





"""simple docstring"""




from __future__ import annotations

import time
from math import sqrt

# 1 for manhattan, 0 for euclidean
a						: Dict     	=			0

a						: Tuple     	=			[
    [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						: Tuple     	=			[[-1, 0], [0, -1], [1, 0], [0, 1]]  # up, left, down, right

a						: Union[str, Any]     	=			tuple[int, int]


class        __UpperCamelCase				:






							def __init__(   self      ,					lowerCAmelCase__      ,					lowerCAmelCase__      ,					lowerCAmelCase__      ,					lowerCAmelCase__      ,					lowerCAmelCase__      ,					lowerCAmelCase__      ,					)	-> None:
								a      :		str	=				pos_x
								a      :		int	=				pos_y
								a      :		Dict	=				(pos_y, pos_x)
								a      :		Dict	=				goal_x
								a      :		List[str]	=				goal_y
								a      :		Union[str, Any]	=				g_cost
								a      :		int	=				parent
								a      :		Optional[int]	=				self.calculate_heuristic()
								a      :		List[str]	=				self.g_cost + self.h_cost






							def     __a   (   self      )	-> float:
								a      :		Union[str, Any]	=				self.pos_x - self.goal_x
								a      :		Tuple	=				self.pos_y - self.goal_y
								if HEURISTIC == 1:
									return abs(lowerCAmelCase__      ) + abs(lowerCAmelCase__      )
								else:
									return sqrt(dy**2 + dx**2      )






							def __lt__(   self      ,					lowerCAmelCase__      )	-> bool:
								return self.f_cost < other.f_cost


class        __UpperCamelCase				:






							def __init__(   self      ,					lowerCAmelCase__      ,					lowerCAmelCase__      )	-> Optional[int]:
								a      :		Any	=				Node(start[1]      ,					start[0]      ,					goal[1]      ,					goal[0]      ,					0      ,					lowerCAmelCase__      )
								a      :		List[Any]	=				Node(goal[1]      ,					goal[0]      ,					goal[1]      ,					goal[0]      ,					9_9999      ,					lowerCAmelCase__      )

								a      :		Optional[int]	=				[self.start]
								a      :		list[Node]	=				[]

								a      :		List[str]	=				False






							def     __a   (   self      )	-> list[TPosition]:
								while self.open_nodes:
									# Open Nodes are sorted using __lt__
									self.open_nodes.sort()
									a      :		Optional[int]	=				self.open_nodes.pop(0      )

									if current_node.pos == self.target.pos:
										return self.retrace_path(lowerCAmelCase__      )

									self.closed_nodes.append(lowerCAmelCase__      )
									a      :		Optional[int]	=				self.get_successors(lowerCAmelCase__      )

									for child_node in successors:
										if child_node in self.closed_nodes:
											continue

										if child_node not in self.open_nodes:
											self.open_nodes.append(lowerCAmelCase__      )
										else:
											# retrieve the best current path
											a      :		Any	=				self.open_nodes.pop(self.open_nodes.index(lowerCAmelCase__      )      )

											if child_node.g_cost < better_node.g_cost:
												self.open_nodes.append(lowerCAmelCase__      )
											else:
												self.open_nodes.append(lowerCAmelCase__      )

								return [self.start.pos]






							def     __a   (   self      ,					lowerCAmelCase__      )	-> list[Node]:
								a      :		Dict	=				[]
								for action in delta:
									a      :		List[Any]	=				parent.pos_x + action[1]
									a      :		int	=				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      ,					parent.g_cost + 1      ,					lowerCAmelCase__      ,					)      )
								return successors






							def     __a   (   self      ,					lowerCAmelCase__      )	-> list[TPosition]:
								a      :		Tuple	=				node
								a      :		Union[str, Any]	=				[]
								while current_node is not None:
									path.append((current_node.pos_y, current_node.pos_x)      )
									a      :		List[str]	=				current_node.parent
								path.reverse()
								return path


class        __UpperCamelCase				:






							def __init__(   self      ,					lowerCAmelCase__      ,					lowerCAmelCase__      )	-> None:
								a      :		Dict	=				AStar(lowerCAmelCase__      ,					lowerCAmelCase__      )
								a      :		Tuple	=				AStar(lowerCAmelCase__      ,					lowerCAmelCase__      )
								a      :		Any	=				False






							def     __a   (   self      )	-> list[TPosition]:
								while self.fwd_astar.open_nodes or self.bwd_astar.open_nodes:
									self.fwd_astar.open_nodes.sort()
									self.bwd_astar.open_nodes.sort()
									a      :		Dict	=				self.fwd_astar.open_nodes.pop(0      )
									a      :		str	=				self.bwd_astar.open_nodes.pop(0      )

									if current_bwd_node.pos == current_fwd_node.pos:
										return self.retrace_bidirectional_path(
										    lowerCAmelCase__      ,					lowerCAmelCase__      )

									self.fwd_astar.closed_nodes.append(lowerCAmelCase__      )
									self.bwd_astar.closed_nodes.append(lowerCAmelCase__      )

									a      :		Union[str, Any]	=				current_bwd_node
									a      :		Tuple	=				current_fwd_node

									a      :		Tuple	=				{
									    self.fwd_astar: self.fwd_astar.get_successors(lowerCAmelCase__      ),
									    self.bwd_astar: self.bwd_astar.get_successors(lowerCAmelCase__      ),
									}

									for astar in [self.fwd_astar, self.bwd_astar]:
										for child_node in successors[astar]:
											if child_node in astar.closed_nodes:
												continue

											if child_node not in astar.open_nodes:
												astar.open_nodes.append(lowerCAmelCase__      )
											else:
												# retrieve the best current path
												a      :		int	=				astar.open_nodes.pop(
												    astar.open_nodes.index(lowerCAmelCase__      )      )

												if child_node.g_cost < better_node.g_cost:
													astar.open_nodes.append(lowerCAmelCase__      )
												else:
													astar.open_nodes.append(lowerCAmelCase__      )

								return [self.fwd_astar.start.pos]






							def     __a   (   self      ,					lowerCAmelCase__      ,					lowerCAmelCase__      )	-> list[TPosition]:
								a      :		str	=				self.fwd_astar.retrace_path(lowerCAmelCase__      )
								a      :		str	=				self.bwd_astar.retrace_path(lowerCAmelCase__      )
								bwd_path.pop()
								bwd_path.reverse()
								a      :		Optional[Any]	=				fwd_path + bwd_path
								return path


if __name__ == "__main__":
		# all coordinates are given in format [y,x]
		a						: int     	=			(0, 0)
		a						: List[str]     	=			(len(grid) - 1, len(grid[0]) - 1)
		for elem in grid:
				print(elem)

		a						: str     	=			time.time()
		a						: Optional[Any]     	=			AStar(init, goal)
		a						: str     	=			a_star.search()
		a						: Any     	=			time.time() - start_time
		print(F'''AStar execution time = {end_time:f} seconds''')

		a						: List[Any]     	=			time.time()
		a						: Optional[int]     	=			BidirectionalAStar(init, goal)
		a						: Optional[Any]     	=			time.time() - bd_start_time
		print(F'''BidirectionalAStar execution time = {bd_end_time:f} seconds''')



'''simple docstring'''

def      UpperCamelCase_						(					snake_case_       :       list[int]						,		snake_case_       :       list[int]      )					->     tuple[float, float]:






 '''simple docstring'''

 if not len(snake_case_      ) == len(snake_case_      ) == 3:
  raise ValueError("""Please enter a valid equation."""      )
 if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
  raise ValueError("""Both a & b of two equations can't be zero."""      )

 # Extract the coefficients
 __lowerCAmelCase							,       __lowerCAmelCase							,       __lowerCAmelCase											=						equationa
 __lowerCAmelCase							,       __lowerCAmelCase							,       __lowerCAmelCase											=						equationa

 # Calculate the determinants of the matrices
 __lowerCAmelCase											=						aa * ba - aa * ba
 __lowerCAmelCase											=						ca * ba - ca * ba
 __lowerCAmelCase											=						aa * ca - aa * ca

 # Check if the system of linear equations has a solution (using Cramer's rule)
 if determinant == 0:
  if determinant_x == determinant_y == 0:
   raise ValueError("""Infinite solutions. (Consistent system)"""      )
  else:
   raise ValueError("""No solution. (Inconsistent system)"""      )
 else:
  if determinant_x == determinant_y == 0:
   # Trivial solution (Inconsistent system)
   return (0.0, 0.0)
  else:
   __lowerCAmelCase											=						determinant_x / determinant
   __lowerCAmelCase											=						determinant_y / determinant
   # Non-Trivial Solution (Consistent system)
   return (x, y)






