
from sklearn.metrics import mean_absolute_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 Absolute Error (MAE) is the mean of the magnitude of difference between the predicted and actual\nvalues.\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\nReturns:\n    mae : mean absolute error.\n        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.\n        MAE output is non-negative floating point. The best value is 0.0.\nExamples:\n\n    >>> mae_metric = datasets.load_metric("mae")\n    >>> predictions = [2.5, 0.0, 2, 8]\n    >>> references = [3, -0.5, 2, 7]\n    >>> results = mae_metric.compute(predictions=predictions, references=references)\n    >>> print(results)\n    {\'mae\': 0.5}\n\n    If you\'re using multi-dimensional lists, then set the config as follows :\n\n    >>> mae_metric = datasets.load_metric("mae", "multilist")\n    >>> predictions = [[0.5, 1], [-1, 1], [7, -6]]\n    >>> references = [[0, 2], [-1, 2], [8, -5]]\n    >>> results = mae_metric.compute(predictions=predictions, references=references)\n    >>> print(results)\n    {\'mae\': 0.75}\n    >>> results = mae_metric.compute(predictions=predictions, references=references, multioutput=\'raw_values\')\n    >>> print(results)\n    {\'mae\': array([0.5, 1. ])}\n'





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




    def 					__a						( self					)    ->				Optional[Any]:
       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 					__a						( self					)    ->				Dict:
       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 					__a						( self    ,    _UpperCamelCase    ,    _UpperCamelCase    ,    _UpperCamelCase=None    ,    _UpperCamelCase="uniform_average"					)    ->				str:
       lowerCAmelCase_      =     mean_absolute_error(_UpperCamelCase    ,    _UpperCamelCase    ,    sample_weight=_UpperCamelCase    ,    multioutput=_UpperCamelCase					)

       return {"mae": mae_score}





# This Python program implements an optimal binary search tree (abbreviated BST)
# building dynamic programming algorithm that delivers O(n^2) performance.
#
# The goal of the optimal BST problem is to build a low-cost BST for a
# given set of nodes, each with its own key and frequency. The frequency
# of the node is defined as how many time the node is being searched.
# The search cost of binary search tree is given by this formula:
#
# cost(1, n) = sum{i = 1 to n}((depth(node_i) + 1) * node_i_freq)
#
# where n is number of nodes in the BST. The characteristic of low-cost
# BSTs is having a faster overall search time than other implementations.
# The reason for their fast search time is that the nodes with high
# frequencies will be placed near the root of the tree while the nodes
# with low frequencies will be placed near the leaves of the tree thus
# reducing search time in the most frequent instances.
import sys
from random import randint





class      _lowerCAmelCase :




				def __init__( self    ,    _UpperCamelCase    ,    _UpperCamelCase					)    ->				str:
							lowerCAmelCase_      =     key
							lowerCAmelCase_      =     freq




				def __str__( self					)    ->				Any:
							return f"""Node(key={self.key}, freq={self.freq})"""






def        lowerCamelCase__    (    __lowerCAmelCase  :  Optional[int]   ,							__lowerCAmelCase  :  Dict   ,							__lowerCAmelCase  :  Optional[Any]   ,							__lowerCAmelCase  :  Optional[int]   ,							__lowerCAmelCase  :  int   ,							__lowerCAmelCase  :  List[Any]    ):




			"""simple docstring"""


			if i > j or i < 0 or j > len(__lowerCAmelCase    ) - 1:
						return

			lowerCAmelCase_      =     root[i][j]
			if parent == -1:  # root does not have a parent
						print(F"""{key[node]} is the root of the binary search tree."""    )
			elif is_left:
						print(F"""{key[node]} is the left child of key {parent}."""    )
			else:
						print(F"""{key[node]} is the right child of key {parent}."""    )

			print_binary_search_tree(__lowerCAmelCase   ,							__lowerCAmelCase   ,							__lowerCAmelCase   ,							node - 1   ,							key[node]   ,							__lowerCAmelCase    )
			print_binary_search_tree(__lowerCAmelCase   ,							__lowerCAmelCase   ,							node + 1   ,							__lowerCAmelCase   ,							key[node]   ,							__lowerCAmelCase    )






def        lowerCamelCase__    (    __lowerCAmelCase  :  Union[str, Any]    ):




			"""simple docstring"""


			nodes.sort(key=lambda __lowerCAmelCase    : node.key    )

			lowerCAmelCase_      =     len(__lowerCAmelCase    )

			lowerCAmelCase_      =     [nodes[i].key for i in range(__lowerCAmelCase    )]
			lowerCAmelCase_      =     [nodes[i].freq for i in range(__lowerCAmelCase    )]

			# This 2D array stores the overall tree cost (which's as minimized as possible);
			# for a single key, cost is equal to frequency of the key.
			lowerCAmelCase_      =     [[freqs[i] if i == j else 0 for j in range(__lowerCAmelCase    )] for i in range(__lowerCAmelCase    )]
			# sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
			# array
			lowerCAmelCase_      =     [[freqs[i] if i == j else 0 for j in range(__lowerCAmelCase    )] for i in range(__lowerCAmelCase    )]
			# stores tree roots that will be used later for constructing binary search tree
			lowerCAmelCase_      =     [[i if i == j else 0 for j in range(__lowerCAmelCase    )] for i in range(__lowerCAmelCase    )]

			for interval_length in range(2   ,							n + 1    ):
						for i in range(n - interval_length + 1    ):
									lowerCAmelCase_      =     i + interval_length - 1

									lowerCAmelCase_      =     sys.maxsize  # set the value to "infinity"
									lowerCAmelCase_      =     total[i][j - 1] + freqs[j]

									# Apply Knuth's optimization
									# Loop without optimization: for r in range(i, j + 1):
									for r in range(root[i][j - 1]   ,							root[i + 1][j] + 1    ):  # r is a temporal root
												lowerCAmelCase_      =     dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
												lowerCAmelCase_      =     dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
												lowerCAmelCase_      =     left + total[i][j] + right

												if dp[i][j] > cost:
															lowerCAmelCase_      =     cost
															lowerCAmelCase_      =     r

			print("Binary search tree nodes:"    )
			for node in nodes:
						print(__lowerCAmelCase    )

			print(F"""\nThe cost of optimal BST for given tree nodes is {dp[0][n - 1]}."""    )
			print_binary_search_tree(__lowerCAmelCase   ,							__lowerCAmelCase   ,							0   ,							n - 1   ,							-1   ,							__lowerCAmelCase    )






def        lowerCamelCase__    (    ):




			"""simple docstring"""


			lowerCAmelCase_      =     [Node(__lowerCAmelCase   ,							randint(1   ,							50    )    ) for i in range(10   ,							0   ,							-1    )]
			find_optimal_binary_search_tree(__lowerCAmelCase    )


if __name__ == "__main__":
			main()



