


def 	__lowercase		(  _UpperCamelCase,			_UpperCamelCase   )			->Union[str, Any]:







      """simple docstring"""

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

      return max_revue




def 	__lowercase		(  _UpperCamelCase,			_UpperCamelCase   )			->Any:







      """simple docstring"""

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




def 	__lowercase		(  _UpperCamelCase,			_UpperCamelCase,			_UpperCamelCase   )			->str:







      """simple docstring"""

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

            lowercase	:      Tuple          =						max_revenue

      return max_rev[n]




def 	__lowercase		(  _UpperCamelCase,			_UpperCamelCase   )			->List[str]:







      """simple docstring"""

      _enforce_args(snake_case_,			snake_case_   )

      # 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	:      Any          =						0

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

            lowercase	:      int          =						max_revenue_i

      return max_rev[n]




def 	__lowercase		(  _UpperCamelCase,			_UpperCamelCase   )			->List[str]:







      """simple docstring"""

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

      if n > len(snake_case_   ):
            lowercase	:      Any          =						(
                """Each integral piece of rod must have a corresponding price. """
                f"""Got n = {n} but length of prices = {len(snake_case_   )}"""
            )
            raise ValueError(snake_case_   )




def 	__lowercase		(  )			->List[Any]:







      """simple docstring"""

      lowercase	:      Tuple          =						[6, 10, 12, 15, 20, 23]
      lowercase	:      List[Any]          =						len(snake_case_   )

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

      lowercase	:      List[Any]          =						top_down_cut_rod(snake_case_,			snake_case_   )
      lowercase	:      List[Any]          =						bottom_up_cut_rod(snake_case_,			snake_case_   )
      lowercase	:      Dict          =						naive_cut_rod_recursive(snake_case_,			snake_case_   )

      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 __future__ import annotations

import numpy as np







def 				lowerCAmelCase_	(     snake_case_     ):
      return np.maximum(0,snake_case_     )


if __name__ == "__main__":
  print(np.array(relu([-1, 0, 5])))  # --> [0, 0, 5]

