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// Multimap implementation -*- C++ -*-

// Copyright (C) 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010

// 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) 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.

 *

 *

 * 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.

 */

/** @file stl_multimap.h

 *  This is an internal header file, included by other library headers.

 *  You should not attempt to use it directly.

 */

#ifndef _STL_MULTIMAP_H

#define _STL_MULTIMAP_H 1

#include <bits/concept_check.h>

#include <initializer_list>

_GLIBCXX_BEGIN_NESTED_NAMESPACE(std, _GLIBCXX_STD_D)

  /**

   *  @brief A standard container made up of (key,value) pairs, which can be

   *  retrieved based on a key, in logarithmic time.

   *

   *  @ingroup associative_containers

   *

   *  Meets the requirements of a <a href="tables.html#65">container</a>, a

   *  <a href="tables.html#66">reversible container</a>, and an

   *  <a href="tables.html#69">associative container</a> (using equivalent

   *  keys).  For a @c multimap<Key,T> the key_type is Key, the mapped_type

   *  is T, and the value_type is std::pair<const Key,T>.

   *

   *  Multimaps support bidirectional iterators.

   *

   *  The private tree data is declared exactly the same way for map and

   *  multimap; the distinction is made entirely in how the tree functions are

   *  called (*_unique versus *_equal, same as the standard).

  */

  template <typename _Key, typename _Tp,

            typename _Compare = std::less<_Key>,

            typename _Alloc = std::allocator<std::pair<const _Key, _Tp> > >

    class multimap

    {

    public:

      typedef _Key                                          key_type;

      typedef _Tp                                           mapped_type;

      typedef std::pair<const _Key, _Tp>                    value_type;

      typedef _Compare                                      key_compare;

      typedef _Alloc                                        allocator_type;

    private:

      // concept requirements

      typedef typename _Alloc::value_type                   _Alloc_value_type;

      __glibcxx_class_requires(_Tp, _SGIAssignableConcept)

      __glibcxx_class_requires4(_Compare, bool, _Key, _Key,

                                _BinaryFunctionConcept)

      __glibcxx_class_requires2(value_type, _Alloc_value_type, _SameTypeConcept)

    public:

      class value_compare

      : public std::binary_function<value_type, value_type, bool>

      {

        friend class multimap<_Key, _Tp, _Compare, _Alloc>;

      protected:

        _Compare comp;

        value_compare(_Compare __c)

        : comp(__c) { }

      public:

        bool operator()(const value_type& __x, const value_type& __y) const

        { return comp(__x.first, __y.first); }

      };

    private:

      /// This turns a red-black tree into a [multi]map.

      typedef typename _Alloc::template rebind<value_type>::other

        _Pair_alloc_type;

      typedef _Rb_tree<key_type, value_type, _Select1st<value_type>,

                       key_compare, _Pair_alloc_type> _Rep_type;

      /// The actual tree structure.

      _Rep_type _M_t;

    public:

      // many of these are specified differently in ISO, but the following are

      // "functionally equivalent"

      typedef typename _Pair_alloc_type::pointer         pointer;

      typedef typename _Pair_alloc_type::const_pointer   const_pointer;

      typedef typename _Pair_alloc_type::reference       reference;

      typedef typename _Pair_alloc_type::const_reference const_reference;

      typedef typename _Rep_type::iterator               iterator;

      typedef typename _Rep_type::const_iterator         const_iterator;

      typedef typename _Rep_type::size_type              size_type;

      typedef typename _Rep_type::difference_type        difference_type;

      typedef typename _Rep_type::reverse_iterator       reverse_iterator;

      typedef typename _Rep_type::const_reverse_iterator const_reverse_iterator;

      // [23.3.2] construct/copy/destroy

      // (get_allocator() is also listed in this section)

      /**

       *  @brief  Default constructor creates no elements.

       */

      multimap()

      : _M_t() { }

      /**

       *  @brief  Creates a %multimap with no elements.

       *  @param  comp  A comparison object.

       *  @param  a  An allocator object.

       */

      explicit

      multimap(const _Compare& __comp,

               const allocator_type& __a = allocator_type())

      : _M_t(__comp, __a) { }

      /**

       *  @brief  %Multimap copy constructor.

       *  @param  x  A %multimap of identical element and allocator types.

       *

       *  The newly-created %multimap uses a copy of the allocation object

       *  used by @a x.

       */

      multimap(const multimap& __x)

      : _M_t(__x._M_t) { }

#ifdef __GXX_EXPERIMENTAL_CXX0X__

      /**

       *  @brief  %Multimap move constructor.

       *  @param   x  A %multimap of identical element and allocator types.

       *

       *  The newly-created %multimap contains the exact contents of @a x.

       *  The contents of @a x are a valid, but unspecified %multimap.

       */

      multimap(multimap&& __x)

      : _M_t(std::forward<_Rep_type>(__x._M_t)) { }

      /**

       *  @brief  Builds a %multimap from an initializer_list.

       *  @param  l  An initializer_list.

       *  @param  comp  A comparison functor.

       *  @param  a  An allocator object.

       *

       *  Create a %multimap consisting of copies of the elements from

       *  the initializer_list.  This is linear in N if the list is already

       *  sorted, and NlogN otherwise (where N is @a __l.size()).

       */

      multimap(initializer_list<value_type> __l,

               const _Compare& __comp = _Compare(),

               const allocator_type& __a = allocator_type())

      : _M_t(__comp, __a)

      { _M_t._M_insert_equal(__l.begin(), __l.end()); }

#endif

      /**

       *  @brief  Builds a %multimap from a range.

       *  @param  first  An input iterator.

       *  @param  last  An input iterator.

       *

       *  Create a %multimap consisting of copies of the elements from

       *  [first,last).  This is linear in N if the range is already sorted,

       *  and NlogN otherwise (where N is distance(first,last)).

       */

      template<typename _InputIterator>

        multimap(_InputIterator __first, _InputIterator __last)

        : _M_t()

        { _M_t._M_insert_equal(__first, __last); }

      /**

       *  @brief  Builds a %multimap from a range.

       *  @param  first  An input iterator.

       *  @param  last  An input iterator.

       *  @param  comp  A comparison functor.

       *  @param  a  An allocator object.

       *

       *  Create a %multimap consisting of copies of the elements from

       *  [first,last).  This is linear in N if the range is already sorted,

       *  and NlogN otherwise (where N is distance(first,last)).

       */

      template<typename _InputIterator>

        multimap(_InputIterator __first, _InputIterator __last,

                 const _Compare& __comp,

                 const allocator_type& __a = allocator_type())

        : _M_t(__comp, __a)

        { _M_t._M_insert_equal(__first, __last); }

      // FIXME There is no dtor declared, but we should have something generated

      // by Doxygen.  I don't know what tags to add to this paragraph to make

      // that happen:

      /**

       *  The dtor only erases the elements, and note that if the elements

       *  themselves are pointers, the pointed-to memory is not touched in any

       *  way.  Managing the pointer is the user's responsibility.

       */

      /**

       *  @brief  %Multimap assignment operator.

       *  @param  x  A %multimap of identical element and allocator types.

       *

       *  All the elements of @a x are copied, but unlike the copy constructor,

       *  the allocator object is not copied.

       */

      multimap&

      operator=(const multimap& __x)

      {

        _M_t = __x._M_t;

        return *this;

      }

#ifdef __GXX_EXPERIMENTAL_CXX0X__

      /**

       *  @brief  %Multimap move assignment operator.

       *  @param  x  A %multimap of identical element and allocator types.

       *

       *  The contents of @a x are moved into this multimap (without copying).

       *  @a x is a valid, but unspecified multimap.

       */

      multimap&

      operator=(multimap&& __x)

      {

        // NB: DR 1204.

        // NB: DR 675.

        this->clear();

        this->swap(__x);

        return *this;

      }

      /**

       *  @brief  %Multimap list assignment operator.

       *  @param  l  An initializer_list.

       *

       *  This function fills a %multimap with copies of the elements

       *  in the initializer list @a l.

       *

       *  Note that the assignment completely changes the %multimap and

       *  that the resulting %multimap's size is the same as the number

       *  of elements assigned.  Old data may be lost.

       */

      multimap&

      operator=(initializer_list<value_type> __l)

      {

        this->clear();

        this->insert(__l.begin(), __l.end());

        return *this;

      }

#endif

      /// Get a copy of the memory allocation object.

      allocator_type

      get_allocator() const

      { return _M_t.get_allocator(); }

      // iterators

      /**

       *  Returns a read/write iterator that points to the first pair in the

       *  %multimap.  Iteration is done in ascending order according to the

       *  keys.

       */

      iterator

      begin()

      { return _M_t.begin(); }

      /**

       *  Returns a read-only (constant) iterator that points to the first pair

       *  in the %multimap.  Iteration is done in ascending order according to

       *  the keys.

       */

      const_iterator

      begin() const

      { return _M_t.begin(); }

      /**

       *  Returns a read/write iterator that points one past the last pair in

       *  the %multimap.  Iteration is done in ascending order according to the

       *  keys.

       */

      iterator

      end()

      { return _M_t.end(); }

      /**

       *  Returns a read-only (constant) iterator that points one past the last

       *  pair in the %multimap.  Iteration is done in ascending order according

       *  to the keys.

       */

      const_iterator

      end() const

      { return _M_t.end(); }

      /**

       *  Returns a read/write reverse iterator that points to the last pair in

       *  the %multimap.  Iteration is done in descending order according to the

       *  keys.

       */

      reverse_iterator

      rbegin()

      { return _M_t.rbegin(); }

      /**

       *  Returns a read-only (constant) reverse iterator that points to the

       *  last pair in the %multimap.  Iteration is done in descending order

       *  according to the keys.

       */

      const_reverse_iterator

      rbegin() const

      { return _M_t.rbegin(); }

      /**

       *  Returns a read/write reverse iterator that points to one before the

       *  first pair in the %multimap.  Iteration is done in descending order

       *  according to the keys.

       */

      reverse_iterator

      rend()

      { return _M_t.rend(); }

      /**

       *  Returns a read-only (constant) reverse iterator that points to one

       *  before the first pair in the %multimap.  Iteration is done in

       *  descending order according to the keys.

       */

      const_reverse_iterator

      rend() const

      { return _M_t.rend(); }

#ifdef __GXX_EXPERIMENTAL_CXX0X__

      /**

       *  Returns a read-only (constant) iterator that points to the first pair

       *  in the %multimap.  Iteration is done in ascending order according to

       *  the keys.

       */

      const_iterator

      cbegin() const

      { return _M_t.begin(); }

      /**

       *  Returns a read-only (constant) iterator that points one past the last

       *  pair in the %multimap.  Iteration is done in ascending order according

       *  to the keys.

       */

      const_iterator

      cend() const

      { return _M_t.end(); }

      /**

       *  Returns a read-only (constant) reverse iterator that points to the

       *  last pair in the %multimap.  Iteration is done in descending order

       *  according to the keys.

       */

      const_reverse_iterator

      crbegin() const

      { return _M_t.rbegin(); }

      /**

       *  Returns a read-only (constant) reverse iterator that points to one

       *  before the first pair in the %multimap.  Iteration is done in

       *  descending order according to the keys.

       */

      const_reverse_iterator

      crend() const

      { return _M_t.rend(); }

#endif

      // capacity

      /** Returns true if the %multimap is empty.  */

      bool

      empty() const

      { return _M_t.empty(); }

      /** Returns the size of the %multimap.  */

      size_type

      size() const

      { return _M_t.size(); }

      /** Returns the maximum size of the %multimap.  */

      size_type

      max_size() const

      { return _M_t.max_size(); }

      // modifiers

      /**

       *  @brief Inserts a std::pair into the %multimap.

       *  @param  x  Pair to be inserted (see std::make_pair for easy creation

       *             of pairs).

       *  @return An iterator that points to the inserted (key,value) pair.

       *

       *  This function inserts a (key, value) pair into the %multimap.

       *  Contrary to a std::map the %multimap does not rely on unique keys and

       *  thus multiple pairs with the same key can be inserted.

       *

       *  Insertion requires logarithmic time.

       */

      iterator

      insert(const value_type& __x)

      { return _M_t._M_insert_equal(__x); }

      /**

       *  @brief Inserts a std::pair into the %multimap.

       *  @param  position  An iterator that serves as a hint as to where the

       *                    pair should be inserted.

       *  @param  x  Pair to be inserted (see std::make_pair for easy creation

       *             of pairs).

       *  @return An iterator that points to the inserted (key,value) pair.

       *

       *  This function inserts a (key, value) pair into the %multimap.

       *  Contrary to a std::map the %multimap does not rely on unique keys and

       *  thus multiple pairs with the same key can be inserted.

       *  Note that the first parameter is only a hint and can potentially

       *  improve the performance of the insertion process.  A bad hint would

       *  cause no gains in efficiency.

       *

       *  For more on @a hinting, see:

       *  http://gcc.gnu.org/onlinedocs/libstdc++/manual/bk01pt07ch17.html

       *

       *  Insertion requires logarithmic time (if the hint is not taken).

       */

      iterator

      insert(iterator __position, const value_type& __x)

      { return _M_t._M_insert_equal_(__position, __x); }

      /**

       *  @brief A template function that attempts to insert a range

       *  of elements.

       *  @param  first  Iterator pointing to the start of the range to be

       *                 inserted.

       *  @param  last  Iterator pointing to the end of the range.

       *

       *  Complexity similar to that of the range constructor.

       */

      template<typename _InputIterator>

        void

        insert(_InputIterator __first, _InputIterator __last)

        { _M_t._M_insert_equal(__first, __last); }

#ifdef __GXX_EXPERIMENTAL_CXX0X__

      /**

       *  @brief Attempts to insert a list of std::pairs into the %multimap.

       *  @param  list  A std::initializer_list<value_type> of pairs to be

       *                inserted.

       *

       *  Complexity similar to that of the range constructor.

       */

      void

      insert(initializer_list<value_type> __l)

      { this->insert(__l.begin(), __l.end()); }

#endif

#ifdef __GXX_EXPERIMENTAL_CXX0X__

      // _GLIBCXX_RESOLVE_LIB_DEFECTS

      // DR 130. Associative erase should return an iterator.

      /**

       *  @brief Erases an element from a %multimap.

       *  @param  position  An iterator pointing to the element to be erased.

       *  @return An iterator pointing to the element immediately following

       *          @a position prior to the element being erased. If no such

       *          element exists, end() is returned.

       *

       *  This function erases an element, pointed to by the given iterator,

       *  from a %multimap.  Note that this function only erases the element,

       *  and that if the element is itself a pointer, the pointed-to memory is

       *  not touched in any way.  Managing the pointer is the user's

       *  responsibility.

       */

      iterator

      erase(iterator __position)

      { return _M_t.erase(__position); }

#else

      /**

       *  @brief Erases an element from a %multimap.

       *  @param  position  An iterator pointing to the element to be erased.

       *

       *  This function erases an element, pointed to by the given iterator,

       *  from a %multimap.  Note that this function only erases the element,

       *  and that if the element is itself a pointer, the pointed-to memory is

       *  not touched in any way.  Managing the pointer is the user's

       *  responsibility.

       */

      void

      erase(iterator __position)

      { _M_t.erase(__position); }

#endif

      /**

       *  @brief Erases elements according to the provided key.

       *  @param  x  Key of element to be erased.

       *  @return  The number of elements erased.

       *

       *  This function erases all elements located by the given key from a

       *  %multimap.

       *  Note that this function only erases the element, and that if

       *  the element is itself a pointer, the pointed-to memory is not touched

       *  in any way.  Managing the pointer is the user's responsibility.

       */

      size_type

      erase(const key_type& __x)

      { return _M_t.erase(__x); }

#ifdef __GXX_EXPERIMENTAL_CXX0X__

      // _GLIBCXX_RESOLVE_LIB_DEFECTS

      // DR 130. Associative erase should return an iterator.

      /**

       *  @brief Erases a [first,last) range of elements from a %multimap.

       *  @param  first  Iterator pointing to the start of the range to be

       *                 erased.

       *  @param  last  Iterator pointing to the end of the range to be erased.

       *  @return The iterator @a last.

       *

       *  This function erases a sequence of elements from a %multimap.

       *  Note that this function only erases the elements, and that if

       *  the elements themselves are pointers, the pointed-to memory is not

       *  touched in any way.  Managing the pointer is the user's responsibility.

       */

      iterator

      erase(iterator __first, iterator __last)

      { return _M_t.erase(__first, __last); }

#else

      // _GLIBCXX_RESOLVE_LIB_DEFECTS

      // DR 130. Associative erase should return an iterator.

      /**

       *  @brief Erases a [first,last) range of elements from a %multimap.

       *  @param  first  Iterator pointing to the start of the range to be

       *                 erased.

       *  @param  last  Iterator pointing to the end of the range to be erased.

       *

       *  This function erases a sequence of elements from a %multimap.

       *  Note that this function only erases the elements, and that if

       *  the elements themselves are pointers, the pointed-to memory is not

       *  touched in any way.  Managing the pointer is the user's responsibility.

       */

      void

      erase(iterator __first, iterator __last)

      { _M_t.erase(__first, __last); }

#endif

      /**

       *  @brief  Swaps data with another %multimap.

       *  @param  x  A %multimap of the same element and allocator types.

       *

       *  This exchanges the elements between two multimaps in constant time.

       *  (It is only swapping a pointer, an integer, and an instance of

       *  the @c Compare type (which itself is often stateless and empty), so it

       *  should be quite fast.)

       *  Note that the global std::swap() function is specialized such that

       *  std::swap(m1,m2) will feed to this function.

       */

      void

      swap(multimap& __x)

      { _M_t.swap(__x._M_t); }

      /**

       *  Erases all elements in a %multimap.  Note that this function only

       *  erases the elements, and that if the elements themselves are pointers,

       *  the pointed-to memory is not touched in any way.  Managing the pointer

       *  is the user's responsibility.

       */

      void

      clear()

      { _M_t.clear(); }

      // observers

      /**

       *  Returns the key comparison object out of which the %multimap

       *  was constructed.

       */

      key_compare

      key_comp() const

      { return _M_t.key_comp(); }

      /**

       *  Returns a value comparison object, built from the key comparison

       *  object out of which the %multimap was constructed.

       */

      value_compare

      value_comp() const

      { return value_compare(_M_t.key_comp()); }

      // multimap operations

      /**

       *  @brief Tries to locate an element in a %multimap.

       *  @param  x  Key of (key, value) pair to be located.

       *  @return  Iterator pointing to sought-after element,

       *           or end() if not found.

       *

       *  This function takes a key and tries to locate the element with which

       *  the key matches.  If successful the function returns an iterator

       *  pointing to the sought after %pair.  If unsuccessful it returns the

       *  past-the-end ( @c end() ) iterator.

       */

      iterator

      find(const key_type& __x)

      { return _M_t.find(__x); }

      /**

       *  @brief Tries to locate an element in a %multimap.

       *  @param  x  Key of (key, value) pair to be located.

       *  @return  Read-only (constant) iterator pointing to sought-after

       *           element, or end() if not found.

       *

       *  This function takes a key and tries to locate the element with which

       *  the key matches.  If successful the function returns a constant

       *  iterator pointing to the sought after %pair.  If unsuccessful it

       *  returns the past-the-end ( @c end() ) iterator.

       */

      const_iterator

      find(const key_type& __x) const

      { return _M_t.find(__x); }

      /**

       *  @brief Finds the number of elements with given key.

       *  @param  x  Key of (key, value) pairs to be located.

       *  @return Number of elements with specified key.

       */

      size_type

      count(const key_type& __x) const

      { return _M_t.count(__x); }

      /**

       *  @brief Finds the beginning of a subsequence matching given key.

       *  @param  x  Key of (key, value) pair to be located.

       *  @return  Iterator pointing to first element equal to or greater

       *           than key, or end().

       *

       *  This function returns the first element of a subsequence of elements

       *  that matches the given key.  If unsuccessful it returns an iterator

       *  pointing to the first element that has a greater value than given key

       *  or end() if no such element exists.

       */

      iterator

      lower_bound(const key_type& __x)

      { return _M_t.lower_bound(__x); }

      /**

       *  @brief Finds the beginning of a subsequence matching given key.

       *  @param  x  Key of (key, value) pair to be located.

       *  @return  Read-only (constant) iterator pointing to first element

       *           equal to or greater than key, or end().

       *

       *  This function returns the first element of a subsequence of elements

       *  that matches the given key.  If unsuccessful the iterator will point

       *  to the next greatest element or, if no such greater element exists, to

       *  end().

       */

      const_iterator

      lower_bound(const key_type& __x) const

      { return _M_t.lower_bound(__x); }

      /**

       *  @brief Finds the end of a subsequence matching given key.

       *  @param  x  Key of (key, value) pair to be located.

       *  @return Iterator pointing to the first element

       *          greater than key, or end().

       */

      iterator

      upper_bound(const key_type& __x)

      { return _M_t.upper_bound(__x); }

      /**

       *  @brief Finds the end of a subsequence matching given key.

       *  @param  x  Key of (key, value) pair to be located.

       *  @return  Read-only (constant) iterator pointing to first iterator

       *           greater than key, or end().

       */

      const_iterator

      upper_bound(const key_type& __x) const

      { return _M_t.upper_bound(__x); }

      /**

       *  @brief Finds a subsequence matching given key.

       *  @param  x  Key of (key, value) pairs to be located.

       *  @return  Pair of iterators that possibly points to the subsequence

       *           matching given key.

       *

       *  This function is equivalent to

       *  @code

       *    std::make_pair(c.lower_bound(val),

       *                   c.upper_bound(val))

       *  @endcode

       *  (but is faster than making the calls separately).

       */

      std::pair<iterator, iterator>

      equal_range(const key_type& __x)

      { return _M_t.equal_range(__x); }

      /**

       *  @brief Finds a subsequence matching given key.

       *  @param  x  Key of (key, value) pairs to be located.

       *  @return  Pair of read-only (constant) iterators that possibly points

       *           to the subsequence matching given key.

       *

       *  This function is equivalent to

       *  @code

       *    std::make_pair(c.lower_bound(val),

       *                   c.upper_bound(val))

       *  @endcode

       *  (but is faster than making the calls separately).

       */

      std::pair<const_iterator, const_iterator>

      equal_range(const key_type& __x) const

      { return _M_t.equal_range(__x); }

      template<typename _K1, typename _T1, typename _C1, typename _A1>

        friend bool

        operator==(const multimap<_K1, _T1, _C1, _A1>&,

                   const multimap<_K1, _T1, _C1, _A1>&);

      template<typename _K1, typename _T1, typename _C1, typename _A1>

        friend bool

        operator<(const multimap<_K1, _T1, _C1, _A1>&,

                  const multimap<_K1, _T1, _C1, _A1>&);

  };

  /**

   *  @brief  Multimap equality comparison.

   *  @param  x  A %multimap.

   *  @param  y  A %multimap of the same type as @a x.

   *  @return  True iff the size and elements of the maps are equal.

   *

   *  This is an equivalence relation.  It is linear in the size of the

   *  multimaps.  Multimaps are considered equivalent if their sizes are equal,

   *  and if corresponding elements compare equal.

  */

  template<typename _Key, typename _Tp, typename _Compare, typename _Alloc>

    inline bool

    operator==(const multimap<_Key, _Tp, _Compare, _Alloc>& __x,

               const multimap<_Key, _Tp, _Compare, _Alloc>& __y)

    { return __x._M_t == __y._M_t; }

  /**

   *  @brief  Multimap ordering relation.

   *  @param  x  A %multimap.

   *  @param  y  A %multimap of the same type as @a x.

   *  @return  True iff @a x is lexicographically less than @a y.

   *

   *  This is a total ordering relation.  It is linear in the size of the

   *  multimaps.  The elements must be comparable with @c <.

   *

   *  See std::lexicographical_compare() for how the determination is made.

  */

  template<typename _Key, typename _Tp, typename _Compare, typename _Alloc>

    inline bool

    operator<(const multimap<_Key, _Tp, _Compare, _Alloc>& __x,

              const multimap<_Key, _Tp, _Compare, _Alloc>& __y)

    { return __x._M_t < __y._M_t; }

  /// Based on operator==

  template<typename _Key, typename _Tp, typename _Compare, typename _Alloc>

    inline bool

    operator!=(const multimap<_Key, _Tp, _Compare, _Alloc>& __x,

               const multimap<_Key, _Tp, _Compare, _Alloc>& __y)

    { return !(__x == __y); }

  /// Based on operator<

  template<typename _Key, typename _Tp, typename _Compare, typename _Alloc>