





'''simple docstring'''
def 				lowercase__   (   __lowercase						:  int				,  __lowercase						:  list     ) ->      int:



       """simple docstring"""






       _enforce_args(__lowercase				,  __lowercase     )
       if n == 0:
              return 0
       __UpperCamelCase       =  float('-inf'     )
       for i in range(1				,  n + 1     ):
              __UpperCamelCase       =  max(
                  __lowercase				,  prices[i - 1] + naive_cut_rod_recursive(n - i				,  __lowercase     )     )

       return max_revue
def 				lowercase__   (   __lowercase						:  int				,  __lowercase						:  list     ) ->      Union[str, Any]:



       """simple docstring"""






       _enforce_args(__lowercase				,  __lowercase     )
       __UpperCamelCase       =  [float('-inf'     ) for _ in range(n + 1     )]
       return _top_down_cut_rod_recursive(__lowercase				,  __lowercase				,  __lowercase     )
def 				lowercase__   (   __lowercase						:  int				,  __lowercase						:  list				,  __lowercase						:  list     ) ->      Union[str, Any]:



       """simple docstring"""






       if max_rev[n] >= 0:
              return max_rev[n]
       elif n == 0:
              return 0
       else:
              __UpperCamelCase       =  float('-inf'     )
              for i in range(1				,  n + 1     ):
                     __UpperCamelCase       =  max(
                         __lowercase				,  prices[i - 1] + _top_down_cut_rod_recursive(n - i				,  __lowercase				,  __lowercase     )				,  )

              __UpperCamelCase       =  max_revenue

       return max_rev[n]
def 				lowercase__   (   __lowercase						:  int				,  __lowercase						:  list     ) ->      str:



       """simple docstring"""






       _enforce_args(__lowercase				,  __lowercase     )

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

       for i in range(1				,  n + 1     ):
              __UpperCamelCase       =  max_rev[i]
              for j in range(1				,  i + 1     ):
                     __UpperCamelCase       =  max(__lowercase				,  prices[j - 1] + max_rev[i - j]     )

              __UpperCamelCase       =  max_revenue_i

       return max_rev[n]
def 				lowercase__   (   __lowercase						:  int				,  __lowercase						:  list     ) ->      Optional[int]:



       """simple docstring"""






       if n < 0:
              __UpperCamelCase       =  F'''n must be greater than or equal to 0. Got n = {n}'''
              raise ValueError(__lowercase     )

       if n > len(__lowercase     ):
              __UpperCamelCase       =  (
                  """Each integral piece of rod must have a corresponding price. """
                  F'''Got n = {n} but length of prices = {len(__lowercase     )}'''
              )
              raise ValueError(__lowercase     )
def 				lowercase__   (   ) ->      Optional[int]:



       """simple docstring"""






       __UpperCamelCase       =  [6, 10, 12, 15, 20, 23]
       __UpperCamelCase       =  len(__lowercase     )

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

       __UpperCamelCase       =  top_down_cut_rod(__lowercase				,  __lowercase     )
       __UpperCamelCase       =  bottom_up_cut_rod(__lowercase				,  __lowercase     )
       __UpperCamelCase       =  naive_cut_rod_recursive(__lowercase				,  __lowercase     )

       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()








from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


UpperCAmelCase_ :						str      =      {'''configuration_opt''': ['''OPT_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''OPTConfig''']}

try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	UpperCAmelCase_ :						Tuple      =      [
	    '''OPT_PRETRAINED_MODEL_ARCHIVE_LIST''',
	    '''OPTForCausalLM''',
	    '''OPTModel''',
	    '''OPTPreTrainedModel''',
	    '''OPTForSequenceClassification''',
	    '''OPTForQuestionAnswering''',
	]

try:
	if not is_tf_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	UpperCAmelCase_ :						Any      =      ['''TFOPTForCausalLM''', '''TFOPTModel''', '''TFOPTPreTrainedModel''']

try:
	if not is_flax_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	UpperCAmelCase_ :						Optional[Any]      =      [
	    '''FlaxOPTForCausalLM''',
	    '''FlaxOPTModel''',
	    '''FlaxOPTPreTrainedModel''',
	]


if TYPE_CHECKING:
	from .configuration_opt import OPT_PRETRAINED_CONFIG_ARCHIVE_MAP, OPTConfig

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_opt import (
		    OPT_PRETRAINED_MODEL_ARCHIVE_LIST,
		    OPTForCausalLM,
		    OPTForQuestionAnswering,
		    OPTForSequenceClassification,
		    OPTModel,
		    OPTPreTrainedModel,
		)

	try:
		if not is_tf_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_tf_opt import TFOPTForCausalLM, TFOPTModel, TFOPTPreTrainedModel

	try:
		if not is_flax_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_flax_opt import FlaxOPTForCausalLM, FlaxOPTModel, FlaxOPTPreTrainedModel

else:
	import sys

	UpperCAmelCase_ :						List[Any]      =      _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)
