

from __future__ import annotations

import time

lowercase_       		=  list[tuple[int, int]]

lowercase_       		=  [
    [0, 0, 0, 0, 0, 0, 0],
    [0, 1, 0, 0, 0, 0, 0],  # 0 are free path whereas 1's are obstacles
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 1, 0, 0, 0, 0],
    [1, 0, 1, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 1, 0, 0],
]

lowercase_       		=  [[-1, 0], [0, -1], [1, 0], [0, 1]]  # up, left, down, right


class  A						:







    """simple docstring"""





    def __init__(      self :       List[Any],lowercase_ :       int,lowercase_ :       int,lowercase_ :       int,lowercase_ :       int,lowercase_ :       Node | None		)->    str:





        '''simple docstring'''







        A__          =   pos_x
        A__          =   pos_y
        A__          =   (pos_y, pos_x)
        A__          =   goal_x
        A__          =   goal_y
        A__          =   parent




class  A						:







    """simple docstring"""





    def __init__(      self :       str,lowercase_ :       tuple[int, int],lowercase_ :       tuple[int, int]		)->    Any:





        '''simple docstring'''







        A__          =   Node(start[1],start[0],goal[1],goal[0],lowercase_		)
        A__          =   Node(goal[1],goal[0],goal[1],goal[0],lowercase_		)

        A__          =   [self.start]
        A__          =   False


    def 						snake_case__     (      self :       Optional[int]		)->    Path | None:





        '''simple docstring'''







        while self.node_queue:
            A__          =   self.node_queue.pop(0		)

            if current_node.pos == self.target.pos:
                A__          =   True
                return self.retrace_path(lowercase_		)

            A__          =   self.get_successors(lowercase_		)

            for node in successors:
                self.node_queue.append(lowercase_		)

        if not self.reached:
            return [self.start.pos]
        return None


    def 						snake_case__     (      self :       Dict,lowercase_ :       Node		)->    list[Node]:





        '''simple docstring'''







        A__          =   []
        for action in delta:
            A__          =   parent.pos_x + action[1]
            A__          =   parent.pos_y + action[0]
            if not (0 <= pos_x <= len(grid[0]		) - 1 and 0 <= pos_y <= len(lowercase_		) - 1):
                continue

            if grid[pos_y][pos_x] != 0:
                continue

            successors.append(
                Node(lowercase_,lowercase_,self.target.pos_y,self.target.pos_x,lowercase_		)		)
        return successors


    def 						snake_case__     (      self :       Tuple,lowercase_ :       Node | None		)->    Path:





        '''simple docstring'''







        A__          =   node
        A__          =   []
        while current_node is not None:
            path.append((current_node.pos_y, current_node.pos_x)		)
            A__          =   current_node.parent
        path.reverse()
        return path




class  A						:







    """simple docstring"""





    def __init__(      self :       Dict,lowercase_ :       List[Any],lowercase_ :       List[str]		)->    Optional[Any]:





        '''simple docstring'''







        A__          =   BreadthFirstSearch(lowercase_,lowercase_		)
        A__          =   BreadthFirstSearch(lowercase_,lowercase_		)
        A__          =   False


    def 						snake_case__     (      self :       List[Any]		)->    Path | None:





        '''simple docstring'''







        while self.fwd_bfs.node_queue or self.bwd_bfs.node_queue:
            A__          =   self.fwd_bfs.node_queue.pop(0		)
            A__          =   self.bwd_bfs.node_queue.pop(0		)

            if current_bwd_node.pos == current_fwd_node.pos:
                A__          =   True
                return self.retrace_bidirectional_path(
                    lowercase_,lowercase_		)

            A__          =   current_bwd_node
            A__          =   current_fwd_node

            A__          =   {
                self.fwd_bfs: self.fwd_bfs.get_successors(lowercase_		),
                self.bwd_bfs: self.bwd_bfs.get_successors(lowercase_		),
            }

            for bfs in [self.fwd_bfs, self.bwd_bfs]:
                for node in successors[bfs]:
                    bfs.node_queue.append(lowercase_		)

        if not self.reached:
            return [self.fwd_bfs.start.pos]
        return None


    def 						snake_case__     (      self :       List[str],lowercase_ :       Node,lowercase_ :       Node		)->    Path:





        '''simple docstring'''







        A__          =   self.fwd_bfs.retrace_path(lowercase_		)
        A__          =   self.bwd_bfs.retrace_path(lowercase_		)
        bwd_path.pop()
        bwd_path.reverse()
        A__          =   fwd_path + bwd_path
        return path


if __name__ == "__main__":
     # all coordinates are given in format [y,x]
     import doctest

     doctest.testmod()
     lowercase_       		=  (0, 0)
     lowercase_       		=  (len(grid) - 1, len(grid[0]) - 1)
     for elem in grid:
          print(elem)

     lowercase_       		=  time.time()
     lowercase_       		=  BreadthFirstSearch(init, goal)
     lowercase_       		=  bfs.search()
     lowercase_       		=  time.time() - start_bfs_time

     print("Unidirectional BFS computation time : ", bfs_time)

     lowercase_       		=  time.time()
     lowercase_       		=  BidirectionalBreadthFirstSearch(init, goal)
     lowercase_       		=  bd_bfs.search()
     lowercase_       		=  time.time() - start_bd_bfs_time

     print("Bidirectional BFS computation time : ", bd_bfs_time)








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  :    str						    =  '\\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  :    List[str]						    =  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 				_UpperCAmelCase    (    datasets.Metric    ):

  """simple docstring"""


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

