






"""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
lowercase__      =				{
    '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			(						__UpperCamelCase )		->					Optional[Any]:

  """simple docstring"""







  lowerCAmelCase_     :							Optional[int]             =    {node: {node} for node in graph}

  lowerCAmelCase_     :							int             =    {node: graph[node][:] for node in graph}

  while len(_A ) > 2:
    # Choose a random edge.
    lowerCAmelCase_     :							List[str]             =    random.choice(list(graph_copy.keys() ) )
    lowerCAmelCase_     :							Optional[Any]             =    random.choice(graph_copy[u] )

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

    lowerCAmelCase_     :							str             =    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.
  lowerCAmelCase_     :							int             =    [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))








"""simple docstring"""

from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_torch_available,
    is_vision_available,
)


lowercase__      =				{
    """configuration_mobilevitv2""": [
        """MOBILEVITV2_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """MobileViTV2Config""",
        """MobileViTV2OnnxConfig""",
    ],
}


try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					lowercase__      =				[
					    """MOBILEVITV2_PRETRAINED_MODEL_ARCHIVE_LIST""",
					    """MobileViTV2ForImageClassification""",
					    """MobileViTV2ForSemanticSegmentation""",
					    """MobileViTV2Model""",
					    """MobileViTV2PreTrainedModel""",
					]

if TYPE_CHECKING:
					from .configuration_mobilevitva import (
					    MOBILEVITV2_PRETRAINED_CONFIG_ARCHIVE_MAP,
					    MobileViTVaConfig,
					    MobileViTVaOnnxConfig,
					)

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_mobilevitva import (
										    MOBILEVITV2_PRETRAINED_MODEL_ARCHIVE_LIST,
										    MobileViTVaForImageClassification,
										    MobileViTVaForSemanticSegmentation,
										    MobileViTVaModel,
										    MobileViTVaPreTrainedModel,
										)

else:
					import sys

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