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// Set implementation -*- C++ -*-

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

// 2011, 2012 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 bits/stl_set.h

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

 *  Do not attempt to use it directly. @headername{set}

 */

#ifndef _STL_SET_H

#define _STL_SET_H 1

#include <bits/concept_check.h>

#if __cplusplus >= 201103L

#include <initializer_list>

#endif

namespace std _GLIBCXX_VISIBILITY(default)

{

_GLIBCXX_BEGIN_NAMESPACE_CONTAINER

  /**

   *  @brief A standard container made up of unique keys, which can be

   *  retrieved in logarithmic time.

   *

   *  @ingroup associative_containers

   *

   *  @tparam _Key  Type of key objects.

   *  @tparam _Compare  Comparison function object type, defaults to less<_Key>.

   *  @tparam _Alloc  Allocator type, defaults to allocator<_Key>.

   *

   *  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 unique keys).

   *

   *  Sets support bidirectional iterators.

   *

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

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

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

  */

  template<typename _Key, typename _Compare = std::less<_Key>,

           typename _Alloc = std::allocator<_Key> >

    class set

    {

      // concept requirements

      typedef typename _Alloc::value_type                   _Alloc_value_type;

      __glibcxx_class_requires(_Key, _SGIAssignableConcept)

      __glibcxx_class_requires4(_Compare, bool, _Key, _Key,

                                _BinaryFunctionConcept)

      __glibcxx_class_requires2(_Key, _Alloc_value_type, _SameTypeConcept)

    public:

      // typedefs:

      //@{

      /// Public typedefs.

      typedef _Key     key_type;

      typedef _Key     value_type;

      typedef _Compare key_compare;

      typedef _Compare value_compare;

      typedef _Alloc   allocator_type;

      //@}

    private:

      typedef typename _Alloc::template rebind<_Key>::other _Key_alloc_type;

      typedef _Rb_tree<key_type, value_type, _Identity<value_type>,

                       key_compare, _Key_alloc_type> _Rep_type;

      _Rep_type _M_t;  // Red-black tree representing set.

    public:

      //@{

      ///  Iterator-related typedefs.

      typedef typename _Key_alloc_type::pointer             pointer;

      typedef typename _Key_alloc_type::const_pointer       const_pointer;

      typedef typename _Key_alloc_type::reference           reference;

      typedef typename _Key_alloc_type::const_reference     const_reference;

      // _GLIBCXX_RESOLVE_LIB_DEFECTS

      // DR 103. set::iterator is required to be modifiable,

      // but this allows modification of keys.

      typedef typename _Rep_type::const_iterator            iterator;

      typedef typename _Rep_type::const_iterator            const_iterator;

      typedef typename _Rep_type::const_reverse_iterator    reverse_iterator;

      typedef typename _Rep_type::const_reverse_iterator const_reverse_iterator;

      typedef typename _Rep_type::size_type                 size_type;

      typedef typename _Rep_type::difference_type           difference_type;

      //@}

      // allocation/deallocation

      /**

       *  @brief  Default constructor creates no elements.

       */

      set()

      : _M_t() { }

      /**

       *  @brief  Creates a %set with no elements.

       *  @param  __comp  Comparator to use.

       *  @param  __a  An allocator object.

       */

      explicit

      set(const _Compare& __comp,

          const allocator_type& __a = allocator_type())

      : _M_t(__comp, _Key_alloc_type(__a)) { }

      /**

       *  @brief  Builds a %set from a range.

       *  @param  __first  An input iterator.

       *  @param  __last  An input iterator.

       *

       *  Create a %set 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>

        set(_InputIterator __first, _InputIterator __last)

        : _M_t()

        { _M_t._M_insert_unique(__first, __last); }

      /**

       *  @brief  Builds a %set 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 %set 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>

        set(_InputIterator __first, _InputIterator __last,

            const _Compare& __comp,

            const allocator_type& __a = allocator_type())

        : _M_t(__comp, _Key_alloc_type(__a))

        { _M_t._M_insert_unique(__first, __last); }

      /**

       *  @brief  %Set copy constructor.

       *  @param  __x  A %set of identical element and allocator types.

       *

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

       *  by @a __x.

       */

      set(const set& __x)

      : _M_t(__x._M_t) { }

#if __cplusplus >= 201103L

     /**

       *  @brief %Set move constructor

       *  @param __x  A %set of identical element and allocator types.

       *

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

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

       */

      set(set&& __x)

      noexcept(is_nothrow_copy_constructible<_Compare>::value)

      : _M_t(std::move(__x._M_t)) { }

      /**

       *  @brief  Builds a %set from an initializer_list.

       *  @param  __l  An initializer_list.

       *  @param  __comp  A comparison functor.

       *  @param  __a  An allocator object.

       *

       *  Create a %set consisting of copies of the elements in the list.

       *  This is linear in N if the list is already sorted, and NlogN

       *  otherwise (where N is @a __l.size()).

       */

      set(initializer_list<value_type> __l,

          const _Compare& __comp = _Compare(),

          const allocator_type& __a = allocator_type())

      : _M_t(__comp, _Key_alloc_type(__a))

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

#endif

      /**

       *  @brief  %Set assignment operator.

       *  @param  __x  A %set 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.

       */

      set&

      operator=(const set& __x)

      {

        _M_t = __x._M_t;

        return *this;

      }

#if __cplusplus >= 201103L

      /**

       *  @brief %Set move assignment operator.

       *  @param __x  A %set of identical element and allocator types.

       *

       *  The contents of @a __x are moved into this %set (without copying).

       *  @a __x is a valid, but unspecified %set.

       */

      set&

      operator=(set&& __x)

      {

        // NB: DR 1204.

        // NB: DR 675.

        this->clear();

        this->swap(__x);

        return *this;

      }

      /**

       *  @brief  %Set list assignment operator.

       *  @param  __l  An initializer_list.

       *

       *  This function fills a %set with copies of the elements in the

       *  initializer list @a __l.

       *

       *  Note that the assignment completely changes the %set and

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

       *  of elements assigned.  Old data may be lost.

       */

      set&

      operator=(initializer_list<value_type> __l)

      {

        this->clear();

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

        return *this;

      }

#endif

      // accessors:

      ///  Returns the comparison object with which the %set was constructed.

      key_compare

      key_comp() const

      { return _M_t.key_comp(); }

      ///  Returns the comparison object with which the %set was constructed.

      value_compare

      value_comp() const

      { return _M_t.key_comp(); }

      ///  Returns the allocator object with which the %set was constructed.

      allocator_type

      get_allocator() const _GLIBCXX_NOEXCEPT

      { return allocator_type(_M_t.get_allocator()); }

      /**

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

       *  element in the %set.  Iteration is done in ascending order according

       *  to the keys.

       */

      iterator

      begin() const _GLIBCXX_NOEXCEPT

      { return _M_t.begin(); }

      /**

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

       *  element in the %set.  Iteration is done in ascending order according

       *  to the keys.

       */

      iterator

      end() const _GLIBCXX_NOEXCEPT

      { return _M_t.end(); }

      /**

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

       *  element in the %set.  Iteration is done in descending order according

       *  to the keys.

       */

      reverse_iterator

      rbegin() const _GLIBCXX_NOEXCEPT

      { return _M_t.rbegin(); }

      /**

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

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

       *  according to the keys.

       */

      reverse_iterator

      rend() const _GLIBCXX_NOEXCEPT

      { return _M_t.rend(); }

#if __cplusplus >= 201103L

      /**

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

       *  element in the %set.  Iteration is done in ascending order according

       *  to the keys.

       */

      iterator

      cbegin() const noexcept

      { return _M_t.begin(); }

      /**

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

       *  element in the %set.  Iteration is done in ascending order according

       *  to the keys.

       */

      iterator

      cend() const noexcept

      { return _M_t.end(); }

      /**

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

       *  element in the %set.  Iteration is done in descending order according

       *  to the keys.

       */

      reverse_iterator

      crbegin() const noexcept

      { return _M_t.rbegin(); }

      /**

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

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

       *  according to the keys.

       */

      reverse_iterator

      crend() const noexcept

      { return _M_t.rend(); }

#endif

      ///  Returns true if the %set is empty.

      bool

      empty() const _GLIBCXX_NOEXCEPT

      { return _M_t.empty(); }

      ///  Returns the size of the %set.

      size_type

      size() const _GLIBCXX_NOEXCEPT

      { return _M_t.size(); }

      ///  Returns the maximum size of the %set.

      size_type

      max_size() const _GLIBCXX_NOEXCEPT

      { return _M_t.max_size(); }

      /**

       *  @brief  Swaps data with another %set.

       *  @param  __x  A %set of the same element and allocator types.

       *

       *  This exchanges the elements between two sets 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(s1,s2) will feed to this function.

       */

      void

      swap(set& __x)

      { _M_t.swap(__x._M_t); }

      // insert/erase

#if __cplusplus >= 201103L

      /**

       *  @brief Attempts to build and insert an element into the %set.

       *  @param __args  Arguments used to generate an element.

       *  @return  A pair, of which the first element is an iterator that points

       *           to the possibly inserted element, and the second is a bool

       *           that is true if the element was actually inserted.

       *

       *  This function attempts to build and insert an element into the %set.

       *  A %set relies on unique keys and thus an element is only inserted if

       *  it is not already present in the %set.

       *

       *  Insertion requires logarithmic time.

       */

      template<typename... _Args>

        std::pair<iterator, bool>

        emplace(_Args&&... __args)

        { return _M_t._M_emplace_unique(std::forward<_Args>(__args)...); }

      /**

       *  @brief Attempts to insert an element into the %set.

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

       *                element should be inserted.

       *  @param  __args  Arguments used to generate the element to be

       *                 inserted.

       *  @return An iterator that points to the element with key equivalent to

       *          the one generated from @a __args (may or may not be the

       *          element itself).

       *

       *  This function is not concerned about whether the insertion took place,

       *  and thus does not return a boolean like the single-argument emplace()

       *  does.  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).

       */

      template<typename... _Args>

        iterator

        emplace_hint(const_iterator __pos, _Args&&... __args)

        {

          return _M_t._M_emplace_hint_unique(__pos,

                                             std::forward<_Args>(__args)...);

        }

#endif

      /**

       *  @brief Attempts to insert an element into the %set.

       *  @param  __x  Element to be inserted.

       *  @return  A pair, of which the first element is an iterator that points

       *           to the possibly inserted element, and the second is a bool

       *           that is true if the element was actually inserted.

       *

       *  This function attempts to insert an element into the %set.  A %set

       *  relies on unique keys and thus an element is only inserted if it is

       *  not already present in the %set.

       *

       *  Insertion requires logarithmic time.

       */

      std::pair<iterator, bool>

      insert(const value_type& __x)

      {

        std::pair<typename _Rep_type::iterator, bool> __p =

          _M_t._M_insert_unique(__x);

        return std::pair<iterator, bool>(__p.first, __p.second);

      }

#if __cplusplus >= 201103L

      std::pair<iterator, bool>

      insert(value_type&& __x)

      {

        std::pair<typename _Rep_type::iterator, bool> __p =

          _M_t._M_insert_unique(std::move(__x));

        return std::pair<iterator, bool>(__p.first, __p.second);

      }

#endif

      /**

       *  @brief Attempts to insert an element into the %set.

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

       *                    element should be inserted.

       *  @param  __x  Element to be inserted.

       *  @return An iterator that points to the element with key of

       *           @a __x (may or may not be the element passed in).

       *

       *  This function is not concerned about whether the insertion took place,

       *  and thus does not return a boolean like the single-argument insert()

       *  does.  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(const_iterator __position, const value_type& __x)

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

#if __cplusplus >= 201103L

      iterator

      insert(const_iterator __position, value_type&& __x)

      { return _M_t._M_insert_unique_(__position, std::move(__x)); }

#endif

      /**

       *  @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_unique(__first, __last); }

#if __cplusplus >= 201103L

      /**

       *  @brief Attempts to insert a list of elements into the %set.

       *  @param  __l  A std::initializer_list<value_type> of elements

       *               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

#if __cplusplus >= 201103L

      // _GLIBCXX_RESOLVE_LIB_DEFECTS

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

      /**

       *  @brief Erases an element from a %set.

       *  @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 %set.  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(const_iterator __position)

      { return _M_t.erase(__position); }

#else

      /**

       *  @brief Erases an element from a %set.

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

       *

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

       *  from a %set.  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 the elements located by the given key from

       *  a %set.

       *  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); }

#if __cplusplus >= 201103L

      // _GLIBCXX_RESOLVE_LIB_DEFECTS

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

      /**

       *  @brief Erases a [__first,__last) range of elements from a %set.

       *  @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 %set.

       *  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(const_iterator __first, const_iterator __last)

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

#else

      /**

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

       *  @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 %set.

       *  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 __first, iterator __last)

      { _M_t.erase(__first, __last); }

#endif

      /**

       *  Erases all elements in a %set.  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() _GLIBCXX_NOEXCEPT

      { _M_t.clear(); }

      // set operations:

      /**

       *  @brief  Finds the number of elements.

       *  @param  __x  Element to located.

       *  @return  Number of elements with specified key.

       *

       *  This function only makes sense for multisets; for set the result will

       *  either be 0 (not present) or 1 (present).

       */

      size_type

      count(const key_type& __x) const

      { return _M_t.find(__x) == _M_t.end() ? 0 : 1; }

      // _GLIBCXX_RESOLVE_LIB_DEFECTS

      // 214.  set::find() missing const overload

      //@{

      /**

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

       *  @param  __x  Element 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 element.  If unsuccessful it returns the

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

       */

      iterator

      find(const key_type& __x)

      { return _M_t.find(__x); }

      const_iterator

      find(const key_type& __x) const

      { return _M_t.find(__x); }

      //@}

      //@{

      /**

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

       *  @param  __x  Key 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); }

      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 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); }

      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 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).

       *

       *  This function probably only makes sense for multisets.

       */

      std::pair<iterator, iterator>

      equal_range(const key_type& __x)

      { return _M_t.equal_range(__x); }

      std::pair<const_iterator, const_iterator>

      equal_range(const key_type& __x) const

      { return _M_t.equal_range(__x); }

      //@}

      template<typename _K1, typename _C1, typename _A1>

        friend bool

        operator==(const set<_K1, _C1, _A1>&, const set<_K1, _C1, _A1>&);

      template<typename _K1, typename _C1, typename _A1>

        friend bool

        operator<(const set<_K1, _C1, _A1>&, const set<_K1, _C1, _A1>&);

    };

  /**

   *  @brief  Set equality comparison.

   *  @param  __x  A %set.

   *  @param  __y  A %set of the same type as @a x.

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

   *

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

   *  Sets are considered equivalent if their sizes are equal, and if

   *  corresponding elements compare equal.

  */

  template<typename _Key, typename _Compare, typename _Alloc>

    inline bool

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

               const set<_Key, _Compare, _Alloc>& __y)

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

  /**

   *  @brief  Set ordering relation.

   *  @param  __x  A %set.

   *  @param  __y  A %set 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

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

   *

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

  */

  template<typename _Key, typename _Compare, typename _Alloc>

    inline bool

    operator<(const set<_Key, _Compare, _Alloc>& __x,

              const set<_Key, _Compare, _Alloc>& __y)

    { return __x._M_t < __y._M_t; }

  ///  Returns !(x == y).

  template<typename _Key, typename _Compare, typename _Alloc>

    inline bool

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

               const set<_Key, _Compare, _Alloc>& __y)

    { return !(__x == __y); }

  ///  Returns y < x.

  template<typename _Key, typename _Compare, typename _Alloc>

    inline bool

    operator>(const set<_Key, _Compare, _Alloc>& __x,

              const set<_Key, _Compare, _Alloc>& __y)

    { return __y < __x; }

  ///  Returns !(y < x)