






'''simple docstring'''



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



 """simple docstring"""




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

 return max_revue


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



 """simple docstring"""




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


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



 """simple docstring"""




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

  lowercase       : Union[str, Any]						=max_revenue

 return max_rev[n]


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



 """simple docstring"""




 _enforce_args(__A       ,   __A      )

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

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

  lowercase       : str						=max_revenue_i

 return max_rev[n]


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



 """simple docstring"""




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

 if n > len(__A      ):
  lowercase       : Optional[int]						=(
      '''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_					(     )							->   Optional[int]:



 """simple docstring"""




 lowercase       : Optional[Any]						=[6, 1_0, 1_2, 1_5, 2_0, 2_3]
 lowercase       : Union[str, 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       : str						=3_6

 lowercase       : Dict						=top_down_cut_rod(__A       ,   __A      )
 lowercase       : Dict						=bottom_up_cut_rod(__A       ,   __A      )
 lowercase       : Union[str, Any]						=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 ..utils import DummyObject, requires_backends
class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Dict  ,   *UpperCAmelCase      :		List[Any]  ,   **UpperCAmelCase      :		Union[str, Any]		)	->	List[Any]:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Any  ,   *UpperCAmelCase      :		Dict  ,   **UpperCAmelCase      :		List[str]		)	->	List[Any]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Dict  ,   *UpperCAmelCase      :		str  ,   **UpperCAmelCase      :		Any		)	->	Any:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Union[str, Any]  ,   *UpperCAmelCase      :		Optional[Any]  ,   **UpperCAmelCase      :		str		)	->	Optional[int]:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Tuple  ,   *UpperCAmelCase      :		Any  ,   **UpperCAmelCase      :		List[Any]		)	->	int:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		List[Any]  ,   *UpperCAmelCase      :		Union[str, Any]  ,   **UpperCAmelCase      :		List[str]		)	->	List[Any]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Any  ,   *UpperCAmelCase      :		int  ,   **UpperCAmelCase      :		Optional[Any]		)	->	Any:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		str  ,   *UpperCAmelCase      :		Tuple  ,   **UpperCAmelCase      :		Union[str, Any]		)	->	Optional[int]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Optional[int]  ,   *UpperCAmelCase      :		Dict  ,   **UpperCAmelCase      :		Optional[int]		)	->	List[str]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Union[str, Any]  ,   *UpperCAmelCase      :		Optional[Any]  ,   **UpperCAmelCase      :		int		)	->	Optional[int]:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Tuple  ,   *UpperCAmelCase      :		Any  ,   **UpperCAmelCase      :		Optional[int]		)	->	List[Any]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		int  ,   *UpperCAmelCase      :		int  ,   **UpperCAmelCase      :		Dict		)	->	Optional[Any]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Optional[int]  ,   *UpperCAmelCase      :		Dict  ,   **UpperCAmelCase      :		Union[str, Any]		)	->	List[str]:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		str  ,   *UpperCAmelCase      :		Optional[int]  ,   **UpperCAmelCase      :		List[str]		)	->	str:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Dict  ,   *UpperCAmelCase      :		Union[str, Any]  ,   **UpperCAmelCase      :		List[Any]		)	->	Dict:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Union[str, Any]  ,   *UpperCAmelCase      :		Any  ,   **UpperCAmelCase      :		Union[str, Any]		)	->	str:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Optional[Any]  ,   *UpperCAmelCase      :		Optional[Any]  ,   **UpperCAmelCase      :		Optional[Any]		)	->	str:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Optional[int]  ,   *UpperCAmelCase      :		Union[str, Any]  ,   **UpperCAmelCase      :		Dict		)	->	Dict:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		int  ,   *UpperCAmelCase      :		List[Any]  ,   **UpperCAmelCase      :		Tuple		)	->	Union[str, Any]:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Any  ,   *UpperCAmelCase      :		int  ,   **UpperCAmelCase      :		Optional[Any]		)	->	str:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Union[str, Any]  ,   *UpperCAmelCase      :		List[str]  ,   **UpperCAmelCase      :		List[str]		)	->	Optional[Any]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Union[str, Any]  ,   *UpperCAmelCase      :		Union[str, Any]  ,   **UpperCAmelCase      :		List[str]		)	->	List[Any]:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Optional[Any]  ,   *UpperCAmelCase      :		Optional[Any]  ,   **UpperCAmelCase      :		Any		)	->	List[Any]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Dict  ,   *UpperCAmelCase      :		Any  ,   **UpperCAmelCase      :		Optional[Any]		)	->	List[Any]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Optional[int]  ,   *UpperCAmelCase      :		Optional[int]  ,   **UpperCAmelCase      :		Any		)	->	Any:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Tuple  ,   *UpperCAmelCase      :		List[str]  ,   **UpperCAmelCase      :		Optional[int]		)	->	List[str]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Union[str, Any]  ,   *UpperCAmelCase      :		Any  ,   **UpperCAmelCase      :		int		)	->	Tuple:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Optional[int]  ,   *UpperCAmelCase      :		Union[str, Any]  ,   **UpperCAmelCase      :		Dict		)	->	int:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		List[str]  ,   *UpperCAmelCase      :		Dict  ,   **UpperCAmelCase      :		Dict		)	->	List[Any]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		str  ,   *UpperCAmelCase      :		Optional[Any]  ,   **UpperCAmelCase      :		str		)	->	int:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Optional[int]  ,   *UpperCAmelCase      :		Any  ,   **UpperCAmelCase      :		Optional[int]		)	->	Optional[int]:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Optional[int]  ,   *UpperCAmelCase      :		Dict  ,   **UpperCAmelCase      :		Optional[Any]		)	->	Dict:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		str  ,   *UpperCAmelCase      :		str  ,   **UpperCAmelCase      :		Any		)	->	int:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Optional[int]  ,   *UpperCAmelCase      :		str  ,   **UpperCAmelCase      :		Any		)	->	Optional[int]:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Optional[int]  ,   *UpperCAmelCase      :		Tuple  ,   **UpperCAmelCase      :		Any		)	->	Dict:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Optional[int]  ,   *UpperCAmelCase      :		Optional[int]  ,   **UpperCAmelCase      :		Optional[Any]		)	->	Dict:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)





class UpperCAmelCase_       (     metaclass=__A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''flax''']






      def __init__(			self      :		Optional[Any]  ,   *UpperCAmelCase      :		str  ,   **UpperCAmelCase      :		int		)	->	Tuple:


       '''simple docstring'''

       requires_backends(self  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Dict  ,   *UpperCAmelCase      :		List[Any]  ,   **UpperCAmelCase      :		Optional[int]		)	->	str:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)






      @classmethod
      def 					A__   (			cls      :		Union[str, Any]  ,   *UpperCAmelCase      :		List[Any]  ,   **UpperCAmelCase      :		Union[str, Any]		)	->	Union[str, Any]:


       '''simple docstring'''

       requires_backends(cls  ,   ['''flax''']		)



