


from __future__ import annotations

import random

# Adjacency list representation of this graph:
# https://en.wikipedia.org/wiki/File:Single_run_of_Karger%E2%80%99s_Mincut_algorithm.svg
_snake_case					=					{
    '''1''': ['''2''', '''3''', '''4''', '''5'''],
    '''2''': ['''1''', '''3''', '''4''', '''5'''],
    '''3''': ['''1''', '''2''', '''4''', '''5''', '''10'''],
    '''4''': ['''1''', '''2''', '''3''', '''5''', '''6'''],
    '''5''': ['''1''', '''2''', '''3''', '''4''', '''7'''],
    '''6''': ['''7''', '''8''', '''9''', '''10''', '''4'''],
    '''7''': ['''6''', '''8''', '''9''', '''10''', '''5'''],
    '''8''': ['''6''', '''7''', '''9''', '''10'''],
    '''9''': ['''6''', '''7''', '''8''', '''10'''],
    '''10''': ['''6''', '''7''', '''8''', '''9''', '''3'''],
}






def 		lowercase_(  SCREAMING_SNAKE_CASE_     ):


  '''simple docstring'''

  lowerCamelCase			: Tuple   =    {node: {node} for node in graph}

  lowerCamelCase			: Optional[Any]   =    {node: graph[node][:] for node in graph}

  while len(SCREAMING_SNAKE_CASE_     ) > 2:
    # Choose a random edge.
    lowerCamelCase			: Any   =    random.choice(list(graph_copy.keys()     )     )
    lowerCamelCase			: List[Any]   =    random.choice(graph_copy[u]     )

    # Contract edge (u, v) to new node uv
    lowerCamelCase			: Union[str, Any]   =    u + v
    lowerCamelCase			: Tuple   =    list(set(graph_copy[u] + graph_copy[v]     )     )
    uv_neighbors.remove(SCREAMING_SNAKE_CASE_     )
    uv_neighbors.remove(SCREAMING_SNAKE_CASE_     )
    lowerCamelCase			: Any   =    uv_neighbors
    for neighbor in uv_neighbors:
      graph_copy[neighbor].append(SCREAMING_SNAKE_CASE_     )

    lowerCamelCase			: Union[str, Any]   =    set(contracted_nodes[u].union(contracted_nodes[v]     )     )

    # Remove nodes u and v.
    del graph_copy[u]
    del graph_copy[v]
    for neighbor in uv_neighbors:
      if u in graph_copy[neighbor]:
        graph_copy[neighbor].remove(SCREAMING_SNAKE_CASE_     )
      if v in graph_copy[neighbor]:
        graph_copy[neighbor].remove(SCREAMING_SNAKE_CASE_     )

    # Find cutset.
  lowerCamelCase			: str   =    [contracted_nodes[node] for node in graph_copy]
  return {
      (node, neighbor)
      for node in groups[0]
      for neighbor in graph[node]
      if neighbor in groups[1]
  }


if __name__ == "__main__":
   print(partition_graph(TEST_GRAPH))







import importlib
import sys
from argparse import REMAINDER, ArgumentParser
from pathlib import Path

import torch_xla.distributed.xla_multiprocessing as xmp






def 		lowercase_(  ):


  '''simple docstring'''

  lowerCamelCase			: str   =    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=SCREAMING_SNAKE_CASE_				,						default=1				,						help="Number of TPU cores to use (1 or 8)."     )

  # positional
  parser.add_argument(
      "training_script"				,						type=SCREAMING_SNAKE_CASE_				,						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=SCREAMING_SNAKE_CASE_     )

  return parser.parse_args()






def 		lowercase_(  ):


  '''simple docstring'''

  lowerCamelCase			: Optional[Any]   =    parse_args()

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

  # Patch sys.argv
  lowerCamelCase			: Union[str, 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()



