
'''simple docstring'''





from __future__ import annotations
def 	snake_case_							(				_a  :				list[int]      ):
      if not list_of_ints:
            return []

      if min(_a      ) < 0:
            raise ValueError("All numbers must be positive"      )

      snake_case_    							=				max(len(bin(_a      )[2:]      ) for x in list_of_ints      )
      return _msd_radix_sort(_a			,       _a      )
def 	snake_case_							(				_a  :				list[int]			,       _a  :				int      ):
      if bit_position == 0 or len(_a      ) in [0, 1]:
            return list_of_ints

      snake_case_    							=				[]
      snake_case_    							=				[]
      # 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(_a      )
            else:
                  # number has a zero at bit bit_position
                  zeros.append(_a      )

    # recursively split both lists further
      snake_case_    							=				_msd_radix_sort(_a			,       bit_position - 1      )
      snake_case_    							=				_msd_radix_sort(_a			,       bit_position - 1      )

      # recombine lists
      snake_case_    							=				zeros
      res.extend(_a      )

      return res
def 	snake_case_							(				_a  :				list[int]      ):
      snake_case_    							=				len(_a      )
      if not list_of_ints or length == 1:
            return

      if min(_a      ) < 0:
            raise ValueError("All numbers must be positive"      )

      snake_case_    							=				max(len(bin(_a      )[2:]      ) for x in list_of_ints      )
      _msd_radix_sort_inplace(_a			,       _a			,       0			,       _a      )
def 	snake_case_							(				_a  :				list[int]			,       _a  :				int			,       _a  :				int			,       _a  :				int      ):
      if bit_position == 0 or end_index - begin_index <= 1:
            return

      bit_position -= 1

      snake_case_    							=				begin_index
      snake_case_    							=				end_index - 1
      while i <= j:
            snake_case_    							=				False
            if not (list_of_ints[i] >> bit_position) & 1:
                  # found zero at the beginning
                  i += 1
                  snake_case_    							=				True
            if (list_of_ints[j] >> bit_position) & 1:
                  # found one at the end
                  j -= 1
                  snake_case_    							=				True

            if changed:
                  continue

            snake_case_							,						snake_case_    							=				list_of_ints[j], list_of_ints[i]
            j -= 1
            if j != i:
                  i += 1

      _msd_radix_sort_inplace(_a			,       _a			,       _a			,       _a      )
      _msd_radix_sort_inplace(_a			,       _a			,       _a			,       _a      )


if __name__ == "__main__":
     import doctest

     doctest.testmod()



'''simple docstring'''





from collections import Counter
from functools import total_ordering

from data_structures.heap.heap import Heap



@total_ordering
class 			lowerCAmelCase__ :



  '''simple docstring'''






  def __init__(self	:			Tuple						,			lowerCAmelCase_	:			str						,			lowerCAmelCase_	:			int     ) ->							None:
        snake_case_    							=				word
        snake_case_    							=				count

  def __eq__(self	:			List[Any]						,			lowerCAmelCase_	:			object     ) ->							bool:
        if not isinstance(lowerCAmelCase_						,			lowerCAmelCase_     ):
              return NotImplemented
        return self.count == other.count


  def __lt__(self	:			Tuple						,			lowerCAmelCase_	:			object     ) ->							bool:
        if not isinstance(lowerCAmelCase_						,			lowerCAmelCase_     ):
              return NotImplemented
        return self.count < other.count

def 	snake_case_							(				_a  :				list[str]			,       _a  :				int      ):
      snake_case_    							=				Heap()
      snake_case_    							=				Counter(_a      )
      heap.build_max_heap(
          [WordCount(_a			,       _a      ) for word, count in count_by_word.items()]      )
      return [heap.extract_max().word for _ in range(min(_a			,       len(_a      )      )      )]


if __name__ == "__main__":
     import doctest

     doctest.testmod()

