



"""simple docstring"""






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

import datasets


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


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


snake_case   					=				r'''
Calculates accuracy after canonicalizing inputs.

Args:
    predictions: list of predictions to score. Each prediction
        is a string that contains natural language and LaTex.
    references: list of reference for each prediction. Each
        reference is a string that contains natural language
        and LaTex.
Returns:
    accuracy: accuracy after canonicalizing inputs
        (e.g., converting "1/2" to "\\frac{1}{2}")

Examples:
    >>> metric = datasets.load_metric("competition_math")
    >>> results = metric.compute(references=["\\frac{1}{2}"], predictions=["1/2"])
    >>> print(results)
    {\'accuracy\': 1.0}
'''



@datasets.utils.file_utils.add_end_docstrings(_DESCRIPTION,_KWARGS_DESCRIPTION  )
class     UpperCAmelCase    (	datasets.Metric  ):



   def    __UpperCAmelCase    (       self    :	Any				):



     """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    __UpperCAmelCase    (       self    :	Dict							,       __lowerCamelCase    :	int							,       __lowerCamelCase    :	List[Any]				):



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










from collections.abc import Sequence
from queue import Queue






class     __a			:



	def __init__(    self				:     str					,						snake_case_				:     List[str]					,						snake_case_				:     Tuple					,						snake_case_				:     Tuple					,						snake_case_				:     Optional[Any]=None					,						snake_case_				:     Dict=None)->				Optional[int]:
						__lowerCAmelCase						 =start
						__lowerCAmelCase						 =end
						__lowerCAmelCase						 =val
						__lowerCAmelCase						 =(start + end) // 2
						__lowerCAmelCase						 =left
						__lowerCAmelCase						 =right



	def __repr__(    self				:     List[Any])->				Dict:
						return F"""SegmentTreeNode(start={self.start}, end={self.end}, val={self.val})"""






class     __a			:



	def __init__(    self				:     List[str]					,						snake_case_				:     Sequence					,						snake_case_				:     int)->				str:
						__lowerCAmelCase						 =collection
						__lowerCAmelCase						 =function
						if self.collection:
											__lowerCAmelCase						 =self._build_tree(0					,						len(snake_case_) - 1)



	def 		UpperCamelCase				(    self				:     Dict					,						snake_case_				:     Tuple					,						snake_case_				:     Optional[int])->				Optional[int]:
						self._update_tree(self.root					,						snake_case_					,						snake_case_)



	def 		UpperCamelCase				(    self				:     Optional[Any]					,						snake_case_				:     Any					,						snake_case_				:     Union[str, Any])->				Union[str, Any]:
						return self._query_range(self.root					,						snake_case_					,						snake_case_)



	def 		UpperCamelCase				(    self				:     List[str]					,						snake_case_				:     List[str]					,						snake_case_				:     List[str])->				List[Any]:
						if start == end:
											return SegmentTreeNode(snake_case_					,						snake_case_					,						self.collection[start])
						__lowerCAmelCase						 =(start + end) // 2
						__lowerCAmelCase						 =self._build_tree(snake_case_					,						snake_case_)
						__lowerCAmelCase						 =self._build_tree(mid + 1					,						snake_case_)
						return SegmentTreeNode(snake_case_					,						snake_case_					,						self.fn(left.val					,						right.val)					,						snake_case_					,						snake_case_)



	def 		UpperCamelCase				(    self				:     Dict					,						snake_case_				:     Tuple					,						snake_case_				:     int					,						snake_case_				:     int)->				List[Any]:
						if node.start == i and node.end == i:
											__lowerCAmelCase						 =val
											return
						if i <= node.mid:
											self._update_tree(node.left					,						snake_case_					,						snake_case_)
						else:
											self._update_tree(node.right					,						snake_case_					,						snake_case_)
						__lowerCAmelCase						 =self.fn(node.left.val					,						node.right.val)



	def 		UpperCamelCase				(    self				:     Tuple					,						snake_case_				:     str					,						snake_case_				:     str					,						snake_case_				:     List[Any])->				Optional[int]:
						if node.start == i and node.end == j:
											return node.val

						if i <= node.mid:
											if j <= node.mid:
																# range in left child tree
																return self._query_range(node.left					,						snake_case_					,						snake_case_)
											else:
																# range in left child tree and right child tree
																return self.fn(
																    self._query_range(node.left					,						snake_case_					,						node.mid)					,						self._query_range(node.right					,						node.mid + 1					,						snake_case_)					,						)
						else:
											# range in right child tree
											return self._query_range(node.right					,						snake_case_					,						snake_case_)



	def 		UpperCamelCase				(    self				:     List[str])->				Tuple:
						if self.root is not None:
											__lowerCAmelCase						 =Queue()
											queue.put(self.root)
											while not queue.empty():
																__lowerCAmelCase						 =queue.get()
																yield node

																if node.left is not None:
																					queue.put(node.left)

																if node.right is not None:
																					queue.put(node.right)


if __name__ == "__main__":
				import operator

				for fn in [operator.add, max, min]:
								print('''*''' * 50)
								lowercase_													=      SegmentTree([2, 1, 5, 3, 4], fn)
								for node in arr.traverse():
												print(node)
								print()

								arr.update(1, 5)
								for node in arr.traverse():
												print(node)
								print()

								print(arr.query_range(3, 4))  # 7
								print(arr.query_range(2, 2))  # 5
								print(arr.query_range(1, 3))  # 13
								print()




