


'''simple docstring'''
def       _lowercase							(					UpperCamelCase__							:       dict      ):
 __A	:		Dict	  =      set()
 # edges = list of graph's edges
 __A	:		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:
  __A  ,__A	:		List[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       _lowercase							(					UpperCamelCase__							:       dict      ):
 __A	:		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'''
import importlib
import sys
from argparse import REMAINDER, ArgumentParser
from pathlib import Path

import torch_xla.distributed.xla_multiprocessing as xmp


def       _lowercase							(					):
 __A	:		List[Any]	  =      ArgumentParser(
     description=(
         'PyTorch TPU distributed training launch helper utility that will spawn up multiple distributed processes'
     )      )

 # Optional arguments for the launch helper
 parser.add_argument('--num_cores',					type=UpperCamelCase__,					default=1,					help='Number of TPU cores to use (1 or 8).'      )

 # positional
 parser.add_argument(
     'training_script',					type=UpperCamelCase__,					help=(
         'The full path to the single TPU training '
         'program/script to be launched in parallel, '
         'followed by all the arguments for the '
         'training script'
     ),					)

 # rest from the training program
 parser.add_argument('training_script_args',					nargs=UpperCamelCase__      )

 return parser.parse_args()


def       _lowercase							(					):
 __A	:		str	  =      parse_args()

 # Import training_script as a module.
 __A	:		Tuple	  =      Path(args.training_script      )
 sys.path.append(str(script_fpath.parent.resolve()      )      )
 __A	:		str	  =      script_fpath.stem
 __A	:		Dict	  =      importlib.import_module(UpperCamelCase__      )

 # Patch sys.argv
 __A	:		Optional[Any]	  =      [args.training_script] + args.training_script_args + ['--tpu_num_cores', str(args.num_cores      )]

 xmp.spawn(mod._mp_fn,					args=(),					nprocs=args.num_cores      )


if __name__ == "__main__":
 main()






