






import numpy as np


class 							__a							:





						'''simple docstring'''



						def __init__(						self       ):
										SCREAMING_SNAKE_CASE_   :	Tuple													=   (0, 0)
										SCREAMING_SNAKE_CASE_   :	Optional[int]													=   None
										SCREAMING_SNAKE_CASE_   :	Tuple													=   0
										SCREAMING_SNAKE_CASE_   :	int													=   0
										SCREAMING_SNAKE_CASE_   :	int													=   0


						def __eq__(						self ,    UpperCamelCase__       ):
										return self.position == cell.position






						def   __snake_case			(						self       ):
										print(self.position       )






class 							__a							:





						'''simple docstring'''



						def __init__(						self ,    UpperCamelCase__=(5, 5)       ):
										SCREAMING_SNAKE_CASE_   :	Optional[int]													=   np.zeros(UpperCamelCase__       )
										SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   world_size[0]
										SCREAMING_SNAKE_CASE_   :	str													=   world_size[1]


						def   __snake_case			(						self       ):
										print(self.w       )






						def   __snake_case			(						self ,    UpperCamelCase__       ):
										SCREAMING_SNAKE_CASE_   :	str													=   [
										    (-1, -1),
										    (-1, 0),
										    (-1, 1),
										    (0, -1),
										    (0, 1),
										    (1, -1),
										    (1, 0),
										    (1, 1),
										]
										SCREAMING_SNAKE_CASE_   :	int													=   cell.position[0]
										SCREAMING_SNAKE_CASE_   :	Optional[int]													=   cell.position[1]
										SCREAMING_SNAKE_CASE_   :	List[Any]													=   []
										for n in neughbour_cord:
														SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   current_x + n[0]
														SCREAMING_SNAKE_CASE_   :	Dict													=   current_y + n[1]
														if 0 <= x < self.world_x_limit and 0 <= y < self.world_y_limit:
																		SCREAMING_SNAKE_CASE_   :	List[Any]													=   Cell()
																		SCREAMING_SNAKE_CASE_   :	Any													=   (x, y)
																		SCREAMING_SNAKE_CASE_   :	Any													=   cell
																		neighbours.append(UpperCamelCase__       )
										return neighbours






def 					_lowerCamelCase(			lowerCAmelCase__				:		Dict    ,    lowerCAmelCase__				:		Union[str, Any]    ,    lowerCAmelCase__				:		List[Any]      ):





				'''simple docstring'''







				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   []
				SCREAMING_SNAKE_CASE_   :	List[str]													=   []
				_open.append(lowerCAmelCase__      )

				while _open:
								SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   np.argmin([n.f for n in _open]      )
								SCREAMING_SNAKE_CASE_   :	List[Any]													=   _open[min_f]
								_closed.append(_open.pop(lowerCAmelCase__      )      )
								if current == goal:
												break
								for n in world.get_neigbours(lowerCAmelCase__      ):
												for c in _closed:
																if c == n:
																				continue
												SCREAMING_SNAKE_CASE_   :	Optional[int]													=   current.g + 1
												SCREAMING_SNAKE_CASE_   :	Optional[int]													=   n.position
												SCREAMING_SNAKE_CASE_   :	Any													=   goal.position
												SCREAMING_SNAKE_CASE_   :	Optional[int]													=   (ya - ya) ** 2 + (xa - xa) ** 2
												SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   n.h + n.g

												for c in _open:
																if c == n and c.f < n.f:
																				continue
												_open.append(lowerCAmelCase__      )
				SCREAMING_SNAKE_CASE_   :	Any													=   []
				while current.parent is not None:
								path.append(current.position      )
								SCREAMING_SNAKE_CASE_   :	str													=   current.parent
				path.append(current.position      )
				return path[::-1]


if __name__ == "__main__":
				A        =			Gridworld()
				# Start position and goal
				A        =			Cell()
				A        =			(0, 0)
				A        =			Cell()
				A        =			(4, 4)
				print(f"""path from {start.position} to {goal.position}""")
				A        =			astar(world, start, goal)
				#   Just for visual reasons.
				for i in s:
								A        =			1
				print(world.w)







from __future__ import annotations

from collections import Counter
from random import random


class 							__a							:





		'''simple docstring'''



		def __init__(						self       ):
						SCREAMING_SNAKE_CASE_   :	List[str]													=   {}


		def   __snake_case			(						self ,    UpperCamelCase__       ):
						SCREAMING_SNAKE_CASE_   :	int													=   {}


		def   __snake_case			(						self ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__       ):
						if nodea not in self.connections:
										self.add_node(UpperCamelCase__       )
						if nodea not in self.connections:
										self.add_node(UpperCamelCase__       )
						SCREAMING_SNAKE_CASE_   :	Tuple													=   probability


		def   __snake_case			(						self       ):
						return list(self.connections       )






		def   __snake_case			(						self ,    UpperCamelCase__       ):
						SCREAMING_SNAKE_CASE_   :	Dict													=   0
						SCREAMING_SNAKE_CASE_   :	List[Any]													=   random()

						for dest in self.connections[node]:
										current_probability += self.connections[node][dest]
										if current_probability > random_value:
														return dest
						return ""






def 					_lowerCamelCase(			lowerCAmelCase__				:		str    ,    lowerCAmelCase__				:		list[tuple[str, str, float]]    ,    lowerCAmelCase__				:		int      ):





				'''simple docstring'''







				SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   MarkovChainGraphUndirectedUnweighted()

				for nodea, nodea, probability in transitions:
								graph.add_transition_probability(lowerCAmelCase__    ,    lowerCAmelCase__    ,    lowerCAmelCase__      )

				SCREAMING_SNAKE_CASE_   :	List[str]													=   Counter(graph.get_nodes()      )
				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   start

				for _ in range(lowerCAmelCase__      ):
								SCREAMING_SNAKE_CASE_   :	Dict													=   graph.transition(lowerCAmelCase__      )
								visited[node] += 1

				return visited


if __name__ == "__main__":
				import doctest

				doctest.testmod()