





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
__A       : Dict						    = {
    """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 							__lowerCAmelCase(					_SCREAMING_SNAKE_CASE							)       ->   int:




    """simple docstring"""




    _A    =       {node: {node} for node in graph}

    _A    =       {node: graph[node][:] for node in graph}

    while len(_SCREAMING_SNAKE_CASE							) > 2:
        # Choose a random edge.
        _A    =       random.choice(list(graph_copy.keys()							)							)
        _A    =       random.choice(graph_copy[u]							)

        # Contract edge (u, v) to new node uv
        _A    =       u + v
        _A    =       list(set(graph_copy[u] + graph_copy[v]							)							)
        uv_neighbors.remove(_SCREAMING_SNAKE_CASE							)
        uv_neighbors.remove(_SCREAMING_SNAKE_CASE							)
        _A    =       uv_neighbors
        for neighbor in uv_neighbors:
            graph_copy[neighbor].append(_SCREAMING_SNAKE_CASE							)

        _A    =       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.
    _A    =       [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))












from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tf_available, is_torch_available


__A       : Dict						    = {"configuration_hubert": ["HUBERT_PRETRAINED_CONFIG_ARCHIVE_MAP", "HubertConfig"]}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __A       : List[str]						    = [
     "HUBERT_PRETRAINED_MODEL_ARCHIVE_LIST",
     "HubertForCTC",
     "HubertForSequenceClassification",
     "HubertModel",
     "HubertPreTrainedModel",
 ]


try:
 if not is_tf_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __A       : Tuple						    = [
     "TF_HUBERT_PRETRAINED_MODEL_ARCHIVE_LIST",
     "TFHubertForCTC",
     "TFHubertModel",
     "TFHubertPreTrainedModel",
 ]

if TYPE_CHECKING:
 from .configuration_hubert import HUBERT_PRETRAINED_CONFIG_ARCHIVE_MAP, HubertConfig

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_hubert import (
      HUBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
      HubertForCTC,
      HubertForSequenceClassification,
      HubertModel,
      HubertPreTrainedModel,
  )

 try:
  if not is_tf_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_tf_hubert import (
      TF_HUBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
      TFHubertForCTC,
      TFHubertModel,
      TFHubertPreTrainedModel,
  )


else:
 import sys

 __A       : Dict						    = _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)





