
from __future__ import annotations

import os
from collections.abc import Mapping

lowercase__		:int			  =   tuple[int, int]







class     lowercase		:




							def __init__(    self       ,A__       ,A__):
												lowercase						     =						vertices
												lowercase						     =						{
												    (min(UpperCamelCase__), max(UpperCamelCase__)): weight for edge, weight in edges.items()
												}




							def 			A__				(    self       ,A__       ,A__):
												self.vertices.add(edge[0])
												self.vertices.add(edge[1])
												lowercase						     =						weight





							def 			A__				(    self):
												lowercase						     =						Graph({min(self.vertices)}       ,{})
												lowercase						     =						4_2
												lowercase						     =						4_2
												lowercase						     =						4_2
												lowercase						     =						4_2

												while len(subgraph.vertices) < len(self.vertices):
																	lowercase						     =						max(self.edges.values()) + 1
																	for edge, weight in self.edges.items():
																						if (edge[0] in subgraph.vertices) ^ (edge[1] in subgraph.vertices):
																											if weight < min_weight:
																																lowercase						     =						edge
																																lowercase						     =						weight

																	subgraph.add_edge(UpperCamelCase__       ,UpperCamelCase__)

												return subgraph



def 	UpperCamelCase   (							lowerCAmelCase__ = "p107_network.txt"		):
					'''simple docstring'''
					lowercase						     =						os.path.abspath(os.path.dirname(__UpperCamelCase		)		)
					lowercase						     =						os.path.join(__UpperCamelCase			,      __UpperCamelCase		)
					lowercase						     =						{}
					lowercase						     =						42
					lowercase						     =						42
					lowercase						     =						42

					with open(__UpperCamelCase		) as f:
										lowercase						     =						f.read().strip().split('''\n'''		)

					lowercase						     =						[line.split(''','''		) for line in data]

					for edgea in range(1			,      len(__UpperCamelCase		)		):
										for edgea in range(__UpperCamelCase		):
															if adjaceny_matrix[edgea][edgea] != "-":
																				lowercase						     =						int(adjaceny_matrix[edgea][edgea]		)

					lowercase						     =						Graph(set(range(len(__UpperCamelCase		)		)		)			,      __UpperCamelCase		)

					lowercase						     =						graph.prims_algorithm()

					lowercase						     =						sum(graph.edges.values()		)
					lowercase						     =						sum(subgraph.edges.values()		)

					return initial_total - optimal_total


if __name__ == "__main__":
							print(F'{solution() = }')






import numpy as np

import datasets


lowercase__		:Dict			  =   "\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"

lowercase__		:List[Any]			  =   "\\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"

lowercase__		:Dict			  =   "\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     lowercase		( datasets.Metric		):




							def 			A__				(    self):
												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       ,A__       ,A__):
												# convert to numpy arrays
												lowercase						     =						np.array(A__)
												lowercase						     =						np.array(A__)

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

												return {"mahalanobis": mahal_dist}




