"""simple docstring"""





from __future__ import annotations





def     a_					(				_lowerCAmelCase  :			list[int]					):





       '''simple docstring'''

       if not list_of_ints:
              return []

       if min(_lowerCAmelCase					) < 0:
              raise ValueError('All numbers must be positive'					)

       lowercase__      :		Dict          =     max(len(bin(_lowerCAmelCase					)[2:]					) for x in list_of_ints					)
       return _msd_radix_sort(_lowerCAmelCase       ,			_lowerCAmelCase					)





def     a_					(				_lowerCAmelCase  :			list[int]       ,			_lowerCAmelCase  :			int					):





       '''simple docstring'''

       if bit_position == 0 or len(_lowerCAmelCase					) in [0, 1]:
              return list_of_ints

       lowercase__      :		int          =     []
       lowercase__      :		Optional[Any]          =     []
       # Split numbers based on bit at bit_position from the right
       for number in list_of_ints:
              if (number >> (bit_position - 1)) & 1:
                     # number has a one at bit bit_position
                     ones.append(_lowerCAmelCase					)
              else:
                     # number has a zero at bit bit_position
                     zeros.append(_lowerCAmelCase					)

    # recursively split both lists further
       lowercase__      :		List[Any]          =     _msd_radix_sort(_lowerCAmelCase       ,			bit_position - 1					)
       lowercase__      :		List[str]          =     _msd_radix_sort(_lowerCAmelCase       ,			bit_position - 1					)

       # recombine lists
       lowercase__      :		Union[str, Any]          =     zeros
       res.extend(_lowerCAmelCase					)

       return res





def     a_					(				_lowerCAmelCase  :			list[int]					):





       '''simple docstring'''

       lowercase__      :		Dict          =     len(_lowerCAmelCase					)
       if not list_of_ints or length == 1:
              return

       if min(_lowerCAmelCase					) < 0:
              raise ValueError('All numbers must be positive'					)

       lowercase__      :		List[str]          =     max(len(bin(_lowerCAmelCase					)[2:]					) for x in list_of_ints					)
       _msd_radix_sort_inplace(_lowerCAmelCase       ,			_lowerCAmelCase       ,			0       ,			_lowerCAmelCase					)





def     a_					(				_lowerCAmelCase  :			list[int]       ,			_lowerCAmelCase  :			int       ,			_lowerCAmelCase  :			int       ,			_lowerCAmelCase  :			int					):





       '''simple docstring'''

       if bit_position == 0 or end_index - begin_index <= 1:
              return

       bit_position -= 1

       lowercase__      :		Union[str, Any]          =     begin_index
       lowercase__      :		Tuple          =     end_index - 1
       while i <= j:
              lowercase__      :		List[str]          =     False
              if not (list_of_ints[i] >> bit_position) & 1:
                     # found zero at the beginning
                     i += 1
                     lowercase__      :		Any          =     True
              if (list_of_ints[j] >> bit_position) & 1:
                     # found one at the end
                     j -= 1
                     lowercase__      :		Tuple          =     True

              if changed:
                     continue

              lowercase__   ,				lowercase__      :		Optional[Any]          =     list_of_ints[j], list_of_ints[i]
              j -= 1
              if j != i:
                     i += 1

       _msd_radix_sort_inplace(_lowerCAmelCase       ,			_lowerCAmelCase       ,			_lowerCAmelCase       ,			_lowerCAmelCase					)
       _msd_radix_sort_inplace(_lowerCAmelCase       ,			_lowerCAmelCase       ,			_lowerCAmelCase       ,			_lowerCAmelCase					)


if __name__ == "__main__":
       import doctest

       doctest.testmod()


"""simple docstring"""





from ..utils import DummyObject, requires_backends


class 					UpperCAmelCase_     (   metaclass=_a):
      lowerCamelCase__		:   List[str]			  =  ["torch", "transformers", "k_diffusion"]


      def __init__(       self		,      *a		,      **a							)	-> Dict:
             requires_backends(self		,      ['torch', 'transformers', 'k_diffusion']							)


      @classmethod
      def 		_UpperCAmelCase	(       cls		,      *a		,      **a							)	-> Tuple:
             requires_backends(cls		,      ['torch', 'transformers', 'k_diffusion']							)


      @classmethod
      def 		_UpperCAmelCase	(       cls		,      *a		,      **a							)	-> Any:
             requires_backends(cls		,      ['torch', 'transformers', 'k_diffusion']							)

