator++();
        return *this;
      }

      _Iter
      operator++(int)
      {
        _Iter ret(base_type::m_p_nd);
        operator++();
        return ret;
      }

      _Iter&
      operator--()
      {
        base_type::operator--();
        return *this;
      }

      _Iter
      operator--(int)
      {
        _Iter ret(base_type::m_p_nd);
        operator--();
        return ret;
      }
    };

#undef PB_DS_CONST_ODIR_IT_C_DEC
#undef PB_DS_ODIR_IT_C_DEC


#define PB_DS_PAT_TRIE_NODE_CONST_ITERATOR_C_DEC \
    _Node_citer<Node, Leaf, Head, Inode, _CIterator, Iterator, _ATraits, _Alloc>

#define PB_DS_PAT_TRIE_NODE_ITERATOR_C_DEC \
    _Node_iter<Node, Leaf, Head, Inode, _CIterator, Iterator, _ATraits, _Alloc>

    /// Node const iterator.
    template<typename Node,
             typename Leaf,
             typename Head,
             typename Inode,
             typename _CIterator,
             typename Iterator,
             typename _Alloc>
    class _Node_citer
    {
    protected:
      typedef typename _Alloc::template rebind<Node>    __rebind_n;
      typedef typename __rebind_n::other::pointer       node_pointer;

      typedef typename _Alloc::template rebind<Leaf>    __rebind_l;
      typedef typename __rebind_l::other::pointer       leaf_pointer;
      typedef typename __rebind_l::other::const_pointer leaf_const_pointer;

      typedef typename _Alloc::template rebind<Inode>   __rebind_in;
      typedef typename __rebind_in::other::pointer      inode_pointer;
      typedef typename __rebind_in::other::const_pointer inode_const_pointer;

      typedef typename Node::a_const_pointer            a_const_pointer;
      typedef typename Node::a_const_iterator           a_const_iterator;

    private:
      a_const_iterator
      pref_begin() const
      {
        if (m_p_nd->m_type == leaf_node)
          {
            leaf_const_pointer lcp = static_cast<leaf_const_pointer>(m_p_nd);
            return m_p_traits->begin(m_p_traits->extract_key(lcp->value()));
          }
        _GLIBCXX_DEBUG_ASSERT(m_p_nd->m_type == i_node);
        return static_cast<inode_const_pointer>(m_p_nd)->pref_b_it();
      }

      a_const_iterator
      pref_end() const
      {
        if (m_p_nd->m_type == leaf_node)
          {
            leaf_const_pointer lcp = static_cast<leaf_const_pointer>(m_p_nd);
            return m_p_traits->end(m_p_traits->extract_key(lcp->value()));
          }
        _GLIBCXX_DEBUG_ASSERT(m_p_nd->m_type == i_node);
        return static_cast<inode_const_pointer>(m_p_nd)->pref_e_it();
      }

    public:
      typedef trivial_iterator_tag                      iterator_category;
      typedef trivial_iterator_difference_type          difference_type;
      typedef typename _Alloc::size_type                size_type;

      typedef _CIterator                                value_type;
      typedef value_type                                reference;
      typedef value_type                                const_reference;

      /// Metadata type.
      typedef typename Node::metadata_type              metadata_type;

      /// Const metadata reference type.
      typedef typename _Alloc::template rebind<metadata_type> __rebind_m;
      typedef typename __rebind_m::other                __rebind_ma;
      typedef typename __rebind_ma::const_reference    metadata_const_reference;

      inline
      _Node_citer(node_pointer p_nd = 0, a_const_pointer p_traits = 0)
      : m_p_nd(const_cast<node_pointer>(p_nd)), m_p_traits(p_traits)
      { }

      /// Subtree valid prefix.
      std::pair<a_const_iterator, a_const_iterator>
      valid_prefix() const
      { return std::make_pair(pref_begin(), pref_end()); }

      /// Const access; returns the __const iterator* associated with
      /// the current leaf.
      const_reference
      operator*() const
      {
        _GLIBCXX_DEBUG_ASSERT(num_children() == 0);
        return _CIterator(m_p_nd);
      }

      /// Metadata access.
      metadata_const_reference
      get_metadata() const
      { return m_p_nd->get_metadata(); }

      /// Returns the number of children in the corresponding node.
      size_type
      num_children() const
      {
        if (m_p_nd->m_type == leaf_node)
          return 0;
        _GLIBCXX_DEBUG_ASSERT(m_p_nd->m_type == i_node);
        inode_pointer inp = static_cast<inode_pointer>(m_p_nd);
        return std::distance(inp->begin(), inp->end());
      }

      /// Returns a __const node __iterator to the corresponding node's
      /// i-th child.
      _Node_citer
      get_child(size_type i) const
      {
        _GLIBCXX_DEBUG_ASSERT(m_p_nd->m_type == i_node);
        inode_pointer inp = static_cast<inode_pointer>(m_p_nd);
        typename Inode::iterator it = inp->begin();
        std::advance(it, i);
        return _Node_citer(*it, m_p_traits);
      }

      /// Compares content to a different iterator object.
      bool
      operator==(const _Node_citer& other) const
      { return m_p_nd == other.m_p_nd; }

      /// Compares content (negatively) to a different iterator object.
      bool
      operator!=(const _Node_citer& other) const
      { return m_p_nd != other.m_p_nd; }

      node_pointer                      m_p_nd;
      a_const_pointer                   m_p_traits;
    };


    /// Node iterator.
    template<typename Node,
             typename Leaf,
             typename Head,
             typename Inode,
             typename _CIterator,
             typename Iterator,
             typename _Alloc>
    class _Node_iter
    : public _Node_citer<Node, Leaf, Head, Inode, _CIterator, Iterator, _Alloc>
    {
    private:
      typedef _Node_citer<Node, Leaf, Head, Inode,
                          _CIterator, Iterator, _Alloc> base_type;
      typedef typename _Alloc::template rebind<Node>    __rebind_n;
      typedef typename __rebind_n::other::pointer       node_pointer;
      typedef typename base_type::inode_pointer         inode_pointer;
      typedef typename base_type::a_const_pointer       a_const_pointer;
      typedef Iterator                                  iterator;

    public:
      typedef typename base_type::size_type             size_type;

      typedef Iterator                                  value_type;
      typedef value_type                                reference;
      typedef value_type                                const_reference;

      _Node_iter(node_pointer p_nd = 0, a_const_pointer p_traits = 0)
      : base_type(p_nd, p_traits)
      { }

      /// Access; returns the iterator*  associated with the current leaf.
      reference
      operator*() const
      {
        _GLIBCXX_DEBUG_ASSERT(base_type::num_children() == 0);
        return iterator(base_type::m_p_nd);
      }

      /// Returns a node __iterator to the corresponding node's i-th child.
      _Node_iter
      get_child(size_type i) const
      {
        _GLIBCXX_DEBUG_ASSERT(base_type::m_p_nd->m_type == i_node);

        typename Inode::iterator it =
          static_cast<inode_pointer>(base_type::m_p_nd)->begin();

        std::advance(it, i);
        return _Node_iter(*it, base_type::m_p_traits);
      }
    };
    };


#define PB_DS_CLASS_T_DEC \
    template<typename _ATraits, typename Metadata>

#define PB_DS_CLASS_C_DEC \
    pat_trie_base::_Inode<_ATraits, Metadata>

    PB_DS_CLASS_T_DEC
    typename PB_DS_CLASS_C_DEC::__rebind_l
    PB_DS_CLASS_C_DEC::s_leaf_alloc;

    PB_DS_CLASS_T_DEC
    typename PB_DS_CLASS_C_DEC::__rebind_in
    PB_DS_CLASS_C_DEC::s_inode_alloc;

    PB_DS_CLASS_T_DEC
    inline typename PB_DS_CLASS_C_DEC::size_type
    PB_DS_CLASS_C_DEC::
    get_pref_pos(a_const_iterator b_it, a_const_iterator e_it,
                 a_const_pointer p_traits) const
    {
      if (static_cast<std::size_t>(std::distance(b_it, e_it)) <= m_e_ind)
        return 0;
      std::advance(b_it, m_e_ind);
      return 1 + p_traits->e_pos(*b_it);
    }

    PB_DS_CLASS_T_DEC
    PB_DS_CLASS_C_DEC::
    _Inode(size_type len, const a_const_iterator it)
    : base_type(i_node), m_e_ind(len), m_pref_b_it(it), m_pref_e_it(it)
    {
      std::advance(m_pref_e_it, m_e_ind);
      std::fill(m_a_p_children, m_a_p_children + arr_size,
                static_cast<node_pointer>(0));
    }

    PB_DS_CLASS_T_DEC
    void
    PB_DS_CLASS_C_DEC::
    update_prefixes(a_const_pointer p_traits)
    {
      node_pointer p_first = *begin();
      if (p_first->m_type == leaf_node)
        {
          leaf_const_pointer p = static_cast<leaf_const_pointer>(p_first);
          m_pref_b_it = p_traits->begin(access_traits::extract_key(p->value()));
        }
      else
        {
          inode_pointer p = static_cast<inode_pointer>(p_first);
          _GLIBCXX_DEBUG_ASSERT(p_first->m_type == i_node);
          m_pref_b_it = p->pref_b_it();
        }
      m_pref_e_it = m_pref_b_it;
      std::advance(m_pref_e_it, m_e_ind);
    }

    PB_DS_CLASS_T_DEC
    typename PB_DS_CLASS_C_DEC::const_iterator
    PB_DS_CLASS_C_DEC::
    begin() const
    {
      typedef node_pointer_pointer pointer_type;
      pointer_type p = const_cast<pointer_type>(m_a_p_children);
      return const_iterator(p + get_begin_pos(), p + arr_size);
    }

    PB_DS_CLASS_T_DEC
    typename PB_DS_CLASS_C_DEC::iterator
    PB_DS_CLASS_C_DEC::
    begin()
    {
      return iterator(m_a_p_children + get_begin_pos(),
                      m_a_p_children + arr_size);
    }

    PB_DS_CLASS_T_DEC
    typename PB_DS_CLASS_C_DEC::const_iterator
    PB_DS_CLASS_C_DEC::
    end() const
    {
      typedef node_pointer_pointer pointer_type;
      pointer_type p = const_cast<pointer_type>(m_a_p_children) + arr_size;
      return const_iterator(p, p);
    }

    PB_DS_CLASS_T_DEC
    typename PB_DS_CLASS_C_DEC::iterator
    PB_DS_CLASS_C_DEC::
    end()
    { return iterator(m_a_p_children + arr_size, m_a_p_children + arr_size); }

    PB_DS_CLASS_T_DEC
    inline typename PB_DS_CLASS_C_DEC::node_pointer
    PB_DS_CLASS_C_DEC::
    get_child_node(a_const_iterator b_it, a_const_iterator e_it,
                   a_const_pointer p_traits)
    {
      const size_type i = get_pref_pos(b_it, e_it, p_traits);
      _GLIBCXX_DEBUG_ASSERT(i < arr_size);
      return m_a_p_children[i];
    }

    PB_DS_CLASS_T_DEC
    inline typename PB_DS_CLASS_C_DEC::iterator
    PB_DS_CLASS_C_DEC::
    get_child_it(a_const_iterator b_it, a_const_iterator e_it,
                 a_const_pointer p_traits)
    {
      const size_type i = get_pref_pos(b_it, e_it, p_traits);
      _GLIBCXX_DEBUG_ASSERT(i < arr_size);
      _GLIBCXX_DEBUG_ASSERT(m_a_p_children[i] != 0);
      return iterator(m_a_p_children + i, m_a_p_children + i);
    }

    PB_DS_CLASS_T_DEC
    inline typename PB_DS_CLASS_C_DEC::node_const_pointer
    PB_DS_CLASS_C_DEC::
    get_child_node(a_const_iterator b_it, a_const_iterator e_it,
                   a_const_pointer p_traits) const
    { return const_cast<node_pointer>(get_child_node(b_it, e_it, p_traits)); }

    PB_DS_CLASS_T_DEC
    typename PB_DS_CLASS_C_DEC::node_pointer
    PB_DS_CLASS_C_DEC::
    get_lower_bound_child_node(a_const_iterator b_it, a_const_iterator e_it,
                               size_type checked_ind,
                               a_const_pointer p_traits)
    {
      if (!should_be_mine(b_it, e_it, checked_ind, p_traits))
        {
          if (p_traits->cmp_prefixes(b_it, e_it, m_pref_b_it,
                                     m_pref_e_it, true))
            return leftmost_descendant();
          return rightmost_descendant();
        }

      size_type i = get_pref_pos(b_it, e_it, p_traits);
      _GLIBCXX_DEBUG_ASSERT(i < arr_size);

      if (m_a_p_children[i] != 0)
        return m_a_p_children[i];

      while (++i < arr_size)
        if (m_a_p_children[i] != 0)
          {
            const node_type& __nt = m_a_p_children[i]->m_type;
            node_pointer ret = m_a_p_children[i];

            if (__nt == leaf_node)
              return ret;

            _GLIBCXX_DEBUG_ASSERT(__nt == i_node);
            inode_pointer inp = static_cast<inode_pointer>(ret);
            return inp->leftmost_descendant();
          }

      return rightmost_descendant();
    }

    PB_DS_CLASS_T_DEC
    inline typename PB_DS_CLASS_C_DEC::node_pointer
    PB_DS_CLASS_C_DEC::
    add_child(node_pointer p_nd, a_const_iterator b_it, a_const_iterator e_it,
              a_const_pointer p_traits)
    {
      const size_type i = get_pref_pos(b_it, e_it, p_traits);
      _GLIBCXX_DEBUG_ASSERT(i < arr_size);
      if (m_a_p_children[i] == 0)
        {
          m_a_p_children[i] = p_nd;
          p_nd->m_p_parent = this;
          return p_nd;
        }
      return m_a_p_children[i];
    }

    PB_DS_CLASS_T_DEC
    typename PB_DS_CLASS_C_DEC::node_const_pointer
    PB_DS_CLASS_C_DEC::
    get_join_child(node_const_pointer p_nd,
                   a_const_pointer p_tr) const
    {
      node_pointer p = const_cast<node_pointer>(p_nd);
      return const_cast<inode_pointer>(this)->get_join_child(p, p_tr);
    }

    PB_DS_CLASS_T_DEC
    typename PB_DS_CLASS_C_DEC::node_pointer
    PB_DS_CLASS_C_DEC::
    get_join_child(node_pointer p_nd, a_const_pointer p_traits)
    {
      size_type i;
      a_const_iterator b_it;
      a_const_iterator e_it;
      if (p_nd->m_type == leaf_node)
        {
          leaf_const_pointer p = static_cast<leaf_const_pointer>(p_nd);

          typedef typename type_traits::key_const_reference kcr;
          kcr r_key = access_traits::extract_key(p->value());
          b_it = p_traits->begin(r_key);
          e_it = p_traits->end(r_key);
        }
      else
        {
          b_it = static_cast<inode_pointer>(p_nd)->pref_b_it();
          e_it = static_cast<inode_pointer>(p_nd)->pref_e_it();
        }
      i = get_pref_pos(b_it, e_it, p_traits);
      _GLIBCXX_DEBUG_ASSERT(i < arr_size);
      return m_a_p_children[i];
    }

    PB_DS_CLASS_T_DEC
    void
    PB_DS_CLASS_C_DEC::
    remove_child(node_pointer p_nd)
    {
      size_type i = 0;
      for (; i < arr_size; ++i)
        if (m_a_p_children[i] == p_nd)
          {
            m_a_p_children[i] = 0;
            return;
          }
      _GLIBCXX_DEBUG_ASSERT(i != arr_size);
    }

    PB_DS_CLASS_T_DEC
    void
    PB_DS_CLASS_C_DEC::
    remove_child(iterator it)
    { *it.m_p_p_cur = 0; }

    PB_DS_CLASS_T_DEC
    void
    PB_DS_CLASS_C_DEC::
    replace_child(node_pointer p_nd, a_const_iterator b_it,
                  a_const_iterator e_it,
                  a_const_pointer p_traits)
    {
      const size_type i = get_pref_pos(b_it, e_it, p_traits);
      _GLIBCXX_DEBUG_ASSERT(i < arr_size);
      m_a_p_children[i] = p_nd;
      p_nd->m_p_parent = this;
    }

    PB_DS_CLASS_T_DEC
    inline typename PB_DS_CLASS_C_DEC::a_const_iterator
    PB_DS_CLASS_C_DEC::
    pref_b_it() const
    { return m_pref_b_it; }

    PB_DS_CLASS_T_DEC
    inline typename PB_DS_CLASS_C_DEC::a_const_iterator
    PB_DS_CLASS_C_DEC::
    pref_e_it() const
    { return m_pref_e_it; }

    PB_DS_CLASS_T_DEC
    bool
    PB_DS_CLASS_C_DEC::
    should_be_mine(a_const_iterator b_it, a_const_iterator e_it,
                   size_type checked_ind,
                   a_const_pointer p_traits) const
    {
      if (m_e_ind == 0)
        return true;

      const size_type num_es = std::distance(b_it, e_it);
      if (num_es < m_e_ind)
        return false;

      a_const_iterator key_b_it = b_it;
      std::advance(key_b_it, checked_ind);
      a_const_iterator key_e_it = b_it;
      std::advance(key_e_it, m_e_ind);

      a_const_iterator value_b_it = m_pref_b_it;
      std::advance(value_b_it, checked_ind);
      a_const_iterator value_e_it = m_pref_b_it;
      std::advance(value_e_it, m_e_ind);

      return p_traits->equal_prefixes(key_b_it, key_e_it, value_b_it,
                                      value_e_it);
    }

    PB_DS_CLASS_T_DEC
    typename PB_DS_CLASS_C_DEC::leaf_pointer
    PB_DS_CLASS_C_DEC::
    leftmost_descendant()
    {
      node_pointer p_pot = *begin();
      if (p_pot->m_type == leaf_node)
        return (static_cast<leaf_pointer>(p_pot));
      _GLIBCXX_DEBUG_ASSERT(p_pot->m_type == i_node);
      return static_cast<inode_pointer>(p_pot)->leftmost_descendant();
    }

    PB_DS_CLASS_T_DEC
    typename PB_DS_CLASS_C_DEC::leaf_const_pointer
    PB_DS_CLASS_C_DEC::
    leftmost_descendant() const
    { return const_cast<inode_pointer>(this)->leftmost_descendant(); }

    PB_DS_CLASS_T_DEC
    typename PB_DS_CLASS_C_DEC::leaf_pointer
    PB_DS_CLASS_C_DEC::
    rightmost_descendant()
    {
      const size_type num_children = std::distance(begin(), end());
      _GLIBCXX_DEBUG_ASSERT(num_children >= 2);

      iterator it = begin();
      std::advance(it, num_children - 1);
      node_pointer p_pot =* it;
      if (p_pot->m_type == leaf_node)
        return static_cast<leaf_pointer>(p_pot);
      _GLIBCXX_DEBUG_ASSERT(p_pot->m_type == i_node);
      return static_cast<inode_pointer>(p_pot)->rightmost_descendant();
    }

    PB_DS_CLASS_T_DEC
    typename PB_DS_CLASS_C_DEC::leaf_const_pointer
    PB_DS_CLASS_C_DEC::
    rightmost_descendant() const
    { return const_cast<inode_pointer>(this)->rightmost_descendant(); }

    PB_DS_CLASS_T_DEC
    typename PB_DS_CLASS_C_DEC::size_type
    PB_DS_CLASS_C_DEC::
    get_begin_pos() const
    {
      size_type i = 0;
      for (; i < arr_size && m_a_p_children[i] == 0; ++i)
        ;
      return i;
    }

#ifdef _GLIBCXX_DEBUG
    PB_DS_CLASS_T_DEC
    typename PB_DS_CLASS_C_DEC::node_debug_info
    PB_DS_CLASS_C_DEC::
    assert_valid_imp(a_const_pointer p_traits,
                     const char* __file, int __line) const
    {
      PB_DS_DEBUG_VERIFY(base_type::m_type == i_node);
      PB_DS_DEBUG_VERIFY(static_cast<size_type>(std::distance(pref_b_it(), pref_e_it())) == m_e_ind);
      PB_DS_DEBUG_VERIFY(std::distance(begin(), end()) >= 2);

      for (typename _Inode::const_iterator it = begin(); it != end(); ++it)
        {
          node_const_pointer p_nd = *it;
          PB_DS_DEBUG_VERIFY(p_nd->m_p_parent == this);
          node_debug_info child_ret = p_nd->assert_valid_imp(p_traits,
                                                             __file, __line);

          PB_DS_DEBUG_VERIFY(static_cast<size_type>(std::distance(child_ret.first, child_ret.second)) >= m_e_ind);
          PB_DS_DEBUG_VERIFY(should_be_mine(child_ret.first, child_ret.second, 0, p_traits));
          PB_DS_DEBUG_VERIFY(get_pref_pos(child_ret.first, child_ret.second, p_traits) == static_cast<size_type>(it.m_p_p_cur - m_a_p_children));
        }
      return std::make_pair(pref_b_it(), pref_e_it());
    }
#endif

#undef PB_DS_CLASS_T_DEC
#undef PB_DS_CLASS_C_DEC
  } // namespace detail
} // namespace __gnu_pbds

#endif