



import numpy as np






class      UpperCamelCase    :



	def __init__(       self		):
							A__							=       (0, 0)
							A__							=       None
							A__							=       0
							A__							=       0
							A__							=       0



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



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






class      UpperCamelCase    :



	def __init__(       self			,	UpperCAmelCase__=(5, 5)		):
							A__							=       np.zeros(UpperCAmelCase__		)
							A__							=       world_size[0]
							A__							=       world_size[1]



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



	def 			__A							(       self			,	UpperCAmelCase__		):
							A__							=       [
							    (-1, -1),
							    (-1, 0),
							    (-1, 1),
							    (0, -1),
							    (0, 1),
							    (1, -1),
							    (1, 0),
							    (1, 1),
							]
							A__							=       cell.position[0]
							A__							=       cell.position[1]
							A__							=       []
							for n in neughbour_cord:
													A__							=       current_x + n[0]
													A__							=       current_y + n[1]
													if 0 <= x < self.world_x_limit and 0 <= y < self.world_y_limit:
																			A__							=       Cell()
																			A__							=       (x, y)
																			A__							=       cell
																			neighbours.append(UpperCAmelCase__		)
							return neighbours





def  UpperCamelCase						(       _A			:				Dict			,							_A			:				int			,							_A			:				Any    )->       List[str]:





						"""simple docstring"""





						A__							=       []
						A__							=       []
						_open.append(_A    )

						while _open:
												A__							=       np.argmin([n.f for n in _open]    )
												A__							=       _open[min_f]
												_closed.append(_open.pop(_A    )    )
												if current == goal:
																		break
												for n in world.get_neigbours(_A    ):
																		for c in _closed:
																								if c == n:
																														continue
																		A__							=       current.g + 1
																		A__						,       A__							=       n.position
																		A__						,       A__							=       goal.position
																		A__							=       (ya - ya) ** 2 + (xa - xa) ** 2
																		A__							=       n.h + n.g

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


if __name__ == "__main__":
						UpperCAmelCase_							:      Optional[int]      =  Gridworld()
						# Start position and goal
						UpperCAmelCase_							:      Union[str, Any]      =  Cell()
						UpperCAmelCase_							:      Optional[int]      =  (0, 0)
						UpperCAmelCase_							:      Union[str, Any]      =  Cell()
						UpperCAmelCase_							:      str      =  (4, 4)
						print(F'''path from {start.position} to {goal.position}''')
						UpperCAmelCase_							:      Tuple      =  astar(world, start, goal)
						#   Just for visual reasons.
						for i in s:
												UpperCAmelCase_							:      Optional[Any]      =  1
						print(world.w)










from __future__ import annotations

from random import random






class      UpperCamelCase    :



	def __init__(       self			,	UpperCAmelCase__ = None		):
							A__							=       value
							A__							=       random()
							A__							=       None
							A__							=       None



	def __repr__(       self		):
							from pprint import pformat

							if self.left is None and self.right is None:
													return F"""'{self.value}: {self.prior:.5}'"""
							else:
													return pformat(
													    {F"""{self.value}: {self.prior:.5}""": (self.left, self.right)}			,	indent=1		)



	def __str__(       self		):
							A__							=       str(self.value		) + " "
							A__							=       str(self.left or ""		)
							A__							=       str(self.right or ""		)
							return value + left + right





def  UpperCamelCase						(       _A			:				Node | None			,							_A			:				int    )->       tuple[Node | None, Node | None]:





						"""simple docstring"""





						if root is None:  # None tree is split into 2 Nones
												return None, None
						elif root.value is None:
												return None, None
						else:
												if value < root.value:
																		A__						,       A__							=       split(root.left			,							_A    )
																		return left, root
												else:
																		A__						,       A__							=       split(root.right			,							_A    )
																		return root, right
def  UpperCamelCase						(       _A			:				Node | None			,							_A			:				Node | None    )->       Node | None:





						"""simple docstring"""





						if (not left) or (not right):  # If one node is None, return the other
												return left or right
						elif left.prior < right.prior:
												A__							=       merge(left.right			,							_A    )
												return left
						else:
												A__							=       merge(_A			,							right.left    )
												return right
def  UpperCamelCase						(       _A			:				Node | None			,							_A			:				int    )->       Node | None:





						"""simple docstring"""





						A__							=       Node(_A    )
						A__						,       A__							=       split(_A			,							_A    )
						return merge(merge(_A			,							_A    )			,							_A    )
def  UpperCamelCase						(       _A			:				Node | None			,							_A			:				int    )->       Node | None:





						"""simple docstring"""





						A__						,       A__							=       split(_A			,							value - 1    )
						A__						,       A__							=       split(_A			,							_A    )
						return merge(_A			,							_A    )
def  UpperCamelCase						(       _A			:				Node | None    )->       None:





						"""simple docstring"""





						if not root:  # None
												return
						else:
												inorder(root.left    )
												print(root.value			,							end=","    )
												inorder(root.right    )
def  UpperCamelCase						(       _A			:				Node | None			,							_A			:				str    )->       Node | None:





						"""simple docstring"""





						for arg in args.split():
												if arg[0] == "+":
																		A__							=       insert(_A			,							int(arg[1:]    )    )

												elif arg[0] == "-":
																		A__							=       erase(_A			,							int(arg[1:]    )    )

												else:
																		print("Unknown command"    )

						return root
def  UpperCamelCase						(       )->       None:





						"""simple docstring"""





						A__							=       None
						print(
						    "enter numbers to create a tree, + value to add value into treap, "
						    "- value to erase all nodes with value. 'q' to quit. "    )

						A__							=       input()
						while args != "q":
												A__							=       interact_treap(_A			,							_A    )
												print(_A    )
												A__							=       input()

						print("good by!"    )


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()





