





'''simple docstring'''


def  __lowerCAmelCase (__lowerCAmelCase   ):  # noqa: E741
		_UpperCAmelCase		:       List[str]								=      len(__lowerCAmelCase   )
		_UpperCAmelCase		:       str								=      0
		_UpperCAmelCase		:       List[str]								=      [0] * n
		_UpperCAmelCase		:       int								=      [False] * n
		_UpperCAmelCase		:       Dict								=      [False] * n

		def dfs(__lowerCAmelCase      , __lowerCAmelCase      , __lowerCAmelCase      , __lowerCAmelCase   ):
				if parent == root:
						out_edge_count += 1
				_UpperCAmelCase		:       List[Any]								=      True
				_UpperCAmelCase		:       str								=      at

				for to in l[at]:
						if to == parent:
								pass
						elif not visited[to]:
								_UpperCAmelCase		:       List[str]								=      dfs(__lowerCAmelCase      , __lowerCAmelCase      , __lowerCAmelCase      , __lowerCAmelCase   )
								_UpperCAmelCase		:       Tuple								=      min(low[at]      , low[to]   )

								# AP found via bridge
								if at < low[to]:
										_UpperCAmelCase		:       Dict								=      True
								# AP found via cycle
								if at == low[to]:
										_UpperCAmelCase		:       Dict								=      True
						else:
								_UpperCAmelCase		:       Optional[int]								=      min(low[at]      , __lowerCAmelCase   )
				return out_edge_count

		for i in range(__lowerCAmelCase   ):
				if not visited[i]:
						_UpperCAmelCase		:       str								=      0
						_UpperCAmelCase		:       Tuple								=      dfs(__lowerCAmelCase      , __lowerCAmelCase      , -1      , __lowerCAmelCase   )
						_UpperCAmelCase		:       Optional[int]								=      out_edge_count > 1

		for x in range(len(__lowerCAmelCase   )   ):
				if is_art[x] is True:
						print(__lowerCAmelCase   )


# Adjacency list of graph
lowerCamelCase__    	=     {
    0: [1, 2],
    1: [0, 2],
    2: [0, 1, 3, 5],
    3: [2, 4],
    4: [3],
    5: [2, 6, 8],
    6: [5, 7],
    7: [6, 8],
    8: [5, 7],
}





compute_ap(data)







'''simple docstring'''


from __future__ import annotations

lowerCamelCase__    	=     {
    'A': ['B', 'C', 'E'],
    'B': ['A', 'D', 'E'],
    'C': ['A', 'F', 'G'],
    'D': ['B'],
    'E': ['A', 'B', 'D'],
    'F': ['C'],
    'G': ['C'],
}






class 	lowerCAmelCase__			:




			def __init__(		self  :     int	,  lowerCamelCase__  :     dict[str, list[str]]	,  lowerCamelCase__  :     str )   ->None:



					'''simple docstring'''







					_UpperCAmelCase		:       Dict								=      graph
					# mapping node to its parent in resulting breadth first tree
					_UpperCAmelCase		:       dict[str, str | None]								=      {}
					_UpperCAmelCase		:       List[Any]								=      source_vertex




			def 							lowerCAmelCase__    (		self  :     Optional[int] )   ->None:



					'''simple docstring'''







					_UpperCAmelCase		:       List[Any]								=      {self.source_vertex}
					_UpperCAmelCase		:       List[Any]								=      None
					_UpperCAmelCase		:       List[str]								=      [self.source_vertex]  # first in first out queue

					while queue:
							_UpperCAmelCase		:       int								=      queue.pop(0 )
							for adjacent_vertex in self.graph[vertex]:
									if adjacent_vertex not in visited:
											visited.add(lowerCamelCase__ )
											_UpperCAmelCase		:       List[Any]								=      vertex
											queue.append(lowerCamelCase__ )






			def 							lowerCAmelCase__    (		self  :     Tuple	,  lowerCamelCase__  :     str )   ->str:



					'''simple docstring'''







					if target_vertex == self.source_vertex:
							return self.source_vertex

					_UpperCAmelCase		:       int								=      self.parent.get(lowerCamelCase__ )
					if target_vertex_parent is None:
							_UpperCAmelCase		:       Tuple								=      (
							    F"""No path from vertex: {self.source_vertex} to vertex: {target_vertex}"""
							)
							raise ValueError(lowerCamelCase__ )

					return self.shortest_path(lowerCamelCase__ ) + F"""->{target_vertex}"""


if __name__ == "__main__":
						lowerCamelCase__    	=     Graph(graph, 'G')
						g.breath_first_search()
						print(g.shortest_path('D'))
						print(g.shortest_path('G'))
						print(g.shortest_path('Foo'))



