
import numpy as np





class 			_lowerCAmelCase      :




				def __init__(      self  )       ->   List[str]:
							lowerCAmelCase_      			=			(0, 0)
							lowerCAmelCase_      			=			None
							lowerCAmelCase_      			=			0
							lowerCAmelCase_      			=			0
							lowerCAmelCase_      			=			0




				def __eq__(      self       ,       _UpperCamelCase  )       ->   int:
							return self.position == cell.position




				def   __a		(      self  )       ->   List[Any]:
							print(self.position  )





class 			_lowerCAmelCase      :




				def __init__(      self       ,       _UpperCamelCase=(5, 5)  )       ->   Optional[int]:
							lowerCAmelCase_      			=			np.zeros(_UpperCamelCase  )
							lowerCAmelCase_      			=			world_size[0]
							lowerCAmelCase_      			=			world_size[1]




				def   __a		(      self  )       ->   Union[str, Any]:
							print(self.w  )




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






def      lowerCamelCase__       (       __lowerCAmelCase						:						str					,							__lowerCAmelCase						:						Optional[int]					,							__lowerCAmelCase						:						Tuple       ):




			"""simple docstring"""


			lowerCAmelCase_      			=			[]
			lowerCAmelCase_      			=			[]
			_open.append(__lowerCAmelCase       )

			while _open:
						lowerCAmelCase_      			=			np.argmin([n.f for n in _open]       )
						lowerCAmelCase_      			=			_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
									lowerCAmelCase_      			=			current.g + 1
									lowerCAmelCase_			,						lowerCAmelCase_      			=			n.position
									lowerCAmelCase_			,						lowerCAmelCase_      			=			goal.position
									lowerCAmelCase_      			=			(ya - ya) ** 2 + (xa - xa) ** 2
									lowerCAmelCase_      			=			n.h + n.g

									for c in _open:
												if c == n and c.f < n.f:
															continue
									_open.append(__lowerCAmelCase       )
			lowerCAmelCase_      			=			[]
			while current.parent is not None:
						path.append(current.position       )
						lowerCAmelCase_      			=			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)





def      lowerCamelCase__       (       __lowerCAmelCase						:						int       ):




			"""simple docstring"""


			if upper_limit < 0:
						raise ValueError("Limit for the Catalan sequence must be ≥ 0"       )

			lowerCAmelCase_      			=			[0] * (upper_limit + 1)

			# Base case: C(0) = C(1) = 1
			lowerCAmelCase_      			=			1
			if upper_limit > 0:
						lowerCAmelCase_      			=			1

			# Recurrence relation: C(i) = sum(C(j).C(i-j-1)), from j = 0 to i
			for i in range(2					,							upper_limit + 1       ):
						for j in range(__lowerCAmelCase       ):
									catalan_list[i] += catalan_list[j] * catalan_list[i - j - 1]

			return catalan_list


if __name__ == "__main__":
			print("\n********* Catalan Numbers Using Dynamic Programming ************\n")
			print("\n*** Enter -1 at any time to quit ***")
			print("\nEnter the upper limit (≥ 0) for the Catalan number sequence: ", end="")
			try:
						while True:
									_A     =  int(input().strip())
									if N < 0:
												print("\n********* Goodbye!! ************")
												break
									else:
												print(f"""The Catalan numbers from 0 through {N} are:""")
												print(catalan_numbers(N))
												print("Try another upper limit for the sequence: ", end="")
			except (NameError, ValueError):
						print("\n********* Invalid input, goodbye! ************\n")

			import doctest

			doctest.testmod()



