






"""simple docstring"""
def        snake_case   (     A__		):
			UpperCAmelCase_  :				Dict      =      0

			# if input_string is "aba" than new_input_string become "a|b|a"
			UpperCAmelCase_  :				str      =      ""
			UpperCAmelCase_  :				Dict      =      ""

			# append each character + "|" in new_string for range(0, length-1)
			for i in input_string[: len(A__		) - 1]:
						new_input_string += i + "|"
			# append last character
			new_input_string += input_string[-1]

			# we will store the starting and ending of previous furthest ending palindromic
			# substring
			UpperCAmelCase_  ,			UpperCAmelCase_  :				Dict      =      0, 0

			# length[i] shows the length of palindromic substring with center i
			UpperCAmelCase_  :				Dict      =      [1 for i in range(len(A__		)		)]

			# for each character in new_string find corresponding palindromic string
			UpperCAmelCase_  :				List[str]      =      0
			for j in range(len(A__		)		):
						UpperCAmelCase_  :				List[Any]      =      1 if j > r else min(length[l + r - j] // 2			,r - j + 1		)
						while (
						    j - k >= 0
						    and j + k < len(A__		)
						    and new_input_string[k + j] == new_input_string[j - k]
						):
									k += 1

						UpperCAmelCase_  :				Tuple      =      2 * k - 1

						# does this string is ending after the previously explored end (that is r) ?
						# if yes the update the new r to the last index of this
						if j + k - 1 > r:
									UpperCAmelCase_  :				int      =      j - k + 1  # noqa: E741
									UpperCAmelCase_  :				int      =      j + k - 1

						# update max_length and start position
						if max_length < length[j]:
									UpperCAmelCase_  :				Union[str, Any]      =      length[j]
									UpperCAmelCase_  :				str      =      j

    # create that string
			UpperCAmelCase_  :				int      =      new_input_string[start - max_length // 2 : start + max_length // 2 + 1]
			for i in s:
						if i != "|":
									output_string += i

			return output_string


if __name__ == "__main__":
			import doctest

			doctest.testmod()











"""simple docstring"""
from __future__ import annotations

import time

lowerCamelCase_       			=   list[tuple[int, int]]

lowerCamelCase_       			=   [
    [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],
]

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







class     UpperCamelCase_ :





	def __init__(   self      :				int			,			lowerCAmelCase_      :				int			,			lowerCAmelCase_      :				int			,			lowerCAmelCase_      :				int			,			lowerCAmelCase_      :				int			,			lowerCAmelCase_      :				Node | None		)		->    List[str]:
				UpperCAmelCase_  :				List[Any]      =      pos_x
				UpperCAmelCase_  :				Dict      =      pos_y
				UpperCAmelCase_  :				List[Any]      =      (pos_y, pos_x)
				UpperCAmelCase_  :				int      =      goal_x
				UpperCAmelCase_  :				int      =      goal_y
				UpperCAmelCase_  :				Union[str, Any]      =      parent







class     UpperCamelCase_ :





	def __init__(   self      :				Dict			,			lowerCAmelCase_      :				tuple[int, int]			,			lowerCAmelCase_      :				tuple[int, int]		)		->    int:
				UpperCAmelCase_  :				Dict      =      Node(start[1]			,			start[0]			,			goal[1]			,			goal[0]			,			lowerCAmelCase_		)
				UpperCAmelCase_  :				List[str]      =      Node(goal[1]			,			goal[0]			,			goal[1]			,			goal[0]			,			lowerCAmelCase_		)

				UpperCAmelCase_  :				List[str]      =      [self.start]
				UpperCAmelCase_  :				List[Any]      =      False





	def   _SCREAMING_SNAKE_CASE   (   self      :				int		)		->    Path | None:
				while self.node_queue:
							UpperCAmelCase_  :				Optional[int]      =      self.node_queue.pop(0		)

							if current_node.pos == self.target.pos:
										UpperCAmelCase_  :				int      =      True
										return self.retrace_path(lowerCAmelCase_		)

							UpperCAmelCase_  :				Union[str, Any]      =      self.get_successors(lowerCAmelCase_		)

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

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





	def   _SCREAMING_SNAKE_CASE   (   self      :				Tuple			,			lowerCAmelCase_      :				Node		)		->    list[Node]:
				UpperCAmelCase_  :				Union[str, Any]      =      []
				for action in delta:
							UpperCAmelCase_  :				Optional[Any]      =      parent.pos_x + action[1]
							UpperCAmelCase_  :				Tuple      =      parent.pos_y + action[0]
							if not (0 <= pos_x <= len(grid[0]		) - 1 and 0 <= pos_y <= len(lowerCAmelCase_		) - 1):
										continue

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

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





	def   _SCREAMING_SNAKE_CASE   (   self      :				Union[str, Any]			,			lowerCAmelCase_      :				Node | None		)		->    Path:
				UpperCAmelCase_  :				Any      =      node
				UpperCAmelCase_  :				Any      =      []
				while current_node is not None:
							path.append((current_node.pos_y, current_node.pos_x)		)
							UpperCAmelCase_  :				int      =      current_node.parent
				path.reverse()
				return path







class     UpperCamelCase_ :





	def __init__(   self      :				str			,			lowerCAmelCase_      :				int			,			lowerCAmelCase_      :				Tuple		)		->    Tuple:
				UpperCAmelCase_  :				Union[str, Any]      =      BreadthFirstSearch(lowerCAmelCase_			,			lowerCAmelCase_		)
				UpperCAmelCase_  :				Any      =      BreadthFirstSearch(lowerCAmelCase_			,			lowerCAmelCase_		)
				UpperCAmelCase_  :				Any      =      False





	def   _SCREAMING_SNAKE_CASE   (   self      :				List[Any]		)		->    Path | None:
				while self.fwd_bfs.node_queue or self.bwd_bfs.node_queue:
							UpperCAmelCase_  :				List[Any]      =      self.fwd_bfs.node_queue.pop(0		)
							UpperCAmelCase_  :				Tuple      =      self.bwd_bfs.node_queue.pop(0		)

							if current_bwd_node.pos == current_fwd_node.pos:
										UpperCAmelCase_  :				Optional[int]      =      True
										return self.retrace_bidirectional_path(
										    lowerCAmelCase_			,			lowerCAmelCase_		)

							UpperCAmelCase_  :				Any      =      current_bwd_node
							UpperCAmelCase_  :				Optional[int]      =      current_fwd_node

							UpperCAmelCase_  :				Any      =      {
							    self.fwd_bfs: self.fwd_bfs.get_successors(lowerCAmelCase_		),
							    self.bwd_bfs: self.bwd_bfs.get_successors(lowerCAmelCase_		),
							}

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

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





	def   _SCREAMING_SNAKE_CASE   (   self      :				int			,			lowerCAmelCase_      :				Node			,			lowerCAmelCase_      :				Node		)		->    Path:
				UpperCAmelCase_  :				Tuple      =      self.fwd_bfs.retrace_path(lowerCAmelCase_		)
				UpperCAmelCase_  :				str      =      self.bwd_bfs.retrace_path(lowerCAmelCase_		)
				bwd_path.pop()
				bwd_path.reverse()
				UpperCAmelCase_  :				int      =      fwd_path + bwd_path
				return path


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

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

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

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

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

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



