





'''simple docstring'''






def 					_a						(       _lowerCamelCase ) ->				Any:



			"""simple docstring"""


			__snake_case					:      List[Any]							      =     [0] * len(_lowerCamelCase )
			__snake_case					:      List[Any]							      =     []
			__snake_case					:      List[Any]							      =     [1] * len(_lowerCamelCase )

			for values in graph.values():
						for i in values:
									indegree[i] += 1

			for i in range(len(_lowerCamelCase ) ):
						if indegree[i] == 0:
									queue.append(_lowerCamelCase )

			while queue:
						__snake_case					:      Dict							      =     queue.pop(0 )
						for x in graph[vertex]:
									indegree[x] -= 1

									if long_dist[vertex] + 1 > long_dist[x]:
												__snake_case					:      int							      =     long_dist[vertex] + 1

									if indegree[x] == 0:
												queue.append(_lowerCamelCase )

			print(max(_lowerCamelCase ) )


# Adjacency list of Graph
__UpperCamelCase					    =	{0: [2, 3, 4], 1: [2, 7], 2: [5], 3: [5, 7], 4: [7], 5: [6], 6: [7], 7: []}

longest_distance(graph)








import numpy as np

import datasets


__a							     =					'\nCompute the Mahalanobis Distance\n\nMahalonobis distance is the distance between a point and a distribution.\nAnd not between two distinct points. It is effectively a multivariate equivalent of the Euclidean distance.\nIt was introduced by Prof. P. C. Mahalanobis in 1936\nand has been used in various statistical applications ever since\n[source: https://www.machinelearningplus.com/statistics/mahalanobis-distance/]\n'

__a							     =					'\\n@article{de2000mahalanobis,\n  title={The mahalanobis distance},\n  author={De Maesschalck, Roy and Jouan-Rimbaud, Delphine and Massart, D{\'e}sir{\'e} L},\n  journal={Chemometrics and intelligent laboratory systems},\n  volume={50},\n  number={1},\n  pages={1--18},\n  year={2000},\n  publisher={Elsevier}\n}\n'

__a							     =					'\nArgs:\n    X: List of datapoints to be compared with the `reference_distribution`.\n    reference_distribution: List of datapoints from the reference distribution we want to compare to.\nReturns:\n    mahalanobis: The Mahalonobis distance for each datapoint in `X`.\nExamples:\n\n    >>> mahalanobis_metric = datasets.load_metric("mahalanobis")\n    >>> results = mahalanobis_metric.compute(reference_distribution=[[0, 1], [1, 0]], X=[[0, 1]])\n    >>> print(results)\n    {\'mahalanobis\': array([0.5])}\n'

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






    """simple docstring"""





    def 				a__ ( self    )					->						Union[str, Any]:
         return datasets.MetricInfo(
             description=_DESCRIPTION  ,citation=_CITATION  ,inputs_description=_KWARGS_DESCRIPTION  ,features=datasets.Features(
                 {
                     '''X''': datasets.Sequence(datasets.Value('''float'''  ,id='''sequence'''    )  ,id='''X'''    ),
                 }    )  ,)





    def 				a__ ( self  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )					->						Any:
         # convert to numpy arrays
         UpperCAmelCase_     :				str  =     np.array(_SCREAMING_SNAKE_CASE    )
         UpperCAmelCase_     :				List[Any]  =     np.array(_SCREAMING_SNAKE_CASE    )

         # Assert that arrays are 2D
         if len(X.shape    ) != 2:
              raise ValueError('''Expected `X` to be a 2D vector'''    )
         if len(reference_distribution.shape    ) != 2:
              raise ValueError('''Expected `reference_distribution` to be a 2D vector'''    )
         if reference_distribution.shape[0] < 2:
              raise ValueError(
                  '''Expected `reference_distribution` to be a 2D vector with more than one element in the first dimension'''    )

         # Get mahalanobis distance for each prediction
         UpperCAmelCase_     :				List[str]  =     X - np.mean(_SCREAMING_SNAKE_CASE    )
         UpperCAmelCase_     :				Dict  =     np.cov(reference_distribution.T    )
         try:
              UpperCAmelCase_     :				Any  =     np.linalg.inv(_SCREAMING_SNAKE_CASE    )
         except np.linalg.LinAlgError:
              UpperCAmelCase_     :				List[str]  =     np.linalg.pinv(_SCREAMING_SNAKE_CASE    )
         UpperCAmelCase_     :				Union[str, Any]  =     np.dot(_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )
         UpperCAmelCase_     :				List[Any]  =     np.dot(_SCREAMING_SNAKE_CASE  ,X_minus_mu.T    ).diagonal()

         return {"mahalanobis": mahal_dist}