stl_algo.h

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  return __rotate(__first, __middle, __last,
                  __DISTANCE_TYPE(__first),
                  __ITERATOR_CATEGORY(__first));
}

template <class _ForwardIter, class _OutputIter>
_OutputIter rotate_copy(_ForwardIter __first, _ForwardIter __middle,
                            _ForwardIter __last, _OutputIter __result) {
  return copy(__first, __middle, copy(__middle, __last, __result));
}

// Return a random number in the range [0, __n).  This function encapsulates
// whether we're using rand (part of the standard C library) or lrand48
// (not standard, but a much better choice whenever it's available).

template <class _Distance>
inline _Distance __random_number(_Distance __n) {
#ifdef __STL_NO_DRAND48
  return rand() % __n;
#else
  return lrand48() % __n;
#endif
}

// random_shuffle

template <class _RandomAccessIter>
inline void random_shuffle(_RandomAccessIter __first,
                           _RandomAccessIter __last) {
  if (__first == __last) return;
  for (_RandomAccessIter __i = __first + 1; __i != __last; ++__i)
    iter_swap(__i, __first + __random_number((__i - __first) + 1));
}

template <class _RandomAccessIter, class _RandomNumberGenerator>
void random_shuffle(_RandomAccessIter __first, _RandomAccessIter __last,
                    _RandomNumberGenerator& __rand) {
  if (__first == __last) return;
  for (_RandomAccessIter __i = __first + 1; __i != __last; ++__i)
    iter_swap(__i, __first + __rand((__i - __first) + 1));
}

// random_sample and random_sample_n (extensions, not part of the standard).

template <class _ForwardIter, class _OutputIter, class _Distance>
_OutputIter random_sample_n(_ForwardIter __first, _ForwardIter __last,
                            _OutputIter __out, const _Distance __n)
{
  _Distance __remaining = 0;
  distance(__first, __last, __remaining);
  _Distance __m = min(__n, __remaining);

  while (__m > 0) {
    if (__random_number(__remaining) < __m) {
      *__out = *__first;
      ++__out;
      --__m;
    }

    --__remaining;
    ++__first;
  }
  return __out;
}

template <class _ForwardIter, class _OutputIter, class _Distance,
          class _RandomNumberGenerator>
_OutputIter random_sample_n(_ForwardIter __first, _ForwardIter __last,
                            _OutputIter __out, const _Distance __n,
                            _RandomNumberGenerator& __rand)
{
  _Distance __remaining = 0;
  distance(__first, __last, __remaining);
  _Distance __m = min(__n, __remaining);

  while (__m > 0) {
    if (__rand(__remaining) < __m) {
      *__out = *__first;
      ++__out;
      --__m;
    }

    --__remaining;
    ++__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) {
  if (__first == __last) return __first;

  while (__pred(*__first))
    if (++__first == __last) return __first;

  _ForwardIter __next = __first;

  while (++__next != __last)
    if (__pred(*__next)) {
      swap(*__first, *__next);
      ++__first;
    }

  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 _Tp, class _Distance>
inline _ForwardIter
__stable_partition_aux(_ForwardIter __first, _ForwardIter __last, 
                       _Predicate __pred, _Tp*, _Distance*)
{
  _Temporary_buffer<_ForwardIter, _Tp> __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 _Tp>
_RandomAccessIter __unguarded_partition(_RandomAccessIter __first, 
                                        _RandomAccessIter __last, 
                                        _Tp __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 _Tp, class _Compare>
_RandomAccessIter __unguarded_partition(_RandomAccessIter __first, 
                                        _RandomAccessIter __last, 
                                        _Tp __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 _Tp>
void __unguarded_linear_insert(_RandomAccessIter __last, _Tp __val) {
  _RandomAccessIter __next = __last;
  --__next;
  while (__val < *__next) {
    *__last = *__next;
    __last = __next;
    --__next;
  }
  *__last = __val;
}

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

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

template <class _RandomAccessIter, class _Tp, class _Compare>
inline void __linear_insert(_RandomAccessIter __first, 
                            _RandomAccessIter __last, _Tp*, _Compare __comp) {
  _Tp __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 _Tp>
void __unguarded_insertion_sort_aux(_RandomAccessIter __first, 
                                    _RandomAccessIter __last, _Tp*) {
  for (_RandomAccessIter __i = __first; __i != __last; ++__i)
    __unguarded_linear_insert(__i, _Tp(*__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 _Tp, class _Compare>
void __unguarded_insertion_sort_aux(_RandomAccessIter __first, 
                                    _RandomAccessIter __last,
                                    _Tp*, _Compare __comp) {