'''simple docstring'''


__lowerCAmelCase	:       List[str]						       =	{
    "A": ["B", "C", "E"],
    "B": ["A", "D", "E"],
    "C": ["A", "F", "G"],
    "D": ["B"],
    "E": ["A", "B", "D"],
    "F": ["C"],
    "G": ["C"],
}





def       lowerCAmelCase					(		UpperCamelCase__				:   dict    ,					UpperCamelCase__				:   List[str]    ,					UpperCamelCase__				:   Optional[Any]       ):


	"""simple docstring"""
	__UpperCAmelCase							=			set()
	# keep track of all the paths to be checked
	__UpperCAmelCase							=			[[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							=			queue.pop(0       )
		# get the last node from the path
		__UpperCAmelCase							=			path[-1]
		if node not in explored:
			__UpperCAmelCase							=			graph[node]
			# go through all neighbour nodes, construct a new path and
			# push it into the queue
			for neighbour in neighbours:
				__UpperCAmelCase							=			list(UpperCamelCase__       )
				new_path.append(UpperCamelCase__       )
				queue.append(UpperCamelCase__       )
				# return path if neighbour is goal
				if neighbour == goal:
					return new_path

            # mark node as explored
			explored.add(UpperCamelCase__       )

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





def       lowerCAmelCase					(		UpperCamelCase__				:   dict    ,					UpperCamelCase__				:   Optional[Any]    ,					UpperCamelCase__				:   str       ):


	"""simple docstring"""
	if not graph or start not in graph or target not in graph:
		return -1
	if start == target:
		return 0
	__UpperCAmelCase							=			[start]
	__UpperCAmelCase							=			set(UpperCamelCase__       )
	# Keep tab on distances from `start` node.
	__UpperCAmelCase							=			{start: 0, target: -1}
	while queue:
		__UpperCAmelCase							=			queue.pop(0       )
		if node == target:
			__UpperCAmelCase							=			(
			    dist[node] if dist[target] == -1 else min(dist[target]    ,					dist[node]       )
			)
		for adjacent in graph[node]:
			if adjacent not in visited:
				visited.add(UpperCamelCase__       )
				queue.append(UpperCamelCase__       )
				__UpperCAmelCase							=			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 __future__ import annotations

import math





def       lowerCAmelCase					(		UpperCamelCase__				:   float    ,					UpperCamelCase__				:   int       ):


	"""simple docstring"""
	__UpperCAmelCase							=			u
	for i in range(1    ,					UpperCamelCase__       ):
		__UpperCAmelCase							=			temp * (u - i)
	return temp





def       lowerCAmelCase					(		):


	"""simple docstring"""
	__UpperCAmelCase							=			int(input('''enter the numbers of values: '''       )       )
	__UpperCAmelCase							=			[]
	for _ in range(UpperCamelCase__       ):
		y.append([]       )
	for i in range(UpperCamelCase__       ):
		for j in range(UpperCamelCase__       ):
			y[i].append(UpperCamelCase__       )
			__UpperCAmelCase							=			0

	print('''enter the values of parameters in a list: '''       )
	__UpperCAmelCase							=			list(map(UpperCamelCase__    ,					input().split()       )       )

	print('''enter the values of corresponding parameters: '''       )
	for i in range(UpperCamelCase__       ):
		__UpperCAmelCase							=			float(input()       )

	__UpperCAmelCase							=			int(input('''enter the value to interpolate: '''       )       )
	__UpperCAmelCase							=			(value - x[0]) / (x[1] - x[0])

	# for calculating forward difference table

	for i in range(1    ,					UpperCamelCase__       ):
		for j in range(n - i       ):
			__UpperCAmelCase							=			y[j + 1][i - 1] - y[j][i - 1]

	__UpperCAmelCase							=			y[0][0]
	for i in range(1    ,					UpperCamelCase__       ):
		summ += (ucal(UpperCamelCase__    ,					UpperCamelCase__       ) * y[0][i]) / math.factorial(UpperCamelCase__       )

	print(f"""the value at {value} is {summ}"""       )


if __name__ == "__main__":
					main()
