stl_algo.h

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	else
	  {
	    std::iter_swap(__first, __last);
	    ++__first;
	  }
    }

  /**
   *  @if maint
   *  This is an uglified reverse(_BidirectionalIterator,
   *                              _BidirectionalIterator)
   *  overloaded for random access iterators.
   *  @endif
  */
  template<typename _RandomAccessIterator>
    void
    __reverse(_RandomAccessIterator __first, _RandomAccessIterator __last,
	      random_access_iterator_tag)
    {
      if (__first == __last)
	return;
      --__last;
      while (__first < __last)
	{
	  std::iter_swap(__first, __last);
	  ++__first;
	  --__last;
	}
    }

  /**
   *  @brief Reverse a sequence.
   *  @param  first  A bidirectional iterator.
   *  @param  last   A bidirectional iterator.
   *  @return   reverse() returns no value.
   *
   *  Reverses the order of the elements in the range @p [first,last),
   *  so that the first element becomes the last etc.
   *  For every @c i such that @p 0<=i<=(last-first)/2), @p reverse()
   *  swaps @p *(first+i) and @p *(last-(i+1))
  */
  template<typename _BidirectionalIterator>
    inline void
    reverse(_BidirectionalIterator __first, _BidirectionalIterator __last)
    {
      // concept requirements
      __glibcxx_function_requires(_Mutable_BidirectionalIteratorConcept<
				  _BidirectionalIterator>)
      __glibcxx_requires_valid_range(__first, __last);
      std::__reverse(__first, __last, std::__iterator_category(__first));
    }

  /**
   *  @brief Copy a sequence, reversing its elements.
   *  @param  first   A bidirectional iterator.
   *  @param  last    A bidirectional iterator.
   *  @param  result  An output iterator.
   *  @return  An iterator designating the end of the resulting sequence.
   *
   *  Copies the elements in the range @p [first,last) to the range
   *  @p [result,result+(last-first)) such that the order of the
   *  elements is reversed.
   *  For every @c i such that @p 0<=i<=(last-first), @p reverse_copy()
   *  performs the assignment @p *(result+(last-first)-i) = *(first+i).
   *  The ranges @p [first,last) and @p [result,result+(last-first))
   *  must not overlap.
  */
  template<typename _BidirectionalIterator, typename _OutputIterator>
    _OutputIterator
    reverse_copy(_BidirectionalIterator __first, _BidirectionalIterator __last,
			     _OutputIterator __result)
    {
      // concept requirements
      __glibcxx_function_requires(_BidirectionalIteratorConcept<
				  _BidirectionalIterator>)
      __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
		typename iterator_traits<_BidirectionalIterator>::value_type>)
      __glibcxx_requires_valid_range(__first, __last);

      while (__first != __last)
	{
	  --__last;
	  *__result = *__last;
	  ++__result;
	}
      return __result;
    }


  /**
   *  @if maint
   *  This is a helper function for the rotate algorithm specialized on RAIs.
   *  It returns the greatest common divisor of two integer values.
   *  @endif
  */
  template<typename _EuclideanRingElement>
    _EuclideanRingElement
    __gcd(_EuclideanRingElement __m, _EuclideanRingElement __n)
    {
      while (__n != 0)
	{
	  _EuclideanRingElement __t = __m % __n;
	  __m = __n;
	  __n = __t;
	}
      return __m;
    }

  /**
   *  @if maint
   *  This is a helper function for the rotate algorithm.
   *  @endif
  */
  template<typename _ForwardIterator>
    void
    __rotate(_ForwardIterator __first,
	     _ForwardIterator __middle,
	     _ForwardIterator __last,
	     forward_iterator_tag)
    {
      if (__first == __middle || __last  == __middle)
	return;

      _ForwardIterator __first2 = __middle;
      do
	{
	  swap(*__first, *__first2);
	  ++__first;
	  ++__first2;
	  if (__first == __middle)
	    __middle = __first2;
	}
      while (__first2 != __last);

      __first2 = __middle;

      while (__first2 != __last)
	{
	  swap(*__first, *__first2);
	  ++__first;
	  ++__first2;
	  if (__first == __middle)
	    __middle = __first2;
	  else if (__first2 == __last)
	    __first2 = __middle;
	}
    }

  /**
   *  @if maint
   *  This is a helper function for the rotate algorithm.
   *  @endif
  */
  template<typename _BidirectionalIterator>
    void
    __rotate(_BidirectionalIterator __first,
	     _BidirectionalIterator __middle,
	     _BidirectionalIterator __last,
	      bidirectional_iterator_tag)
    {
      // concept requirements
      __glibcxx_function_requires(_Mutable_BidirectionalIteratorConcept<
				  _BidirectionalIterator>)

      if (__first == __middle || __last  == __middle)
	return;

      std::__reverse(__first,  __middle, bidirectional_iterator_tag());
      std::__reverse(__middle, __last,   bidirectional_iterator_tag());

      while (__first != __middle && __middle != __last)
	{
	  swap(*__first, *--__last);
	  ++__first;
	}

      if (__first == __middle)
	std::__reverse(__middle, __last,   bidirectional_iterator_tag());
      else
	std::__reverse(__first,  __middle, bidirectional_iterator_tag());
    }

  /**
   *  @if maint
   *  This is a helper function for the rotate algorithm.
   *  @endif
  */
  template<typename _RandomAccessIterator>
    void
    __rotate(_RandomAccessIterator __first,
	     _RandomAccessIterator __middle,
	     _RandomAccessIterator __last,
	     random_access_iterator_tag)
    {
      // concept requirements
      __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
				  _RandomAccessIterator>)

      if (__first == __middle || __last  == __middle)
	return;

      typedef typename iterator_traits<_RandomAccessIterator>::difference_type
	_Distance;
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
	_ValueType;

      const _Distance __n = __last   - __first;
      const _Distance __k = __middle - __first;
      const _Distance __l = __n - __k;

      if (__k == __l)
	{
	  std::swap_ranges(__first, __middle, __middle);
	  return;
	}

      const _Distance __d = __gcd(__n, __k);

      for (_Distance __i = 0; __i < __d; __i++)
	{
	  _ValueType __tmp = *__first;
	  _RandomAccessIterator __p = __first;

	  if (__k < __l)
	    {
	      for (_Distance __j = 0; __j < __l / __d; __j++)
		{
		  if (__p > __first + __l)
		    {
		      *__p = *(__p - __l);
		      __p -= __l;
		    }

		  *__p = *(__p + __k);
		  __p += __k;
		}
	    }
	  else
	    {
	      for (_Distance __j = 0; __j < __k / __d - 1; __j ++)
		{
		  if (__p < __last - __k)
		    {
		      *__p = *(__p + __k);
		      __p += __k;
		    }
		  *__p = * (__p - __l);
		  __p -= __l;
		}
	    }

	  *__p = __tmp;
	  ++__first;
	}
    }

  /**
   *  @brief Rotate the elements of a sequence.
   *  @param  first   A forward iterator.
   *  @param  middle  A forward iterator.
   *  @param  last    A forward iterator.
   *  @return  Nothing.
   *
   *  Rotates the elements of the range @p [first,last) by @p (middle-first)
   *  positions so that the element at @p middle is moved to @p first, the
   *  element at @p middle+1 is moved to @first+1 and so on for each element
   *  in the range @p [first,last).
   *
   *  This effectively swaps the ranges @p [first,middle) and
   *  @p [middle,last).
   *
   *  Performs @p *(first+(n+(last-middle))%(last-first))=*(first+n) for
   *  each @p n in the range @p [0,last-first).
  */
  template<typename _ForwardIterator>
    inline void
    rotate(_ForwardIterator __first, _ForwardIterator __middle,
	   _ForwardIterator __last)
    {
      // concept requirements
      __glibcxx_function_requires(_Mutable_ForwardIteratorConcept<
				  _ForwardIterator>)
      __glibcxx_requires_valid_range(__first, __middle);
      __glibcxx_requires_valid_range(__middle, __last);

      typedef typename iterator_traits<_ForwardIterator>::iterator_category
	_IterType;
      std::__rotate(__first, __middle, __last, _IterType());
    }

  /**
   *  @brief Copy a sequence, rotating its elements.
   *  @param  first   A forward iterator.
   *  @param  middle  A forward iterator.
   *  @param  last    A forward iterator.
   *  @param  result  An output iterator.
   *  @return   An iterator designating the end of the resulting sequence.
   *
   *  Copies the elements of the range @p [first,last) to the range
   *  beginning at @result, rotating the copied elements by @p (middle-first)
   *  positions so that the element at @p middle is moved to @p result, the
   *  element at @p middle+1 is moved to @result+1 and so on for each element
   *  in the range @p [first,last).
   *
   *  Performs @p *(result+(n+(last-middle))%(last-first))=*(first+n) for
   *  each @p n in the range @p [0,last-first).
  */
  template<typename _ForwardIterator, typename _OutputIterator>
    _OutputIterator
    rotate_copy(_ForwardIterator __first, _ForwardIterator __middle,
                _ForwardIterator __last, _OutputIterator __result)
    {
      // concept requirements
      __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
      __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
		typename iterator_traits<_ForwardIterator>::value_type>)
      __glibcxx_requires_valid_range(__first, __middle);
      __glibcxx_requires_valid_range(__middle, __last);

      return std::copy(__first, __middle,
                       std::copy(__middle, __last, __result));
    }

  /**
   *  @brief Randomly shuffle the elements of a sequence.
   *  @param  first   A forward iterator.
   *  @param  last    A forward iterator.
   *  @return  Nothing.
   *
   *  Reorder the elements in the range @p [first,last) using a random
   *  distribution, so that every possible ordering of the sequence is
   *  equally likely.
  */
  template<typename _RandomAccessIterator>
    inline void
    random_shuffle(_RandomAccessIterator __first, _RandomAccessIterator __last)
    {
      // concept requirements
      __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
	    _RandomAccessIterator>)
      __glibcxx_requires_valid_range(__first, __last);

      if (__first != __last)
	for (_RandomAccessIterator __i = __first + 1; __i != __last; ++__i)
	  std::iter_swap(__i, __first + (std::rand() % ((__i - __first) + 1)));
    }

  /**
   *  @brief Shuffle the elements of a sequence using a random number
   *         generator.
   *  @param  first   A forward iterator.
   *  @param  last    A forward iterator.
   *  @param  rand    The RNG functor or function.
   *  @return  Nothing.
   *
   *  Reorders the elements in the range @p [first,last) using @p rand to
   *  provide a random distribution. Calling @p rand(N) for a positive
   *  integer @p N should return a randomly chosen integer from the
   *  range [0,N).
  */
  template<typename _RandomAccessIterator, typename _RandomNumberGenerator>
    void
    random_shuffle(_RandomAccessIterator __first, _RandomAccessIterator __last,
		   _RandomNumberGenerator& __rand)
    {
      // concept requirements
      __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
	    _RandomAccessIterator>)
      __glibcxx_requires_valid_range(__first, __last);

      if (__first == __last)
	return;
      for (_RandomAccessIterator __i = __first + 1; __i != __last; ++__i)
	std::iter_swap(__i, __first + __rand((__i - __first) + 1));
    }


  /**
   *  @if maint
   *  This is a helper function...
   *  @endif
  */
  template<typename _ForwardIterator, typename _Predicate>
    _ForwardIterator
    __partition(_ForwardIterator __first, _ForwardIterator __last,
		_Predicate __pred,
		forward_iterator_tag)
    {
      if (