


'''simple docstring'''





def        _SCREAMING_SNAKE_CASE  (	UpperCamelCase							,   UpperCamelCase      ):



    """simple docstring"""





    _enforce_args(UpperCamelCase							,   UpperCamelCase      )
    if n == 0:
        return 0
    lowerCAmelCase__			:  List[str]											= float("""-inf"""      )
    for i in range(1							,   n + 1      ):
        lowerCAmelCase__			:  Optional[int]											= max(
            UpperCamelCase							,   prices[i - 1] + naive_cut_rod_recursive(n - i							,   UpperCamelCase      )      )

    return max_revue
def        _SCREAMING_SNAKE_CASE  (	UpperCamelCase							,   UpperCamelCase      ):



    """simple docstring"""





    _enforce_args(UpperCamelCase							,   UpperCamelCase      )
    lowerCAmelCase__			:  int											= [float("""-inf"""      ) for _ in range(n + 1      )]
    return _top_down_cut_rod_recursive(UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase      )
def        _SCREAMING_SNAKE_CASE  (	UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase      ):



    """simple docstring"""





    if max_rev[n] >= 0:
        return max_rev[n]
    elif n == 0:
        return 0
    else:
        lowerCAmelCase__			:  Optional[int]											= float("""-inf"""      )
        for i in range(1							,   n + 1      ):
            lowerCAmelCase__			:  Dict											= max(
                UpperCamelCase							,   prices[i - 1] + _top_down_cut_rod_recursive(n - i							,   UpperCamelCase							,   UpperCamelCase      )							,   )

        lowerCAmelCase__			:  Union[str, Any]											= max_revenue

    return max_rev[n]
def        _SCREAMING_SNAKE_CASE  (	UpperCamelCase							,   UpperCamelCase      ):



    """simple docstring"""





    _enforce_args(UpperCamelCase							,   UpperCamelCase      )

    # length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
    # length 0.
    lowerCAmelCase__			:  int											= [float("""-inf"""      ) for _ in range(n + 1      )]
    lowerCAmelCase__			:  int											= 0

    for i in range(1							,   n + 1      ):
        lowerCAmelCase__			:  Optional[int]											= max_rev[i]
        for j in range(1							,   i + 1      ):
            lowerCAmelCase__			:  Optional[int]											= max(UpperCamelCase							,   prices[j - 1] + max_rev[i - j]      )

        lowerCAmelCase__			:  Optional[Any]											= max_revenue_i

    return max_rev[n]
def        _SCREAMING_SNAKE_CASE  (	UpperCamelCase							,   UpperCamelCase      ):



    """simple docstring"""





    if n < 0:
        lowerCAmelCase__			:  List[Any]											= f"""n must be greater than or equal to 0. Got n = {n}"""
        raise ValueError(UpperCamelCase      )

    if n > len(UpperCamelCase      ):
        lowerCAmelCase__			:  List[Any]											= (
            """Each integral piece of rod must have a corresponding price. """
            f"""Got n = {n} but length of prices = {len(UpperCamelCase      )}"""
        )
        raise ValueError(UpperCamelCase      )
def        _SCREAMING_SNAKE_CASE  (	):



    """simple docstring"""





    lowerCAmelCase__			:  List[str]											= [6, 10, 12, 15, 20, 23]
    lowerCAmelCase__			:  Tuple											= len(UpperCamelCase      )

    # the best revenue comes from cutting the rod into 6 pieces, each
    # of length 1 resulting in a revenue of 6 * 6 = 36.
    lowerCAmelCase__			:  int											= 36

    lowerCAmelCase__			:  Tuple											= top_down_cut_rod(UpperCamelCase							,   UpperCamelCase      )
    lowerCAmelCase__			:  Tuple											= bottom_up_cut_rod(UpperCamelCase							,   UpperCamelCase      )
    lowerCAmelCase__			:  Union[str, Any]											= naive_cut_rod_recursive(UpperCamelCase							,   UpperCamelCase      )

    assert expected_max_revenue == max_rev_top_down
    assert max_rev_top_down == max_rev_bottom_up
    assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
 main()







'''simple docstring'''





from ..utils import DummyObject, requires_backends






class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				int           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		Optional[int]:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Optional[Any]           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		str:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				str           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		Optional[Any]:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Union[str, Any]           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		List[Any]:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				int           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		Tuple:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Dict           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		Dict:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Optional[Any]           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		List[str]:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Optional[Any]           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		List[Any]:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Dict           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		Any:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Tuple           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		Union[str, Any]:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Optional[int]           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		List[str]:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Optional[Any]           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		Union[str, Any]:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Optional[int]           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		List[str]:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				List[str]           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		Any:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Tuple           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		List[str]:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Dict           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		List[Any]:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Union[str, Any]           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		List[Any]:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Tuple           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		str:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				List[Any]           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		Optional[int]:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				int           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		Optional[Any]:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Tuple           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		Dict:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				str           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		List[Any]:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Union[str, Any]           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		List[Any]:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				List[str]           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		Any:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Optional[Any]           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		Optional[Any]:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Optional[int]           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		str:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Any           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		int:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				List[Any]           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		List[str]:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Tuple           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		str:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				Optional[Any]           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		Optional[int]:
      requires_backends(self  ,["""sentencepiece"""]				)







class 	lowerCAmelCase_(    metaclass=SCREAMING_SNAKE_CASE_					):
  '''simple docstring'''




  __lowercase							:				List[Any]           =				['''sentencepiece''']




  def __init__(   self  ,*__UpperCAmelCase  ,**__UpperCAmelCase				)   ->		List[Any]:
      requires_backends(self  ,["""sentencepiece"""]				)


