




def SCREAMING_SNAKE_CASE							(			lowercase_					,							lowercase_		)  ->			Union[str, Any]:



       """simple docstring"""

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

       return max_revue







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



       """simple docstring"""

       _enforce_args(__snake_case					,							__snake_case		)
       A__ 					=       [float('''-inf'''		) for _ in range(n + 1		)]
       return _top_down_cut_rod_recursive(__snake_case					,							__snake_case					,							__snake_case		)







def SCREAMING_SNAKE_CASE							(			lowercase_					,							lowercase_					,							lowercase_		)  ->			Any:



       """simple docstring"""

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

              A__ 					=       max_revenue

       return max_rev[n]







def SCREAMING_SNAKE_CASE							(			lowercase_					,							lowercase_		)  ->			Any:



       """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.
       A__ 					=       [float('''-inf'''		) for _ in range(n + 1		)]
       A__ 					=       0

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

              A__ 					=       max_revenue_i

       return max_rev[n]







def SCREAMING_SNAKE_CASE							(			lowercase_					,							lowercase_		)  ->			List[Any]:



       """simple docstring"""

       if n < 0:
              A__ 					=       f"""n must be greater than or equal to 0. Got n = {n}"""
              raise ValueError(__snake_case		)

       if n > len(__snake_case		):
              A__ 					=       (
                  '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 SCREAMING_SNAKE_CASE							(			)  ->			Tuple:



       """simple docstring"""

       A__ 					=       [6, 10, 12, 15, 20, 23]
       A__ 					=       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.
       A__ 					=       36

       A__ 					=       top_down_cut_rod(__snake_case					,							__snake_case		)
       A__ 					=       bottom_up_cut_rod(__snake_case					,							__snake_case		)
       A__ 					=       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()









'''simple docstring'''




from __future__ import annotations






def 			_lowerCAmelCase     (    __snake_case    :					list[int]					,				__snake_case    :					list[int]					,				__snake_case    :					int     )	->	tuple[float, list[float]]:
     __A		:					int						=			list(range(len(__snake_case     )     )     )
     __A		:					Optional[Any]						=			[v / w for v, w in zip(__snake_case					,				__snake_case     )]
     index.sort(key=lambda __snake_case     : ratio[i]					,				reverse=__snake_case     )

     __A		:					float						=			0
     __A		:					list[float]						=			[0] * len(__snake_case     )
     for i in index:
          if weight[i] <= capacity:
               __A		:					Optional[int]						=			1
               max_value += value[i]
               capacity -= weight[i]
          else:
               __A		:					List[Any]						=			capacity / weight[i]
               max_value += value[i] * capacity / weight[i]
               break

     return max_value, fractions


if __name__ == "__main__":
  import doctest

  doctest.testmod()