



"""simple docstring"""







def   lowerCAmelCase__			(     lowerCamelCase__				,      lowerCamelCase__			) ->							Tuple:
							_enforce_args(lowerCamelCase__				,      lowerCamelCase__			)
							if n == 0:
														return 0
							A         =					float('-inf'			)
							for i in range(1				,      n + 1			):
														A         =					max(
														    lowerCamelCase__				,      prices[i - 1] + naive_cut_rod_recursive(n - i				,      lowerCamelCase__			)			)

							return max_revue

def   lowerCAmelCase__			(     lowerCamelCase__				,      lowerCamelCase__			) ->							Any:
							_enforce_args(lowerCamelCase__				,      lowerCamelCase__			)
							A         =					[float('-inf'			) for _ in range(n + 1			)]
							return _top_down_cut_rod_recursive(lowerCamelCase__				,      lowerCamelCase__				,      lowerCamelCase__			)

def   lowerCAmelCase__			(     lowerCamelCase__				,      lowerCamelCase__				,      lowerCamelCase__			) ->							Dict:
							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(
																					    lowerCamelCase__				,      prices[i - 1] + _top_down_cut_rod_recursive(n - i				,      lowerCamelCase__				,      lowerCamelCase__			)				,      )

														A         =					max_revenue

							return max_rev[n]

def   lowerCAmelCase__			(     lowerCamelCase__				,      lowerCamelCase__			) ->							str:
							_enforce_args(lowerCamelCase__				,      lowerCamelCase__			)

							# 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(lowerCamelCase__				,      prices[j - 1] + max_rev[i - j]			)

														A         =					max_revenue_i

							return max_rev[n]

def   lowerCAmelCase__			(     lowerCamelCase__				,      lowerCamelCase__			) ->							Dict:
							if n < 0:
														A         =					f"""n must be greater than or equal to 0. Got n = {n}"""
														raise ValueError(lowerCamelCase__			)

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

def   lowerCAmelCase__			(     ) ->							Union[str, Any]:
							A         =					[6, 10, 12, 15, 20, 23]
							A         =					len(lowerCamelCase__			)

							# 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(lowerCamelCase__				,      lowerCamelCase__			)
							A         =					bottom_up_cut_rod(lowerCamelCase__				,      lowerCamelCase__			)
							A         =					naive_cut_rod_recursive(lowerCamelCase__				,      lowerCamelCase__			)

							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"""







import re

def   lowerCAmelCase__			(     lowerCamelCase__			) ->							list:
							return [char.split() for char in re.split(R'[^ a-z A-Z 0-9 \s]'				,      str_			)]

def   lowerCAmelCase__			(     lowerCamelCase__			) ->							str:
							A         =					split_input(str_			)
							return "".join(
							    [''.join([char.capitalize() for char in sub_str]			) for sub_str in string_split]			)

def   lowerCAmelCase__			(     lowerCamelCase__				,      lowerCamelCase__				,      lowerCamelCase__			) ->							str:
							try:
														A         =					split_input(lowerCamelCase__			)
														if upper:
																					A         =					''.join(
																					    [
																					        separator.join([char.upper() for char in sub_str]			)
																					        for sub_str in string_split
																					    ]			)
														else:
																					A         =					''.join(
																					    [
																					        separator.join([char.lower() for char in sub_str]			)
																					        for sub_str in string_split
																					    ]			)
														return res_str
							except IndexError:
														return "not valid string"

def   lowerCAmelCase__			(     lowerCamelCase__			) ->							str:
							return to_simple_case(lowerCamelCase__			)

def   lowerCAmelCase__			(     lowerCamelCase__			) ->							str:
							try:
														A         =					to_simple_case(lowerCamelCase__			)
														return res_str[0].lower() + res_str[1:]
							except IndexError:
														return "not valid string"

def   lowerCAmelCase__			(     lowerCamelCase__				,      lowerCamelCase__			) ->							str:
							return to_complex_case(lowerCamelCase__				,      lowerCamelCase__				,      '_'			)

def   lowerCAmelCase__			(     lowerCamelCase__				,      lowerCamelCase__			) ->							str:
							return to_complex_case(lowerCamelCase__				,      lowerCamelCase__				,      '-'			)


if __name__ == "__main__":
							__import__('doctest').testmod()



