




def      lowerCamelCase_						(			UpperCamelCase__							: int					,	UpperCamelCase__							: list )	->			Union[str, Any]:





				"""simple docstring"""


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

				return max_revue







def      lowerCamelCase_						(			UpperCamelCase__							: int					,	UpperCamelCase__							: list )	->			List[Any]:





				"""simple docstring"""


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







def      lowerCamelCase_						(			UpperCamelCase__							: int					,	UpperCamelCase__							: list					,	UpperCamelCase__							: list )	->			int:





				"""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(
												    UpperCamelCase__					,	prices[i - 1] + _top_down_cut_rod_recursive(n - i					,	UpperCamelCase__					,	UpperCamelCase__ )					,	)

								__lowerCamelCase									=       max_revenue

				return max_rev[n]







def      lowerCamelCase_						(			UpperCamelCase__							: int					,	UpperCamelCase__							: list )	->			Optional[Any]:





				"""simple docstring"""


				_enforce_args(UpperCamelCase__					,	UpperCamelCase__ )

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

								__lowerCamelCase									=       max_revenue_i

				return max_rev[n]







def      lowerCamelCase_						(			UpperCamelCase__							: int					,	UpperCamelCase__							: list )	->			str:





				"""simple docstring"""


				if n < 0:
								__lowerCamelCase									=       F"""n must be greater than or equal to 0. Got n = {n}"""
								raise ValueError(UpperCamelCase__ )

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







def      lowerCamelCase_						(			)	->			Any:





				"""simple docstring"""


				__lowerCamelCase									=       [6, 10, 12, 15, 20, 23]
				__lowerCamelCase									=       len(UpperCamelCase__ )

				# 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(UpperCamelCase__					,	UpperCamelCase__ )
				__lowerCamelCase									=       bottom_up_cut_rod(UpperCamelCase__					,	UpperCamelCase__ )
				__lowerCamelCase									=       naive_cut_rod_recursive(UpperCamelCase__					,	UpperCamelCase__ )

				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 sklearn.metrics import mean_squared_error

import datasets


__A								=       "\\n@article{scikit-learn,\n title={Scikit-learn: Machine Learning in {P}ython},\n author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V.\n         and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P.\n         and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and\n         Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.},\n journal={Journal of Machine Learning Research},\n volume={12},\n pages={2825--2830},\n year={2011}\n}\n"

__A								=       "\\nMean Squared Error(MSE) is the average of the square of difference between the predicted\nand actual values.\n"


__A								=       "\nArgs:\n    predictions: array-like of shape (n_samples,) or (n_samples, n_outputs)\n        Estimated target values.\n    references: array-like of shape (n_samples,) or (n_samples, n_outputs)\n        Ground truth (correct) target values.\n    sample_weight: array-like of shape (n_samples,), default=None\n        Sample weights.\n    multioutput: {\"raw_values\", \"uniform_average\"} or array-like of shape (n_outputs,), default=\"uniform_average\"\n        Defines aggregating of multiple output values. Array-like value defines weights used to average errors.\n\n        \"raw_values\" : Returns a full set of errors in case of multioutput input.\n\n        \"uniform_average\" : Errors of all outputs are averaged with uniform weight.\n\n    squared : bool, default=True\n        If True returns MSE value, if False returns RMSE (Root Mean Squared Error) value.\n\nReturns:\n    mse : mean squared error.\nExamples:\n\n    >>> mse_metric = datasets.load_metric(\"mse\")\n    >>> predictions = [2.5, 0.0, 2, 8]\n    >>> references = [3, -0.5, 2, 7]\n    >>> results = mse_metric.compute(predictions=predictions, references=references)\n    >>> print(results)\n    {'mse': 0.375}\n    >>> rmse_result = mse_metric.compute(predictions=predictions, references=references, squared=False)\n    >>> print(rmse_result)\n    {'mse': 0.6123724356957945}\n\n    If you're using multi-dimensional lists, then set the config as follows :\n\n    >>> mse_metric = datasets.load_metric(\"mse\", \"multilist\")\n    >>> predictions = [[0.5, 1], [-1, 1], [7, -6]]\n    >>> references = [[0, 2], [-1, 2], [8, -5]]\n    >>> results = mse_metric.compute(predictions=predictions, references=references)\n    >>> print(results)\n    {'mse': 0.7083333333333334}\n    >>> results = mse_metric.compute(predictions=predictions, references=references, multioutput='raw_values')\n    >>> print(results) # doctest: +NORMALIZE_WHITESPACE\n    {'mse': array([0.41666667, 1. ])}\n"







@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION     ,							_KWARGS_DESCRIPTION					)
class        __lowerCAmelCase					(			datasets.Metric					):

			"""simple docstring"""







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



							'''simple docstring'''
							return datasets.MetricInfo(
							    description=_DESCRIPTION     ,		citation=_CITATION     ,		inputs_description=_KWARGS_DESCRIPTION     ,		features=datasets.Features(self._get_feature_types()				)     ,		reference_urls=[
							        'https://scikit-learn.org/stable/modules/generated/sklearn.metrics.mean_squared_error.html'
							    ]     ,		)


			def  lowercase_       ( self				)       -> Tuple:



							'''simple docstring'''
							if self.config_name == "multilist":
											return {
											    "predictions": datasets.Sequence(datasets.Value('float'				)				),
											    "references": datasets.Sequence(datasets.Value('float'				)				),
											}
							else:
											return {
											    "predictions": datasets.Value('float'				),
											    "references": datasets.Value('float'				),
											}






			def  lowercase_       ( self     ,		lowerCamelCase__     ,		lowerCamelCase__     ,		lowerCamelCase__=None     ,		lowerCamelCase__="uniform_average"     ,		lowerCamelCase__=True				)       -> List[Any]:



							'''simple docstring'''
							__lowerCamelCase									=       mean_squared_error(
							    lowerCamelCase__     ,		lowerCamelCase__     ,		sample_weight=lowerCamelCase__     ,		multioutput=lowerCamelCase__     ,		squared=lowerCamelCase__				)

							return {"mse": mse}


