stl_algo.h

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                                        *(__last - 1), __comp)),
       __comp);
    __introsort_loop(__cut, __last, (_T*) 0, __depth_limit, __comp);
    __last = __cut;
  }
}

template <class _RandomAccessIter>
inline void sort(_RandomAccessIter __first, _RandomAccessIter __last) {
  if (__first != __last) {
    __introsort_loop(__first, __last,
                     __VALUE_TYPE(__first),
                     __lg(__last - __first) * 2);
    __final_insertion_sort(__first, __last);
  }
}

template <class _RandomAccessIter, class _Compare>
inline void sort(_RandomAccessIter __first, _RandomAccessIter __last,
                 _Compare __comp) {
  if (__first != __last) {
    __introsort_loop(__first, __last,
                     __VALUE_TYPE(__first),
                     __lg(__last - __first) * 2,
                     __comp);
    __final_insertion_sort(__first, __last, __comp);
  }
}

// stable_sort() and its auxiliary functions.

template <class _RandomAccessIter>
void __inplace_stable_sort(_RandomAccessIter __first,
                           _RandomAccessIter __last) {
  if (__last - __first < 15) {
    __insertion_sort(__first, __last);
    return;
  }
  _RandomAccessIter __middle = __first + (__last - __first) / 2;
  __inplace_stable_sort(__first, __middle);
  __inplace_stable_sort(__middle, __last);
  __merge_without_buffer(__first, __middle, __last,
                         __middle - __first,
                         __last - __middle);
}

template <class _RandomAccessIter, class _Compare>
void __inplace_stable_sort(_RandomAccessIter __first,
                           _RandomAccessIter __last, _Compare __comp) {
  if (__last - __first < 15) {
    __insertion_sort(__first, __last, __comp);
    return;
  }
  _RandomAccessIter __middle = __first + (__last - __first) / 2;
  __inplace_stable_sort(__first, __middle, __comp);
  __inplace_stable_sort(__middle, __last, __comp);
  __merge_without_buffer(__first, __middle, __last,
                         __middle - __first,
                         __last - __middle,
                         __comp);
}

template <class _RandomAccessIter1, class _RandomAccessIter2,
          class _Distance>
void __merge_sort_loop(_RandomAccessIter1 __first,
                       _RandomAccessIter1 __last, 
                       _RandomAccessIter2 __result, _Distance __step_size) {
  _Distance __two_step = 2 * __step_size;

  while (__last - __first >= __two_step) {
    __result = merge(__first, __first + __step_size,
                     __first + __step_size, __first + __two_step,
                     __result);
    __first += __two_step;
  }

  __step_size = min(_Distance(__last - __first), __step_size);
  merge(__first, __first + __step_size, __first + __step_size, __last,
        __result);
}

template <class _RandomAccessIter1, class _RandomAccessIter2,
          class _Distance, class _Compare>
void __merge_sort_loop(_RandomAccessIter1 __first,
                       _RandomAccessIter1 __last, 
                       _RandomAccessIter2 __result, _Distance __step_size,
                       _Compare __comp) {
  _Distance __two_step = 2 * __step_size;

  while (__last - __first >= __two_step) {
    __result = merge(__first, __first + __step_size,
                     __first + __step_size, __first + __two_step,
                     __result,
                     __comp);
    __first += __two_step;
  }
  __step_size = min(_Distance(__last - __first), __step_size);

  merge(__first, __first + __step_size,
        __first + __step_size, __last,
        __result,
        __comp);
}

const int __stl_chunk_size = 7;
        
template <class _RandomAccessIter, class _Distance>
void __chunk_insertion_sort(_RandomAccessIter __first, 
                            _RandomAccessIter __last, _Distance __chunk_size)
{
  while (__last - __first >= __chunk_size) {
    __insertion_sort(__first, __first + __chunk_size);
    __first += __chunk_size;
  }
  __insertion_sort(__first, __last);
}

template <class _RandomAccessIter, class _Distance, class _Compare>
void __chunk_insertion_sort(_RandomAccessIter __first, 
                            _RandomAccessIter __last,
                            _Distance __chunk_size, _Compare __comp)
{
  while (__last - __first >= __chunk_size) {
    __insertion_sort(__first, __first + __chunk_size, __comp);
    __first += __chunk_size;
  }
  __insertion_sort(__first, __last, __comp);
}

template <class _RandomAccessIter, class _Pointer, class _Distance>
void __merge_sort_with_buffer(_RandomAccessIter __first, 
                              _RandomAccessIter __last,
                              _Pointer __buffer, _Distance*) {
  _Distance __len = __last - __first;
  _Pointer __buffer_last = __buffer + __len;

  _Distance __step_size = __stl_chunk_size;
  __chunk_insertion_sort(__first, __last, __step_size);

  while (__step_size < __len) {
    __merge_sort_loop(__first, __last, __buffer, __step_size);
    __step_size *= 2;
    __merge_sort_loop(__buffer, __buffer_last, __first, __step_size);
    __step_size *= 2;
  }
}

template <class _RandomAccessIter, class _Pointer, class _Distance,
          class _Compare>
void __merge_sort_with_buffer(_RandomAccessIter __first, 
                              _RandomAccessIter __last, _Pointer __buffer,
                              _Distance*, _Compare __comp) {
  _Distance __len = __last - __first;
  _Pointer __buffer_last = __buffer + __len;

  _Distance __step_size = __stl_chunk_size;
  __chunk_insertion_sort(__first, __last, __step_size, __comp);

  while (__step_size < __len) {
    __merge_sort_loop(__first, __last, __buffer, __step_size, __comp);
    __step_size *= 2;
    __merge_sort_loop(__buffer, __buffer_last, __first, __step_size, __comp);
    __step_size *= 2;
  }
}

template <class _RandomAccessIter, class _Pointer, class _Distance>
void __stable_sort_adaptive(_RandomAccessIter __first, 
                            _RandomAccessIter __last, _Pointer __buffer,
                            _Distance __buffer_size) {
  _Distance __len = (__last - __first + 1) / 2;
  _RandomAccessIter __middle = __first + __len;
  if (__len > __buffer_size) {
    __stable_sort_adaptive(__first, __middle, __buffer, __buffer_size);
    __stable_sort_adaptive(__middle, __last, __buffer, __buffer_size);
  }
  else {
    __merge_sort_with_buffer(__first, __middle, __buffer, (_Distance*)0);
    __merge_sort_with_buffer(__middle, __last, __buffer, (_Distance*)0);
  }
  __merge_adaptive(__first, __middle, __last, _Distance(__middle - __first), 
                   _Distance(__last - __middle), __buffer, __buffer_size);
}

template <class _RandomAccessIter, class _Pointer, class _Distance, 
          class _Compare>
void __stable_sort_adaptive(_RandomAccessIter __first, 
                            _RandomAccessIter __last, _Pointer __buffer,
                            _Distance __buffer_size, _Compare __comp) {
  _Distance __len = (__last - __first + 1) / 2;
  _RandomAccessIter __middle = __first + __len;
  if (__len > __buffer_size) {
    __stable_sort_adaptive(__first, __middle, __buffer, __buffer_size, 
                           __comp);
    __stable_sort_adaptive(__middle, __last, __buffer, __buffer_size, 
                           __comp);
  }
  else {
    __merge_sort_with_buffer(__first, __middle, __buffer, (_Distance*)0,
                               __comp);
    __merge_sort_with_buffer(__middle, __last, __buffer, (_Distance*)0,
                               __comp);
  }
  __merge_adaptive(__first, __middle, __last, _Distance(__middle - __first), 
                   _Distance(__last - __middle), __buffer, __buffer_size,
                   __comp);
}

template <class _RandomAccessIter, class _T, class _Distance>
inline void __stable_sort_aux(_RandomAccessIter __first,
                              _RandomAccessIter __last, _T*, _Distance*) {
  _Temporary_buffer<_RandomAccessIter, _T> buf(__first, __last);
  if (buf.begin() == 0)
    __inplace_stable_sort(__first, __last);
  else 
    __stable_sort_adaptive(__first, __last, buf.begin(),
                           _Distance(buf.size()));
}

template <class _RandomAccessIter, class _T, class _Distance, class _Compare>
inline void __stable_sort_aux(_RandomAccessIter __first,
                              _RandomAccessIter __last, _T*, _Distance*,
                              _Compare __comp) {
  _Temporary_buffer<_RandomAccessIter, _T> buf(__first, __last);
  if (buf.begin() == 0)
    __inplace_stable_sort(__first, __last, __comp);
  else 
    __stable_sort_adaptive(__first, __last, buf.begin(),
                           _Distance(buf.size()),
                           __comp);
}

template <class _RandomAccessIter>
inline void stable_sort(_RandomAccessIter __first,
                        _RandomAccessIter __last) {
  __stable_sort_aux(__first, __last,
                    __VALUE_TYPE(__first),
                    __DISTANCE_TYPE(__first));
}

template <class _RandomAccessIter, class _Compare>
inline void stable_sort(_RandomAccessIter __first,
                        _RandomAccessIter __last, _Compare __comp) {
  __stable_sort_aux(__first, __last,
                    __VALUE_TYPE(__first),
                    __DISTANCE_TYPE(__first), 
                    __comp);
}

// partial_sort, partial_sort_copy, and auxiliary functions.

template <class _RandomAccessIter, class _T>
void __partial_sort(_RandomAccessIter __first, _RandomAccessIter __middle,
                    _RandomAccessIter __last, _T*) {
  make_heap(__first, __middle);
  for (_RandomAccessIter __i = __middle; __i < __last; ++__i)
    if (*__i < *__first) 
      __pop_heap(__first, __middle, __i, _T(*__i),
                 __DISTANCE_TYPE(__first));
  sort_heap(__first, __middle);
}

template <class _RandomAccessIter>
inline void partial_sort(_RandomAccessIter __first,
                         _RandomAccessIter __middle,
                         _RandomAccessIter __last) {
  __partial_sort(__first, __middle, __last, __VALUE_TYPE(__first));
}

template <class _RandomAccessIter, class _T, class _Compare>
void __partial_sort(_RandomAccessIter __first, _RandomAccessIter __middle,
                    _RandomAccessIter __last, _T*, _Compare __comp) {
  make_heap(__first, __middle, __comp);
  for (_RandomAccessIter __i = __middle; __i < __last; ++__i)
    if (__comp(*__i, *__first))
      __pop_heap(__first, __middle, __i, _T(*__i), __comp,
                 __DISTANCE_TYPE(__first));
  sort_heap(__first, __middle, __comp);
}

template <class _RandomAccessIter, class _Compare>
inline void partial_sort(_RandomAccessIter __first,
                         _RandomAccessIter __middle,
                         _RandomAccessIter __last, _Compare __comp) {
  __partial_sort(__first, __middle, __last, __VALUE_TYPE(__first), __comp);
}

template <class _InputIter, class _RandomAccessIter, class _Distance,
          class _T>
_RandomAccessIter __partial_sort_copy(_InputIter __first,
                                         _InputIter __last,
                                         _RandomAccessIter __result_first,
                                         _RandomAccessIter __result_last, 
                                         _Distance*, _T*) {
  if (__result_first == __result_last) return __result_last;
  _RandomAccessIter __result_real_last = __result_first;
  while(__first != __last && __result_real_last != __result_last) {
    *__result_real_last = *__first;
    ++__result_real_last;
    ++__first;
  }
  make_heap(__result_first, __result_real_last);
  while (__first != __last) {
    if (*__first < *__result_first) 
      __adjust_heap(__result_first, _Distance(0),
                    _Distance(__result_real_last - __result_first),
                    _T(*__first));
    ++__first;
  }
  sort_heap(__result_first, __result_real_last);
  return __result_real_last;
}

template <class _InputIter, class _RandomAccessIter>
inline _RandomAccessIter
partial_sort_copy(_InputIter __first, _InputIter __last,
                  _RandomAccessIter __result_first,
                  _RandomAccessIter __result_last) {
  return __partial_sort_copy(__first, __last, __result_first, __result_last, 
                             __DISTANCE_TYPE(__result_first),
                             __VALUE_TYPE(__first));
}

template <class _InputIter, class _RandomAccessIter, class _Compare,
          class _Distance, class _T>
_RandomAccessIter __partial_sort_copy(_InputIter __first,
                                         _InputIter __last,
                                         _RandomAccessIter __result_first,
                                         _RandomAccessIter __result_last,
                                         _Compare __comp, _Distance*, _T*) {
  if (__result_first == __result_last) return __result_last;
  _RandomAccessIter __result_real_last = __result_first;
  while(__first != __last && __result_real_last != __result_last) {
    *__result_real_last = *__first;
    ++__result_real_last;
    ++__first;
  }
  make_heap(__result_first, __result_real_last, __comp);
  while (__first != __last) {
    if (__comp(*__first, *__result_first))
      __adjust_heap(__result_first, _Distance(0),
                    _Distance(__result_real_last - __result_first),
                    _T(*__first),
                    __comp);
    ++__first;
  }
  sort_heap(__result_first, __result_real_last, __comp);
  return __result_real_last;
}

template <class _InputIter, class _RandomAccessIter, class _Compare>
inline _RandomAccessIter
partial_sort_copy(_InputIter __first, _InputIter __last,
                  _RandomAccessIter __result_first,
                  _RandomAccessIter __result_last, _Compare __comp) {
  return __partial_sort_copy(__first, __last, __result_first, __result_last,
                             __comp,
                             __DISTANCE_TYPE(__result_first),
                             __VALUE_TYPE(__first));
}

// nth_element() and its auxiliary functions.  

template <class _RandomAccessIter, class _T>
void __nth_element(_RandomAccessIter __first, _RandomAccessIter __nth,
                   _RandomAccessIter __last, _T*) {
  while (__last - __first > 3) {
    _RandomAccessIter __cut =
      __unguarded_partition(__first, __last,
                            _T(__median(*__first,
                                        *(__first + (__last - __first)/2),
                                        *(__last - 1))));
    if (__cut <= __nth)
      __first = __cut;
    else 
      __last = __cut;
  }
  __insertion_sort(__first, __last);
}

template <class _RandomAccessIter>
inline void nth_element(_RandomAccessIter __first, _RandomAccessIter __nth,
                        _RandomAccessIter __last) {
  __nth_element(__first, __nth, __last, __VALUE_TYPE(__first));
}

template <class _RandomAccessIter, class _T, class _Compare>
void __nth_element(_RandomAccessIter __first, _RandomAccessIter __nth,
                   _RandomAccessIter __last, _T*, _Compare __comp) {
  while (__last - __first > 3) {
    _RandomAccessIter __cut =
      __unguarded_partition(__first, __last,
                            _T(__median(*__first,
                                        *(__first + (__last - __first)/2), 
                                        *(__last - 1),
                                        __comp)),
                            __comp);
    if (__cut <= __nth)
      __first = __cut;
    else 
      __last = __cut;
  }
  __insertion_sort(__first, __last, __comp);