




from typing import TYPE_CHECKING

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


a_ 		=  {
    "configuration_xlm_prophetnet": ["XLM_PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP", "XLMProphetNetConfig"],
}

try:
 if not is_sentencepiece_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 a_ 		=  ["XLMProphetNetTokenizer"]

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 a_ 		=  [
     "XLM_PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST",
     "XLMProphetNetDecoder",
     "XLMProphetNetEncoder",
     "XLMProphetNetForCausalLM",
     "XLMProphetNetForConditionalGeneration",
     "XLMProphetNetModel",
     "XLMProphetNetPreTrainedModel",
 ]


if TYPE_CHECKING:
 from .configuration_xlm_prophetnet import XLM_PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP, XLMProphetNetConfig

 try:
  if not is_sentencepiece_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .tokenization_xlm_prophetnet import XLMProphetNetTokenizer

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_xlm_prophetnet import (
      XLM_PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST,
      XLMProphetNetDecoder,
      XLMProphetNetEncoder,
      XLMProphetNetForCausalLM,
      XLMProphetNetForConditionalGeneration,
      XLMProphetNetModel,
      XLMProphetNetPreTrainedModel,
  )

else:
 import sys

 a_ 		=  _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)








"""simple docstring"""
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   :      List[str]       =				{
    """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 					a__ ( a :					dict[str, list[str]]		):

  """simple docstring"""







  _snake_case  :    List[Any]            = {node: {node} for node in graph}

  _snake_case  :    str            = {node: graph[node][:] for node in graph}

  while len(a		) > 2:
    # Choose a random edge.
    _snake_case  :    str            = random.choice(list(graph_copy.keys()		)		)
    _snake_case  :    Union[str, Any]            = random.choice(graph_copy[u]		)

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

    _snake_case  :    Dict            = 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(a		)
      if v in graph_copy[neighbor]:
        graph_copy[neighbor].remove(a		)

    # Find cutset.
  _snake_case  :    List[Any]            = [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))

