






'''simple docstring'''



def 							lowercase_				(    __A :       int					,      __A :       list			)       ->      Union[str, Any]:



 """simple docstring"""




 _enforce_args(__A					,      __A			)
 if n == 0:
  return 0
 lowercase					:   List[str]				  =float('''-inf'''			)
 for i in range(1					,      n + 1			):
  lowercase					:   List[Any]				  =max(
      __A					,      prices[i - 1] + naive_cut_rod_recursive(n - i					,      __A			)			)

 return max_revue


def 							lowercase_				(    __A :       int					,      __A :       list			)       ->      Dict:



 """simple docstring"""




 _enforce_args(__A					,      __A			)
 lowercase					:   Any				  =[float('''-inf'''			) for _ in range(n + 1			)]
 return _top_down_cut_rod_recursive(__A					,      __A					,      __A			)


def 							lowercase_				(    __A :       int					,      __A :       list					,      __A :       list			)       ->      Optional[int]:



 """simple docstring"""




 if max_rev[n] >= 0:
  return max_rev[n]
 elif n == 0:
  return 0
 else:
  lowercase					:   Optional[int]				  =float('''-inf'''			)
  for i in range(1					,      n + 1			):
   lowercase					:   List[str]				  =max(
       __A					,      prices[i - 1] + _top_down_cut_rod_recursive(n - i					,      __A					,      __A			)					,      )

  lowercase					:   List[str]				  =max_revenue

 return max_rev[n]


def 							lowercase_				(    __A :       int					,      __A :       list			)       ->      Optional[Any]:



 """simple docstring"""




 _enforce_args(__A					,      __A			)

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

 for i in range(1					,      n + 1			):
  lowercase					:   int				  =max_rev[i]
  for j in range(1					,      i + 1			):
   lowercase					:   Union[str, Any]				  =max(__A					,      prices[j - 1] + max_rev[i - j]			)

  lowercase					:   Union[str, Any]				  =max_revenue_i

 return max_rev[n]


def 							lowercase_				(    __A :       int					,      __A :       list			)       ->      Tuple:



 """simple docstring"""




 if n < 0:
  lowercase					:   List[str]				  =F'n must be greater than or equal to 0. Got n = {n}'
  raise ValueError(__A			)

 if n > len(__A			):
  lowercase					:   List[Any]				  =(
      '''Each integral piece of rod must have a corresponding price. '''
      F'Got n = {n} but length of prices = {len(__A			)}'
  )
  raise ValueError(__A			)


def 							lowercase_				(    )       ->      Tuple:



 """simple docstring"""




 lowercase					:   str				  =[6, 1_0, 1_2, 1_5, 2_0, 2_3]
 lowercase					:   Optional[Any]				  =len(__A			)

 # the best revenue comes from cutting the rod into 6 pieces, each
 # of length 1 resulting in a revenue of 6 * 6 = 36.
 lowercase					:   int				  =3_6

 lowercase					:   str				  =top_down_cut_rod(__A					,      __A			)
 lowercase					:   int				  =bottom_up_cut_rod(__A					,      __A			)
 lowercase					:   str				  =naive_cut_rod_recursive(__A					,      __A			)

 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 typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available


SCREAMING_SNAKE_CASE						=	{
    'configuration_m2m_100': ['M2M_100_PRETRAINED_CONFIG_ARCHIVE_MAP', 'M2M100Config', 'M2M100OnnxConfig'],
    'tokenization_m2m_100': ['M2M100Tokenizer'],
}


try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      SCREAMING_SNAKE_CASE						=	[
          'M2M_100_PRETRAINED_MODEL_ARCHIVE_LIST',
          'M2M100ForConditionalGeneration',
          'M2M100Model',
          'M2M100PreTrainedModel',
      ]


if TYPE_CHECKING:
      from .configuration_mam_aaa import M2M_100_PRETRAINED_CONFIG_ARCHIVE_MAP, MaMaaaConfig, MaMaaaOnnxConfig
      from .tokenization_mam_aaa import MaMaaaTokenizer

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_mam_aaa import (
                M2M_100_PRETRAINED_MODEL_ARCHIVE_LIST,
                MaMaaaForConditionalGeneration,
                MaMaaaModel,
                MaMaaaPreTrainedModel,
            )


else:
      import sys

      SCREAMING_SNAKE_CASE						=	_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)



