





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
UpperCAmelCase__    :      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   _lowercase       (    _UpperCAmelCase					)    ->	set[tuple[str, str]]:
				lowerCamelCase									={node: {node} for node in graph}

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

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

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

								lowerCamelCase									=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.
				lowerCamelCase									=[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_torch_available,
)


UpperCAmelCase__    :      Optional[Any]       					={
    '''configuration_rwkv''': ['''RWKV_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''RwkvConfig''', '''RwkvOnnxConfig'''],
}

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							UpperCAmelCase__    :      Optional[Any]       					=[
							    '''RWKV_PRETRAINED_MODEL_ARCHIVE_LIST''',
							    '''RwkvForCausalLM''',
							    '''RwkvModel''',
							    '''RwkvPreTrainedModel''',
							]


if TYPE_CHECKING:
							from .configuration_rwkv import RWKV_PRETRAINED_CONFIG_ARCHIVE_MAP, RwkvConfig, RwkvOnnxConfig

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_rwkv import (
														    RWKV_PRETRAINED_MODEL_ARCHIVE_LIST,
														    RwkvForCausalLM,
														    RwkvModel,
														    RwkvPreTrainedModel,
														)
else:
							import sys

							UpperCAmelCase__    :      int       					=_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)





