




'''simple docstring'''







from __future__ import annotations

import time

A     =list[tuple[int, int]]

A     =[
    [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],
]

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


class 			_a  :
       def __init__(	self						:	Any   ,				lowercase						:	int   ,				lowercase						:	int   ,				lowercase						:	int   ,				lowercase						:	int   ,				lowercase						:	Node | None				):



           '''simple docstring'''

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






class 			_a  :
       def __init__(	self						:	Tuple   ,				lowercase						:	tuple[int, int]   ,				lowercase						:	tuple[int, int]				):



           '''simple docstring'''

           UpperCAmelCase			       =		Node(start[1]   ,				start[0]   ,				goal[1]   ,				goal[0]   ,				_a				)
           UpperCAmelCase			       =		Node(goal[1]   ,				goal[0]   ,				goal[1]   ,				goal[0]   ,				_a				)

           UpperCAmelCase			       =		[self.start]
           UpperCAmelCase			       =		False
       def     A      (	self						:	Union[str, Any]				):



           '''simple docstring'''

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

               if current_node.pos == self.target.pos:
                   UpperCAmelCase			       =		True
                   return self.retrace_path(_a				)

               UpperCAmelCase			       =		self.get_successors(_a				)

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

           if not self.reached:
               return [self.start.pos]
           return None
       def     A      (	self						:	List[Any]   ,				lowercase						:	Node				):



           '''simple docstring'''

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

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

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







       def     A      (	self						:	List[str]   ,				lowercase						:	Node | None				):



           '''simple docstring'''

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






class 			_a  :
       def __init__(	self						:	int   ,				lowercase						:	str   ,				lowercase						:	Optional[int]				):



           '''simple docstring'''

           UpperCAmelCase			       =		BreadthFirstSearch(_a   ,				_a				)
           UpperCAmelCase			       =		BreadthFirstSearch(_a   ,				_a				)
           UpperCAmelCase			       =		False
       def     A      (	self						:	Tuple				):



           '''simple docstring'''

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

               if current_bwd_node.pos == current_fwd_node.pos:
                   UpperCAmelCase			       =		True
                   return self.retrace_bidirectional_path(
                       _a   ,				_a				)

               UpperCAmelCase			       =		current_bwd_node
               UpperCAmelCase			       =		current_fwd_node

               UpperCAmelCase			       =		{
                   self.fwd_bfs: self.fwd_bfs.get_successors(_a				),
                   self.bwd_bfs: self.bwd_bfs.get_successors(_a				),
               }

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

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







       def     A      (	self						:	Dict   ,				lowercase						:	Node   ,				lowercase						:	Node				):



           '''simple docstring'''

           UpperCAmelCase			       =		self.fwd_bfs.retrace_path(_a				)
           UpperCAmelCase			       =		self.bwd_bfs.retrace_path(_a				)
           bwd_path.pop()
           bwd_path.reverse()
           UpperCAmelCase			       =		fwd_path + bwd_path
           return path


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

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

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

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

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

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






'''simple docstring'''







from __future__ import annotations

from random import choice





def 					UpperCAmelCase_		(__a      :    str ):






   """simple docstring"""

   return choice(__a )





def 					UpperCAmelCase_		(__a      :    list[int] ,	__a      :    int ):






   """simple docstring"""

   _a				:	Dict			=   random_pivot(__a )

   # partition based on pivot
   # linear time
   _a				:	Optional[int]			=   [e for e in lst if e < pivot]
   _a				:	List[str]			=   [e for e in lst if e > pivot]

   # if we get lucky, pivot might be the element we want.
   # we can easily see this:
   # small (elements smaller than k)
   # + pivot (kth element)
   # + big (elements larger than k)
   if len(__a ) == k - 1:
      return pivot
   # pivot is in elements bigger than k
   elif len(__a ) < k - 1:
      return kth_number(__a ,	k - len(__a ) - 1 )
   # pivot is in elements smaller than k
   else:
      return kth_number(__a ,	__a )


if __name__ == "__main__":
  import doctest

  doctest.testmod()



