




"""simple docstring"""




def 					a__				(       snake_case__       )		->      Tuple:
			lowerCamelCase       =      set()
			# edges = list of graph's edges
			lowerCamelCase       =      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:
						lowerCamelCase   ,     lowerCamelCase       =      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 					a__				(       snake_case__       )		->      Optional[int]:
			lowerCamelCase       =      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"""




from __future__ import annotations



def 					a__				(       snake_case__ ,				snake_case__ = None ,				snake_case__ = None       )		->      None:
			if start is None:
						lowerCamelCase       =      0

			if end is None:
						lowerCamelCase       =      len(snake_case__       ) - 1

			if start >= end:
						return

			lowerCamelCase       =      (start + end) // 2

			slowsort(snake_case__ ,				snake_case__ ,				snake_case__       )
			slowsort(snake_case__ ,				mid + 1 ,				snake_case__       )

			if sequence[end] < sequence[mid]:
						lowerCamelCase   ,     lowerCamelCase       =      sequence[mid], sequence[end]

			slowsort(snake_case__ ,				snake_case__ ,				end - 1       )


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

					testmod()



