



'''simple docstring'''

def      __lowerCamelCase     (      lowerCAmelCase_  )			->      set:
		_a     :      Dict        =							set()
		# edges = list of graph's edges
		_a     :      Any        =							get_edges(lowerCAmelCase_  )

		# While there are still elements in edges list, take an arbitrary edge
		# (from_node, to_node) and add his extremity to chosen_vertices and then
		# remove all arcs adjacent to the from_node and to_node
		while edges:
				_a       ,					_a     :      Optional[int]        =							edges.pop()
				chosen_vertices.add(lowerCAmelCase_  )
				chosen_vertices.add(lowerCAmelCase_  )
				for edge in edges.copy():
						if from_node in edge or to_node in edge:
								edges.discard(lowerCAmelCase_  )
		return chosen_vertices



def      __lowerCamelCase     (      lowerCAmelCase_  )			->      set:
		_a     :      List[Any]        =							set()
		for from_node, to_nodes in graph.items():
				for to_node in to_nodes:
						edges.add((from_node, to_node)  )
		return edges


if __name__ == "__main__":
							import doctest

							doctest.testmod()

							# graph = {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
							# print(f"Matching vertex cover:\n{matching_min_vertex_cover(graph)}")









'''simple docstring'''

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



def      __lowerCamelCase     (      lowerCAmelCase_						,			lowerCAmelCase_						,			lowerCAmelCase_  )			->      list[str]:
		_a     :      List[Any]        =							set()
		# keep track of all the paths to be checked
		_a     :      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
				_a     :      Tuple        =							queue.pop(0  )
				# get the last node from the path
				_a     :      Tuple        =							path[-1]
				if node not in explored:
						_a     :      Optional[Any]        =							graph[node]
						# go through all neighbour nodes, construct a new path and
						# push it into the queue
						for neighbour in neighbours:
								_a     :      Any        =							list(lowerCAmelCase_  )
								new_path.append(lowerCAmelCase_  )
								queue.append(lowerCAmelCase_  )
								# return path if neighbour is goal
								if neighbour == goal:
										return new_path

            # mark node as explored
						explored.add(lowerCAmelCase_  )

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



def      __lowerCamelCase     (      lowerCAmelCase_						,			lowerCAmelCase_						,			lowerCAmelCase_  )			->      int:
		if not graph or start not in graph or target not in graph:
				return -1
		if start == target:
				return 0
		_a     :      Optional[int]        =							[start]
		_a     :      Dict        =							set(lowerCAmelCase_  )
		# Keep tab on distances from `start` node.
		_a     :      Dict        =							{start: 0, target: -1}
		while queue:
				_a     :      List[str]        =							queue.pop(0  )
				if node == target:
						_a     :      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(lowerCAmelCase_  )
								queue.append(lowerCAmelCase_  )
								_a     :      Any        =							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




