


'''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
lowerCAmelCase  =				{
    """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				:					dict[str, list[str]]		)				->  set[tuple[str, str]]:







     """simple docstring"""
     _A				=       {node: {node} for node in graph}

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

     while len(__UpperCamelCase		) > 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(__UpperCamelCase		)
          uv_neighbors.remove(__UpperCamelCase		)
          _A				=       uv_neighbors
          for neighbor in uv_neighbors:
               graph_copy[neighbor].append(__UpperCamelCase		)

          _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(__UpperCamelCase		)
               if v in graph_copy[neighbor]:
                    graph_copy[neighbor].remove(__UpperCamelCase		)

    # 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))









'''simple docstring'''
# Copyright 2023 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import TYPE_CHECKING

# rely on isort to merge the imports
from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_torch_available,
)


lowerCAmelCase  =				{
    """configuration_convnextv2""": [
        """CONVNEXTV2_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """ConvNextV2Config""",
    ]
}

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    lowerCAmelCase  =				[
        """CONVNEXTV2_PRETRAINED_MODEL_ARCHIVE_LIST""",
        """ConvNextV2ForImageClassification""",
        """ConvNextV2Model""",
        """ConvNextV2PreTrainedModel""",
        """ConvNextV2Backbone""",
    ]


if TYPE_CHECKING:
    from .configuration_convnextva import (
        CONVNEXTV2_PRETRAINED_CONFIG_ARCHIVE_MAP,
        ConvNextVaConfig,
    )

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_convnextva import (
            CONVNEXTV2_PRETRAINED_MODEL_ARCHIVE_LIST,
            ConvNextVaBackbone,
            ConvNextVaForImageClassification,
            ConvNextVaModel,
            ConvNextVaPreTrainedModel,
        )

else:
    import sys

    lowerCAmelCase  =				_LazyModule(__name__, globals()["""__file__"""], _import_structure)





