





"""simple docstring"""




UpperCamelCase_									={
    """A""": ["""B""", """C""", """E"""],
    """B""": ["""A""", """D""", """E"""],
    """C""": ["""A""", """F""", """G"""],
    """D""": ["""B"""],
    """E""": ["""A""", """B""", """D"""],
    """F""": ["""C"""],
    """G""": ["""C"""],
}





def 	a_    (							_lowercase	,						_lowercase	,						_lowercase       ):
						_UpperCamelCase      : Dict         =   set()
						# keep track of all the paths to be checked
						_UpperCamelCase      : List[Any]         =   [[start]]

						# return path if start is goal
						if start == goal:
												return [start]

						# keeps looping until all possible paths have been checked
						while queue:
												# pop the first path from the queue
												_UpperCamelCase      : Optional[Any]         =   queue.pop(0       )
												# get the last node from the path
												_UpperCamelCase      : Optional[Any]         =   path[-1]
												if node not in explored:
																		_UpperCamelCase      : Optional[int]         =   graph[node]
																		# go through all neighbour nodes, construct a new path and
																		# push it into the queue
																		for neighbour in neighbours:
																								_UpperCamelCase      : List[Any]         =   list(_lowercase       )
																								new_path.append(_lowercase       )
																								queue.append(_lowercase       )
																								# return path if neighbour is goal
																								if neighbour == goal:
																														return new_path

            # mark node as explored
																		explored.add(_lowercase       )

    # in case there's no path between the 2 nodes
						return []





def 	a_    (							_lowercase	,						_lowercase	,						_lowercase       ):
						if not graph or start not in graph or target not in graph:
												return -1
						if start == target:
												return 0
						_UpperCamelCase      : Union[str, Any]         =   [start]
						_UpperCamelCase      : Optional[int]         =   set(_lowercase       )
						# Keep tab on distances from `start` node.
						_UpperCamelCase      : List[str]         =   {start: 0, target: -1}
						while queue:
												_UpperCamelCase      : Tuple         =   queue.pop(0       )
												if node == target:
																		_UpperCamelCase      : List[Any]         =   (
																		    dist[node] if dist[target] == -1 else min(dist[target]	,						dist[node]       )
																		)
												for adjacent in graph[node]:
																		if adjacent not in visited:
																								visited.add(_lowercase       )
																								queue.append(_lowercase       )
																								_UpperCamelCase      : int         =   dist[node] + 1
						return dist[target]


if __name__ == "__main__":
						print(bfs_shortest_path(demo_graph, """G""", """D"""))  # returns ['G', 'C', 'A', 'B', 'D']
						print(bfs_shortest_path_distance(demo_graph, """G""", """D"""))  # returns 4










"""simple docstring"""




from functools import lru_cache





@lru_cache
def 	a_    (							_lowercase       ):
						if num < 0:
												raise ValueError('''Number should not be negative.'''       )

						return 1 if num in (0, 1) else num * factorial(num - 1       )


if __name__ == "__main__":
						import doctest

						doctest.testmod()



