stl_algo.h

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    ++__first;
  }
  return __out;
}

template <class _InputIter, class _RandomAccessIter, class _Distance>
_RandomAccessIter __random_sample(_InputIter __first, _InputIter __last,
                                  _RandomAccessIter __out,
                                  const _Distance __n)
{
  _Distance __m = 0;
  _Distance __t = __n;
  for ( ; __first != __last && __m < __n; ++__m, ++__first) 
    __out[__m] = *__first;

  while (__first != __last) {
    ++__t;
    _Distance __M = __random_number(__t);
    if (__M < __n)
      __out[__M] = *__first;
    ++__first;
  }

  return __out + __m;
}

template <class _InputIter, class _RandomAccessIter,
          class _RandomNumberGenerator, class _Distance>
_RandomAccessIter __random_sample(_InputIter __first, _InputIter __last,
                                  _RandomAccessIter __out,
                                  _RandomNumberGenerator& __rand,
                                  const _Distance __n)
{
  _Distance __m = 0;
  _Distance __t = __n;
  for ( ; __first != __last && __m < __n; ++__m, ++__first)
    __out[__m] = *__first;

  while (__first != __last) {
    ++__t;
    _Distance __M = __rand(__t);
    if (__M < __n)
      __out[__M] = *__first;
    ++__first;
  }

  return __out + __m;
}

template <class _InputIter, class _RandomAccessIter>
inline _RandomAccessIter
random_sample(_InputIter __first, _InputIter __last,
              _RandomAccessIter __out_first, _RandomAccessIter __out_last) 
{
  return __random_sample(__first, __last,
                         __out_first, __out_last - __out_first);
}


template <class _InputIter, class _RandomAccessIter, 
          class _RandomNumberGenerator>
inline _RandomAccessIter
random_sample(_InputIter __first, _InputIter __last,
              _RandomAccessIter __out_first, _RandomAccessIter __out_last,
              _RandomNumberGenerator& __rand) 
{
  return __random_sample(__first, __last,
                         __out_first, __rand,
                         __out_last - __out_first);
}

// partition, stable_partition, and their auxiliary functions

template <class _ForwardIter, class _Predicate>
_ForwardIter __partition(_ForwardIter __first,
		         _ForwardIter __last,
			 _Predicate   __pred,
			 forward_iterator_tag) {
  while (__first != __last && __pred(*__first)) ++__first;
  if (__first == __last) return __first;

  _ForwardIter __mid = __first;
  while (__mid != __last && !__pred(*__mid)) ++__mid;
  if (__mid == __last) return __first;

  do {
    swap(*__first++, *__mid);
    while (__mid != __last && !__pred(*__mid)) ++__mid;
  }  while (__mid != __last);

  return __first;
}

template <class _BidirectionalIter, class _Predicate>
_BidirectionalIter __partition(_BidirectionalIter __first,
                               _BidirectionalIter __last,
			       _Predicate __pred,
			       bidirectional_iterator_tag) {
  while (true) {
    while (true)
      if (__first == __last)
        return __first;
      else if (__pred(*__first))
        ++__first;
      else
        break;
    --__last;
    while (true)
      if (__first == __last)
        return __first;
      else if (!__pred(*__last))
        --__last;
      else
        break;
    iter_swap(__first, __last);
    ++__first;
  }
}

template <class _ForwardIter, class _Predicate>
inline _ForwardIter partition(_ForwardIter __first,
   			      _ForwardIter __last,
			      _Predicate   __pred) {
  return __partition(__first, __last, __pred, __ITERATOR_CATEGORY(__first));
}


template <class _ForwardIter, class _Predicate, class _Distance>
_ForwardIter __inplace_stable_partition(_ForwardIter __first,
                                        _ForwardIter __last,
                                        _Predicate __pred, _Distance __len) {
  if (__len == 1)
    return __pred(*__first) ? __last : __first;
  _ForwardIter __middle = __first;
  advance(__middle, __len / 2);
  return rotate(__inplace_stable_partition(__first, __middle, __pred, 
                                           __len / 2),
                __middle,
                __inplace_stable_partition(__middle, __last, __pred,
                                           __len - __len / 2));
}

template <class _ForwardIter, class _Pointer, class _Predicate, 
          class _Distance>
_ForwardIter __stable_partition_adaptive(_ForwardIter __first,
                                         _ForwardIter __last,
                                         _Predicate __pred, _Distance __len,
                                         _Pointer __buffer,
                                         _Distance __buffer_size) 
{
  if (__len <= __buffer_size) {
    _ForwardIter __result1 = __first;
    _Pointer __result2 = __buffer;
    for ( ; __first != __last ; ++__first)
      if (__pred(*__first)) {
        *__result1 = *__first;
        ++__result1;
      }
      else {
        *__result2 = *__first;
        ++__result2;
      }
    copy(__buffer, __result2, __result1);
    return __result1;
  }
  else {
    _ForwardIter __middle = __first;
    advance(__middle, __len / 2);
    return __rotate(__stable_partition_adaptive(
                          __first, __middle, __pred,
                          __len / 2, __buffer, __buffer_size),
                    __middle,
                    __stable_partition_adaptive(
                          __middle, __last, __pred,
                          __len - __len / 2, __buffer, __buffer_size));
  }
}

template <class _ForwardIter, class _Predicate, class _T, class _Distance>
inline _ForwardIter __stable_partition_aux(_ForwardIter __first,
                                           _ForwardIter __last, 
                                           _Predicate __pred, _T*, _Distance*)
{
  _Temporary_buffer<_ForwardIter, _T> __buf(__first, __last);
  if (__buf.size() > 0)
    return __stable_partition_adaptive(__first, __last, __pred,
                                       _Distance(__buf.requested_size()),
                                       __buf.begin(), __buf.size());
  else
    return __inplace_stable_partition(__first, __last, __pred, 
                                      _Distance(__buf.requested_size()));
}

template <class _ForwardIter, class _Predicate>
inline _ForwardIter stable_partition(_ForwardIter __first,
                                     _ForwardIter __last, 
                                     _Predicate __pred) {
  if (__first == __last)
    return __first;
  else
    return __stable_partition_aux(__first, __last, __pred,
                                  __VALUE_TYPE(__first),
                                  __DISTANCE_TYPE(__first));
}

template <class _RandomAccessIter, class _T>
_RandomAccessIter __unguarded_partition(_RandomAccessIter __first, 
                                        _RandomAccessIter __last, 
                                        _T __pivot) 
{
  while (true) {
    while (*__first < __pivot)
      ++__first;
    --__last;
    while (__pivot < *__last)
      --__last;
    if (!(__first < __last))
      return __first;
    iter_swap(__first, __last);
    ++__first;
  }
}    

template <class _RandomAccessIter, class _T, class _Compare>
_RandomAccessIter __unguarded_partition(_RandomAccessIter __first, 
                                        _RandomAccessIter __last, 
                                        _T __pivot, _Compare __comp) 
{
  while (true) {
    while (__comp(*__first, __pivot))
      ++__first;
    --__last;
    while (__comp(__pivot, *__last))
      --__last;
    if (!(__first < __last))
      return __first;
    iter_swap(__first, __last);
    ++__first;
  }
}

const int __stl_threshold = 16;

// sort() and its auxiliary functions. 

template <class _RandomAccessIter, class _T>
void __unguarded_linear_insert(_RandomAccessIter __last, _T __val) {
  _RandomAccessIter __next = __last;
  --__next;
  while (__val < *__next) {
    *__last = *__next;
    __last = __next;
    --__next;
  }
  *__last = __val;
}

template <class _RandomAccessIter, class _T, class _Compare>
void __unguarded_linear_insert(_RandomAccessIter __last, _T __val, 
                               _Compare __comp) {
  _RandomAccessIter __next = __last;
  --__next;  
  while (__comp(__val, *__next)) {
    *__last = *__next;
    __last = __next;
    --__next;
  }
  *__last = __val;
}

template <class _RandomAccessIter, class _T>
inline void __linear_insert(_RandomAccessIter __first, 
                            _RandomAccessIter __last, _T*) {
  _T __val = *__last;
  if (__val < *__first) {
    copy_backward(__first, __last, __last + 1);
    *__first = __val;
  }
  else
    __unguarded_linear_insert(__last, __val);
}

template <class _RandomAccessIter, class _T, class _Compare>
inline void __linear_insert(_RandomAccessIter __first, 
                            _RandomAccessIter __last, _T*, _Compare __comp) {
  _T __val = *__last;
  if (__comp(__val, *__first)) {
    copy_backward(__first, __last, __last + 1);
    *__first = __val;
  }
  else
    __unguarded_linear_insert(__last, __val, __comp);
}

template <class _RandomAccessIter>
void __insertion_sort(_RandomAccessIter __first, _RandomAccessIter __last) {
  if (__first == __last) return; 
  for (_RandomAccessIter __i = __first + 1; __i != __last; ++__i)
    __linear_insert(__first, __i, __VALUE_TYPE(__first));
}

template <class _RandomAccessIter, class _Compare>
void __insertion_sort(_RandomAccessIter __first,
                      _RandomAccessIter __last, _Compare __comp) {
  if (__first == __last) return;
  for (_RandomAccessIter __i = __first + 1; __i != __last; ++__i)
    __linear_insert(__first, __i, __VALUE_TYPE(__first), __comp);
}

template <class _RandomAccessIter, class _T>
void __unguarded_insertion_sort_aux(_RandomAccessIter __first, 
                                    _RandomAccessIter __last, _T*) {
  for (_RandomAccessIter __i = __first; __i != __last; ++__i)
    __unguarded_linear_insert(__i, _T(*__i));
}

template <class _RandomAccessIter>
inline void __unguarded_insertion_sort(_RandomAccessIter __first, 
                                _RandomAccessIter __last) {
  __unguarded_insertion_sort_aux(__first, __last, __VALUE_TYPE(__first));
}

template <class _RandomAccessIter, class _T, class _Compare>
void __unguarded_insertion_sort_aux(_RandomAccessIter __first, 
                                    _RandomAccessIter __last,
                                    _T*, _Compare __comp) {
  for (_RandomAccessIter __i = __first; __i != __last; ++__i)
    __unguarded_linear_insert(__i, _T(*__i), __comp);
}

template <class _RandomAccessIter, class _Compare>
inline void __unguarded_insertion_sort(_RandomAccessIter __first, 
                                       _RandomAccessIter __last,
                                       _Compare __comp) {
  __unguarded_insertion_sort_aux(__first, __last, __VALUE_TYPE(__first),
                                 __comp);
}

template <class _RandomAccessIter>
void __final_insertion_sort(_RandomAccessIter __first, 
                            _RandomAccessIter __last) {
  if (__last - __first > __stl_threshold) {
    __insertion_sort(__first, __first + __stl_threshold);
    __unguarded_insertion_sort(__first + __stl_threshold, __last);
  }
  else
    __insertion_sort(__first, __last);
}

template <class _RandomAccessIter, class _Compare>
void __final_insertion_sort(_RandomAccessIter __first, 
                            _RandomAccessIter __last, _Compare __comp) {
  if (__last - __first > __stl_threshold) {
    __insertion_sort(__first, __first + __stl_threshold, __comp);
    __unguarded_insertion_sort(__first + __stl_threshold, __last, __comp);
  }
  else
    __insertion_sort(__first, __last, __comp);
}

template <class _Size>
inline _Size __lg(_Size __n) {
  _Size __k;
  for (__k = 0; __n != 1; __n >>= 1) ++__k;
  return __k;
}

template <class _RandomAccessIter, class _T, class _Size>
void __introsort_loop(_RandomAccessIter __first,
                      _RandomAccessIter __last, _T*,
                      _Size __depth_limit)
{
  while (__last - __first > __stl_threshold) {
    if (__depth_limit == 0) {
      partial_sort(__first, __last, __last);
      return;
    }
    --__depth_limit;
    _RandomAccessIter __cut =
      __unguarded_partition(__first, __last,
                            _T(__median(*__first,
                                        *(__first + (__last - __first)/2),
                                        *(__last - 1))));
    __introsort_loop(__cut, __last, (_T*) 0, __depth_limit);
    __last = __cut;
  }
}

template <class _RandomAccessIter, class _T, class _Size, class _Compare>
void __introsort_loop(_RandomAccessIter __first,
                      _RandomAccessIter __last, _T*,
                      _Size __depth_limit, _Compare __comp)
{
  while (__last - __first > __stl_threshold) {
    if (__depth_limit == 0) {
      partial_sort(__first, __last, __last, __comp);
      return;
    }
    --__depth_limit;
    _RandomAccessIter __cut =
      __unguarded_partition(__first, __last,
                            _T(__median(*__first,
                                        *(__first + (__last - __first)/2),