



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

import datasets


UpperCAmelCase__       =	"\\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"


UpperCAmelCase__       =	"\\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"


UpperCAmelCase__       =	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       __lowerCAmelCase   (      datasets.Metric						):



			def    _lowerCamelCase	(						self       :  int)       ->   int:



						"""simple docstring"""






						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    _lowerCamelCase	(						self       :  Optional[int]			,		A       :  Union[str, Any]			,		A       :  Any)       ->   Optional[int]:



						"""simple docstring"""






						_UpperCAmelCase			=       0.0
						for i, j in zip(A			,		A):
									n_correct += 1.0 if math_equivalence.is_equiv(A			,		A) else 0.0
						_UpperCAmelCase			=       n_correct / len(A)
						return {
						    "accuracy": accuracy,
						}





UpperCAmelCase__       =	{
    "A": ["B", "C", "E"],
    "B": ["A", "D", "E"],
    "C": ["A", "F", "G"],
    "D": ["B"],
    "E": ["A", "B", "D"],
    "F": ["C"],
    "G": ["C"],
}





def 							A     (					_UpperCAmelCase    :       dict							,       _UpperCAmelCase    :       Optional[int]							,       _UpperCAmelCase    :       List[Any]   )    ->			list[str]:







			'''simple docstring'''
			_UpperCAmelCase			=       set()
			# keep track of all the paths to be checked
			_UpperCAmelCase			=       [[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
						_UpperCAmelCase			=       queue.pop(0   )
						# get the last node from the path
						_UpperCAmelCase			=       path[-1]
						if node not in explored:
									_UpperCAmelCase			=       graph[node]
									# go through all neighbour nodes, construct a new path and
									# push it into the queue
									for neighbour in neighbours:
												_UpperCAmelCase			=       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 							A     (					_UpperCAmelCase    :       dict							,       _UpperCAmelCase    :       Any							,       _UpperCAmelCase    :       List[str]   )    ->			int:







			'''simple docstring'''
			if not graph or start not in graph or target not in graph:
						return -1
			if start == target:
						return 0
			_UpperCAmelCase			=       [start]
			_UpperCAmelCase			=       set(_UpperCAmelCase   )
			# Keep tab on distances from `start` node.
			_UpperCAmelCase			=       {start: 0, target: -1}
			while queue:
						_UpperCAmelCase			=       queue.pop(0   )
						if node == target:
									_UpperCAmelCase			=       (
									    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   )
												_UpperCAmelCase			=       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
