


from __future__ import annotations

import os
from collections.abc import Mapping

__lowerCAmelCase	: Optional[int]  				=tuple[int, int]
class        _lowercase      :






				'''simple docstring'''



				def __init__(       self			:Optional[Any]			,			lowerCAmelCase__			:set[int]			,			lowerCAmelCase__			:Mapping[EdgeT, int]	)		->			None:
										__SCREAMING_SNAKE_CASE						:     set[int]					=		vertices
										__SCREAMING_SNAKE_CASE						:     dict[EdgeT, int]					=		{
										    (min(lowerCAmelCase__	), max(lowerCAmelCase__	)): weight for edge, weight in edges.items()
										}


				def 		__magic_name__(       self			:List[str]			,			lowerCAmelCase__			:EdgeT			,			lowerCAmelCase__			:int	)		->			None:
										self.vertices.add(edge[0]	)
										self.vertices.add(edge[1]	)
										__SCREAMING_SNAKE_CASE						:     List[str]					=		weight



				def 		__magic_name__(       self			:List[str]	)		->			Graph:
										__SCREAMING_SNAKE_CASE						:     Graph					=		Graph({min(self.vertices	)}			,			{}	)
										__SCREAMING_SNAKE_CASE						:     EdgeT
										__SCREAMING_SNAKE_CASE						:     int
										__SCREAMING_SNAKE_CASE						:     EdgeT
										__SCREAMING_SNAKE_CASE						:     int

										while len(subgraph.vertices	) < len(self.vertices	):
																__SCREAMING_SNAKE_CASE						:     int					=		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:
																																		__SCREAMING_SNAKE_CASE						:     Union[str, Any]					=		edge
																																		__SCREAMING_SNAKE_CASE						:     Dict					=		weight

																subgraph.add_edge(lowerCAmelCase__			,			lowerCAmelCase__	)

										return subgraph




def        _UpperCamelCase							(      lowercase__ = "p107_network.txt"      ):
						__SCREAMING_SNAKE_CASE						:     str					=		os.path.abspath(os.path.dirname(lowercase__      )      )
						__SCREAMING_SNAKE_CASE						:     str					=		os.path.join(lowercase__    ,       lowercase__      )
						__SCREAMING_SNAKE_CASE						:     dict[EdgeT, int]					=		{}
						__SCREAMING_SNAKE_CASE						:     list[str]
						__SCREAMING_SNAKE_CASE						:     int
						__SCREAMING_SNAKE_CASE						:     int

						with open(lowercase__      ) as f:
												__SCREAMING_SNAKE_CASE						:     int					=		f.read().strip().split('''\n'''      )

						__SCREAMING_SNAKE_CASE						:     Union[str, Any]					=		[line.split(''','''      ) for line in data]

						for edgea in range(1    ,       len(lowercase__      )      ):
												for edgea in range(lowercase__      ):
																		if adjaceny_matrix[edgea][edgea] != "-":
																								__SCREAMING_SNAKE_CASE						:     List[str]					=		int(adjaceny_matrix[edgea][edgea]      )

						__SCREAMING_SNAKE_CASE						:     Graph					=		Graph(set(range(len(lowercase__      )      )      )    ,       lowercase__      )

						__SCREAMING_SNAKE_CASE						:     Graph					=		graph.prims_algorithm()

						__SCREAMING_SNAKE_CASE						:     int					=		sum(graph.edges.values()      )
						__SCREAMING_SNAKE_CASE						:     int					=		sum(subgraph.edges.values()      )

						return initial_total - optimal_total


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




import math_equivalence  # From: git+https://github.com/hendrycks/math.git

import datasets


__lowerCAmelCase	: Optional[Any]  				='\\n@article{hendrycksmath2021,\n  title={Measuring Mathematical Problem Solving With the MATH Dataset},\n  author={Dan Hendrycks\n    and Collin Burns\n    and Saurav Kadavath\n    and Akul Arora\n    and Steven Basart\n    and Eric Tang\n    and Dawn Song\n    and Jacob Steinhardt},\n  journal={arXiv preprint arXiv:2103.03874},\n  year={2021}\n}\n'


__lowerCAmelCase	: Any  				='\\nThis metric is used to assess performance on the Mathematics Aptitude Test of Heuristics (MATH) dataset.\nIt first canonicalizes the inputs (e.g., converting "1/2" to "\\frac{1}{2}") and then computes accuracy.\n'


__lowerCAmelCase	: Optional[Any]  				=r'\nCalculates accuracy after canonicalizing inputs.\n\nArgs:\n    predictions: list of predictions to score. Each prediction\n        is a string that contains natural language and LaTex.\n    references: list of reference for each prediction. Each\n        reference is a string that contains natural language\n        and LaTex.\nReturns:\n    accuracy: accuracy after canonicalizing inputs\n        (e.g., converting "1/2" to "\\frac{1}{2}")\n\nExamples:\n    >>> metric = datasets.load_metric("competition_math")\n    >>> results = metric.compute(references=["\\frac{1}{2}"], predictions=["1/2"])\n    >>> print(results)\n    {\'accuracy\': 1.0}\n'
@datasets.utils.file_utils.add_end_docstrings(_DESCRIPTION						,			_KWARGS_DESCRIPTION       )
class        _lowercase      (			datasets.Metric       ):






				'''simple docstring'''



				def 		__magic_name__(       self			:Optional[Any]	)		->			List[str]:
										return datasets.MetricInfo(
										    description=_DESCRIPTION			,			citation=_CITATION			,			inputs_description=_KWARGS_DESCRIPTION			,			features=datasets.Features(
										        {
										            '''predictions''': datasets.Value('''string'''	),
										            '''references''': datasets.Value('''string'''	),
										        }	)			,			homepage='''https://github.com/hendrycks/math'''			,			codebase_urls=['''https://github.com/hendrycks/math''']			,			)



				def 		__magic_name__(       self			:Any			,			lowerCAmelCase__			:Optional[int]			,			lowerCAmelCase__			:Any	)		->			Optional[int]:
										__SCREAMING_SNAKE_CASE						:     Tuple					=		0.0
										for i, j in zip(lowerCAmelCase__			,			lowerCAmelCase__	):
																n_correct += 1.0 if math_equivalence.is_equiv(lowerCAmelCase__			,			lowerCAmelCase__	) else 0.0
										__SCREAMING_SNAKE_CASE						:     str					=		n_correct / len(lowerCAmelCase__	)
										return {
										    "accuracy": accuracy,
										}
