




def     _SCREAMING_SNAKE_CASE    (							lowercase			: int			,							lowercase			: list  ):


      '''simple docstring'''



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

      return max_revue

def     _SCREAMING_SNAKE_CASE    (							lowercase			: int			,							lowercase			: list  ):


      '''simple docstring'''



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

def     _SCREAMING_SNAKE_CASE    (							lowercase			: int			,							lowercase			: list			,							lowercase			: list  ):


      '''simple docstring'''



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

            lowerCamelCase_	  =					max_revenue

      return max_rev[n]

def     _SCREAMING_SNAKE_CASE    (							lowercase			: int			,							lowercase			: list  ):


      '''simple docstring'''



      _enforce_args(lowercase			,							lowercase  )

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

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

            lowerCamelCase_	  =					max_revenue_i

      return max_rev[n]

def     _SCREAMING_SNAKE_CASE    (							lowercase			: int			,							lowercase			: list  ):


      '''simple docstring'''



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

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

def     _SCREAMING_SNAKE_CASE    (							):


      '''simple docstring'''



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

      lowerCamelCase_	  =					top_down_cut_rod(lowercase			,							lowercase  )
      lowerCamelCase_	  =					bottom_up_cut_rod(lowercase			,							lowercase  )
      lowerCamelCase_	  =					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()









def     _SCREAMING_SNAKE_CASE    (							lowercase			: list[int]			,							lowercase			: list[int]  ):


      '''simple docstring'''



      lowerCamelCase_	  =					len(lowercase  )
      print('The following activities are selected:'  )

      # The first activity is always selected
      lowerCamelCase_	  =					0
      print(lowercase			,							end=','  )

      # Consider rest of the activities
      for j in range(lowercase  ):
            # If this activity has start time greater than
            # or equal to the finish time of previously
            # selected activity, then select it
            if start[j] >= finish[i]:
                  print(lowercase			,							end=','  )
                  lowerCamelCase_	  =					j


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 lowerCamelCase       :	Tuple									=     [1, 3, 0, 5, 8, 5]
 lowerCamelCase       :	int									=     [2, 4, 6, 7, 9, 9]
 print_max_activities(start, finish)



