
def 							SCREAMING_SNAKE_CASE_      (			UpperCamelCase__		):
      UpperCamelCase__    :   int					=				set()
      # edges = list of graph's edges
      UpperCamelCase__    :   Union[str, Any]					=				get_edges(UpperCamelCase__		)

      # 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__    :   Any					=				edges.pop()
            chosen_vertices.add(UpperCamelCase__		)
            chosen_vertices.add(UpperCamelCase__		)
            for edge in edges.copy():
                  if from_node in edge or to_node in edge:
                        edges.discard(UpperCamelCase__		)
      return chosen_vertices


def 							SCREAMING_SNAKE_CASE_      (			UpperCamelCase__		):
      UpperCamelCase__    :   str					=				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)}")




import math


def 							SCREAMING_SNAKE_CASE_      (			UpperCamelCase__		):
      UpperCamelCase__    :   List[str]					=				math.loga(math.sqrt(4 * positive_integer + 1		) / 2 + 1 / 2		)

      return exponent == int(UpperCamelCase__		)


def 							SCREAMING_SNAKE_CASE_      (			UpperCamelCase__ = 1 / 1_2_3_4_5		):
      UpperCamelCase__    :   Dict					=				0
      UpperCamelCase__    :   Tuple					=				0

      UpperCamelCase__    :   Optional[Any]					=				3
      while True:
            UpperCamelCase__    :   Union[str, Any]					=				(integer**2 - 1) / 4
            # if candidate is an integer, then there is a partition for k
            if partition_candidate == int(UpperCamelCase__		):
                  UpperCamelCase__    :   int					=				int(UpperCamelCase__		)
                  total_partitions += 1
                  if check_partition_perfect(UpperCamelCase__		):
                        perfect_partitions += 1
            if perfect_partitions > 0:
                  if perfect_partitions / total_partitions < max_proportion:
                        return int(UpperCamelCase__		)
            integer += 1


if __name__ == "__main__":
    print(F'''{solution() = }''')


