





'''simple docstring'''




def 	UpperCAmelCase_							(					__lowercase							:      dict       )		->       set:


     '''simple docstring'''



     _UpperCAmelCase     							=   set()
     # edges = list of graph's edges
     _UpperCAmelCase     							=   get_edges(__lowercase       )

     # 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:
          _UpperCAmelCase							,  _UpperCAmelCase     							=   edges.pop()
          chosen_vertices.add(__lowercase       )
          chosen_vertices.add(__lowercase       )
          for edge in edges.copy():
               if from_node in edge or to_node in edge:
                    edges.discard(__lowercase       )
     return chosen_vertices
def 	UpperCAmelCase_							(					__lowercase							:      dict       )		->       set:


     '''simple docstring'''



     _UpperCAmelCase     							=   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)}")





def       _snake_case	(   lowerCAmelCase							:   int	):
		"""simple docstring"""







		SCREAMING_SNAKE_CASE_  :		Tuple				      =    int(lowerCAmelCase	)
		if decimal in (0, 1):  # Exit cases for the recursion
				return str(lowerCAmelCase	)
		SCREAMING_SNAKE_CASE_      ,    SCREAMING_SNAKE_CASE_  :		Dict				      =    divmod(lowerCAmelCase   , 2	)
		return binary_recursive(lowerCAmelCase	) + str(lowerCAmelCase	)




def       _snake_case	(   lowerCAmelCase							:   str	):
		"""simple docstring"""







		SCREAMING_SNAKE_CASE_  :		str				      =    str(lowerCAmelCase	).strip()
		if not number:
				raise ValueError("No input value was provided"	)
		SCREAMING_SNAKE_CASE_  :		List[str]				      =    "-" if number.startswith("-"	) else ""
		SCREAMING_SNAKE_CASE_  :		Optional[Any]				      =    number.lstrip("-"	)
		if not number.isnumeric():
				raise ValueError("Input value is not an integer"	)
		return f'{negative}0b{binary_recursive(int(lowerCAmelCase	)	)}'


if __name__ == "__main__":
		from doctest import testmod

		testmod()
