





"""simple docstring"""




import math




class  _a						:






				def __init__( self		:    Optional[int], lowerCAmelCase__		:    int, lowerCAmelCase__		:    int, lowerCAmelCase__		:    int, lowerCAmelCase__		:    List[Any]							)	->      Any:




										'''simple docstring'''



										_UpperCamelCase			:					Any     =    x
										_UpperCamelCase			:					str     =    y
										_UpperCamelCase			:					str     =    step_size
										_UpperCamelCase			:					Dict     =    function_to_optimize






				def 				snake_case	( self		:    int							)	->      int:




										'''simple docstring'''



										return self.function(self.x, self.y							)






				def 				snake_case	( self		:    Tuple							)	->      List[str]:




										'''simple docstring'''



										_UpperCamelCase			:					Union[str, Any]     =    self.step_size
										return [
										    SearchProblem(lowerCAmelCase__, lowerCAmelCase__, lowerCAmelCase__, self.function							)
										    for x, y in (
										        (self.x - step_size, self.y - step_size),
										        (self.x - step_size, self.y),
										        (self.x - step_size, self.y + step_size),
										        (self.x, self.y - step_size),
										        (self.x, self.y + step_size),
										        (self.x + step_size, self.y - step_size),
										        (self.x + step_size, self.y),
										        (self.x + step_size, self.y + step_size),
										    )
										]






				def __hash__( self		:    Optional[Any]							)	->      List[Any]:




										'''simple docstring'''



										return hash(str(self							)							)






				def __eq__( self		:    str, lowerCAmelCase__		:    Union[str, Any]							)	->      List[str]:




										'''simple docstring'''



										if isinstance(lowerCAmelCase__, lowerCAmelCase__							):
																return hash(str(self							)							) == hash(str(lowerCAmelCase__							)							)
										return False






				def __str__( self		:    Union[str, Any]							)	->      Optional[int]:




										'''simple docstring'''



										return f"""x: {self.x} y: {self.y}"""





def        a_				(							_lowercase       ,						_lowercase = True       ,						_lowercase = math.inf       ,						_lowercase = -math.inf       ,						_lowercase = math.inf       ,						_lowercase = -math.inf       ,						_lowercase = False       ,						_lowercase = 1_0000       ,						):
						_UpperCamelCase			:					Dict     =    search_prob
						_UpperCamelCase			:					Tuple     =    []  # list to store the current score at each iteration
						_UpperCamelCase			:					Optional[int]     =    0
						_UpperCamelCase			:					int     =    False
						_UpperCamelCase			:					List[str]     =    set()
						while not solution_found and iterations < max_iter:
												visited.add(_lowercase   )
												iterations += 1
												_UpperCamelCase			:					List[str]     =    current_state.score()
												scores.append(_lowercase   )
												_UpperCamelCase			:					List[Any]     =    current_state.get_neighbors()
												_UpperCamelCase			:					int     =    -math.inf
												_UpperCamelCase			:					int     =    math.inf
												_UpperCamelCase			:					Union[str, Any]     =    None  # to hold the next best neighbor
												for neighbor in neighbors:
																		if neighbor in visited:
																								continue  # do not want to visit the same state again
																		if (
																		    neighbor.x > max_x
																		    or neighbor.x < min_x
																		    or neighbor.y > max_y
																		    or neighbor.y < min_y
																		):
																								continue  # neighbor outside our bounds
																		_UpperCamelCase			:					Optional[int]     =    neighbor.score() - current_score
																		if find_max:  # finding max
																								# going to direction with greatest ascent
																								if change > max_change and change > 0:
																														_UpperCamelCase			:					Any     =    change
																														_UpperCamelCase			:					Any     =    neighbor
																		else:  # finding min
																								# to direction with greatest descent
																								if change < min_change and change < 0:
																														_UpperCamelCase			:					Union[str, Any]     =    change
																														_UpperCamelCase			:					Tuple     =    neighbor
												if next_state is not None:
																		# we found at least one neighbor which improved the current state
																		_UpperCamelCase			:					List[Any]     =    next_state
												else:
																		# since we have no neighbor that improves the solution we stop the search
																		_UpperCamelCase			:					List[str]     =    True

						if visualization:
												from matplotlib import pyplot as plt

												plt.plot(range(_lowercase   )       ,						_lowercase   )
												plt.xlabel('''Iterations'''   )
												plt.ylabel('''Function values'''   )
												plt.show()

						return current_state


if __name__ == "__main__":
						import doctest

						doctest.testmod()





						def        a_				(							_lowercase       ,						_lowercase   ):
												return (x**2) + (y**2)

						# starting the problem with initial coordinates (3, 4)
						UpperCamelCase_           =SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
						UpperCamelCase_           =hill_climbing(prob, find_max=False)
						print(
						    """The minimum score for f(x, y) = x^2 + y^2 found via hill climbing: """
						    F"{local_min.score()}"
						)

						# starting the problem with initial coordinates (12, 47)
						UpperCamelCase_           =SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
						UpperCamelCase_           =hill_climbing(
						    prob, find_max=False, max_x=100, min_x=5, max_y=50, min_y=-5, visualization=True
						)
						print(
						    """The minimum score for f(x, y) = x^2 + y^2 with the domain 100 > x > 5 """
						    F"and 50 > y > - 5 found via hill climbing: {local_min.score()}"
						)





						def        a_				(							_lowercase       ,						_lowercase   ):
												return (3 * x**2) - (6 * y)

						UpperCamelCase_           =SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
						UpperCamelCase_           =hill_climbing(prob, find_max=True)






						print(
						    """The maximum score for f(x, y) = x^2 + y^2 found via hill climbing: """
						    F"{local_min.score()}"
						)










"""simple docstring"""




from sklearn.metrics import mean_absolute_error

import datasets


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

UpperCamelCase_           ="""\
Mean Absolute Error (MAE) is the mean of the magnitude of difference between the predicted and actual
values.
"""


UpperCamelCase_           ="""
Args:
    predictions: array-like of shape (n_samples,) or (n_samples, n_outputs)
        Estimated target values.
    references: array-like of shape (n_samples,) or (n_samples, n_outputs)
        Ground truth (correct) target values.
    sample_weight: array-like of shape (n_samples,), default=None
        Sample weights.
    multioutput: {\"raw_values\", \"uniform_average\"} or array-like of shape (n_outputs,), default=\"uniform_average\"
        Defines aggregating of multiple output values. Array-like value defines weights used to average errors.

                 \"raw_values\" : Returns a full set of errors in case of multioutput input.

                 \"uniform_average\" : Errors of all outputs are averaged with uniform weight.

Returns:
    mae : mean absolute error.
        If multioutput is \"raw_values\", then mean absolute error is returned for each output separately. If multioutput is \"uniform_average\" or an ndarray of weights, then the weighted average of all output errors is returned.
        MAE output is non-negative floating point. The best value is 0.0.
Examples:

    >>> mae_metric = datasets.load_metric(\"mae\")
    >>> predictions = [2.5, 0.0, 2, 8]
    >>> references = [3, -0.5, 2, 7]
    >>> results = mae_metric.compute(predictions=predictions, references=references)
    >>> print(results)
    {'mae': 0.5}

    If you're using multi-dimensional lists, then set the config as follows :

    >>> mae_metric = datasets.load_metric(\"mae\", \"multilist\")
    >>> predictions = [[0.5, 1], [-1, 1], [7, -6]]
    >>> references = [[0, 2], [-1, 2], [8, -5]]
    >>> results = mae_metric.compute(predictions=predictions, references=references)
    >>> print(results)
    {'mae': 0.75}
    >>> results = mae_metric.compute(predictions=predictions, references=references, multioutput='raw_values')
    >>> print(results)
    {'mae': array([0.5, 1. ])}
"""




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






				def 				snake_case	( self		:    Optional[int]							)	->      List[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_absolute_error.html'''
										    ], )






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




										'''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 				snake_case	( self		:    List[Any], lowerCAmelCase__		:    Dict, lowerCAmelCase__		:    Union[str, Any], lowerCAmelCase__		:    Tuple=None, lowerCAmelCase__		:    Tuple="uniform_average"							)	->      Optional[int]:




										'''simple docstring'''



										_UpperCamelCase			:					List[str]     =    mean_absolute_error(lowerCAmelCase__, lowerCAmelCase__, sample_weight=lowerCAmelCase__, multioutput=lowerCAmelCase__							)

										return {"mae": mae_score}



