




'''simple docstring'''


import numpy as np

import datasets


_snake_case   :   List[Any]     							=	'\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'

_snake_case   :   Dict     							=	'\\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'

_snake_case   :   Any     							=	'\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					):







							def      __lowerCAmelCase    (						self :						str      )    ->							Optional[Any]:


														"""simple docstring"""


														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      __lowerCAmelCase    (						self :						List[str]							,    lowerCAmelCase_ :						Union[str, Any]							,    lowerCAmelCase_ :						Tuple      )    ->							int:


														"""simple docstring"""


														_a			  =       np.array(_lowerCAmelCase      )
														_a			  =       np.array(_lowerCAmelCase      )

														# 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
														_a			  =       X - np.mean(_lowerCAmelCase      )
														_a			  =       np.cov(reference_distribution.T      )
														try:
																					_a			  =       np.linalg.inv(_lowerCAmelCase      )
														except np.linalg.LinAlgError:
																					_a			  =       np.linalg.pinv(_lowerCAmelCase      )
														_a			  =       np.dot(_lowerCAmelCase							,    _lowerCAmelCase      )
														_a			  =       np.dot(_lowerCAmelCase							,    X_minus_mu.T      ).diagonal()

														return {"mahalanobis": mahal_dist}







'''simple docstring'''


_snake_case   :   Any     							=	{
    'A': ['B', 'C', 'E'],
    'B': ['A', 'D', 'E'],
    'C': ['A', 'F', 'G'],
    'D': ['B'],
    'E': ['A', 'B', 'D'],
    'F': ['C'],
    'G': ['C'],
}
def 	snake_case_					(UpperCamelCase :						dict				,		UpperCamelCase :						Dict				,		UpperCamelCase :						Optional[int]   ):





							'''simple docstring'''


							_a			  =       set()
							# keep track of all the paths to be checked
							_a			  =       [[start]]

							# return path if start is goal
							if start == goal:
														return [start]

							# keeps looping until all possible paths have been checked
							while queue:
														# pop the first path from the queue
														_a			  =       queue.pop(0   )
														# get the last node from the path
														_a			  =       path[-1]
														if node not in explored:
																					_a			  =       graph[node]
																					# go through all neighbour nodes, construct a new path and
																					# push it into the queue
																					for neighbour in neighbours:
																												_a			  =       list(UpperCamelCase   )
																												new_path.append(UpperCamelCase   )
																												queue.append(UpperCamelCase   )
																												# return path if neighbour is goal
																												if neighbour == goal:
																																			return new_path

            # mark node as explored
																					explored.add(UpperCamelCase   )

    # in case there's no path between the 2 nodes
							return []
def 	snake_case_					(UpperCamelCase :						dict				,		UpperCamelCase :						Optional[int]				,		UpperCamelCase :						Dict   ):





							'''simple docstring'''


							if not graph or start not in graph or target not in graph:
														return -1
							if start == target:
														return 0
							_a			  =       [start]
							_a			  =       set(UpperCamelCase   )
							# Keep tab on distances from `start` node.
							_a			  =       {start: 0, target: -1}
							while queue:
														_a			  =       queue.pop(0   )
														if node == target:
																					_a			  =       (
																					    dist[node] if dist[target] == -1 else min(dist[target]				,		dist[node]   )
																					)
														for adjacent in graph[node]:
																					if adjacent not in visited:
																												visited.add(UpperCamelCase   )
																												queue.append(UpperCamelCase   )
																												_a			  =       dist[node] + 1
							return dist[target]


if __name__ == "__main__":
				print(bfs_shortest_path(demo_graph, 'G', 'D'))  # returns ['G', 'C', 'A', 'B', 'D']
				print(bfs_shortest_path_distance(demo_graph, 'G', 'D'))  # returns 4

