






def       snake_case_		(     lowerCAmelCase_       :						int       ,       lowerCAmelCase_       :						list      ):
							_enforce_args(lowerCAmelCase_       ,       lowerCAmelCase_      )
							if n == 0:
														return 0
							__lowercase      :							List[str]				=     float("""-inf"""      )
							for i in range(1       ,       n + 1      ):
														__lowercase      :							Optional[int]				=     max(
														    lowerCAmelCase_       ,       prices[i - 1] + naive_cut_rod_recursive(n - i       ,       lowerCAmelCase_      )      )

							return max_revue
def       snake_case_		(     lowerCAmelCase_       :						int       ,       lowerCAmelCase_       :						list      ):
							_enforce_args(lowerCAmelCase_       ,       lowerCAmelCase_      )
							__lowercase      :							str				=     [float("""-inf"""      ) for _ in range(n + 1      )]
							return _top_down_cut_rod_recursive(lowerCAmelCase_       ,       lowerCAmelCase_       ,       lowerCAmelCase_      )
def       snake_case_		(     lowerCAmelCase_       :						int       ,       lowerCAmelCase_       :						list       ,       lowerCAmelCase_       :						list      ):
							if max_rev[n] >= 0:
														return max_rev[n]
							elif n == 0:
														return 0
							else:
														__lowercase      :							Any				=     float("""-inf"""      )
														for i in range(1       ,       n + 1      ):
																					__lowercase      :							str				=     max(
																					    lowerCAmelCase_       ,       prices[i - 1] + _top_down_cut_rod_recursive(n - i       ,       lowerCAmelCase_       ,       lowerCAmelCase_      )       ,       )

														__lowercase      :							Any				=     max_revenue

							return max_rev[n]
def       snake_case_		(     lowerCAmelCase_       :						int       ,       lowerCAmelCase_       :						list      ):
							_enforce_args(lowerCAmelCase_       ,       lowerCAmelCase_      )

							# length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
							# length 0.
							__lowercase      :							Union[str, Any]				=     [float("""-inf"""      ) for _ in range(n + 1      )]
							__lowercase      :							Optional[Any]				=     0

							for i in range(1       ,       n + 1      ):
														__lowercase      :							List[str]				=     max_rev[i]
														for j in range(1       ,       i + 1      ):
																					__lowercase      :							Tuple				=     max(lowerCAmelCase_       ,       prices[j - 1] + max_rev[i - j]      )

														__lowercase      :							Optional[Any]				=     max_revenue_i

							return max_rev[n]
def       snake_case_		(     lowerCAmelCase_       :						int       ,       lowerCAmelCase_       :						list      ):
							if n < 0:
														__lowercase      :							Dict				=     F"n must be greater than or equal to 0. Got n = {n}"
														raise ValueError(lowerCAmelCase_      )

							if n > len(lowerCAmelCase_      ):
														__lowercase      :							Optional[int]				=     (
														    """Each integral piece of rod must have a corresponding price. """
														    F"Got n = {n} but length of prices = {len(lowerCAmelCase_      )}"
														)
														raise ValueError(lowerCAmelCase_      )
def       snake_case_		(     ):
							__lowercase      :							Dict				=     [6, 10, 12, 15, 20, 23]
							__lowercase      :							Union[str, Any]				=     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.
							__lowercase      :							str				=     36

							__lowercase      :							str				=     top_down_cut_rod(lowerCAmelCase_       ,       lowerCAmelCase_      )
							__lowercase      :							int				=     bottom_up_cut_rod(lowerCAmelCase_       ,       lowerCAmelCase_      )
							__lowercase      :							Dict				=     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()







from .imports import is_tqdm_available


if is_tqdm_available():
	from tqdm.auto import tqdm as _tqdm

from ..state import PartialState
def       snake_case_		(     lowerCAmelCase_       :						bool = True       ,       *lowerCAmelCase_       :						int       ,       **lowerCAmelCase_       :						List[str]      ):
							if not is_tqdm_available():
														raise ImportError("""Accelerate's `tqdm` module requires `tqdm` to be installed. Please run `pip install tqdm`."""      )
							__lowercase      :							List[str]				=     False
							if main_process_only:
														__lowercase      :							Optional[int]				=     PartialState().local_process_index == 0
							return _tqdm(*lowerCAmelCase_       ,       **lowerCAmelCase_       ,       disable=lowerCAmelCase_      )