




'''simple docstring'''


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

import datasets


_snake_case   :   Tuple     							=	'\\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'


_snake_case   :   int     							=	'\\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'


_snake_case   :   Dict     							=	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     A					(	datasets.Metric					):







							def      __lowerCAmelCase    (						self :						List[str]      )    ->							Dict:


														"""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 :						int							,    lowerCAmelCase_ :						List[str]							,    lowerCAmelCase_ :						str      )    ->							str:


														"""simple docstring"""


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







'''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

