






"""simple docstring"""

from typing import TYPE_CHECKING

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


lowercase__      =				{
    """configuration_videomae""": ["""VIDEOMAE_PRETRAINED_CONFIG_ARCHIVE_MAP""", """VideoMAEConfig"""],
}

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					lowercase__      =				[
					    """VIDEOMAE_PRETRAINED_MODEL_ARCHIVE_LIST""",
					    """VideoMAEForPreTraining""",
					    """VideoMAEModel""",
					    """VideoMAEPreTrainedModel""",
					    """VideoMAEForVideoClassification""",
					]

try:
					if not is_vision_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					lowercase__      =				["""VideoMAEFeatureExtractor"""]
					lowercase__      =				["""VideoMAEImageProcessor"""]

if TYPE_CHECKING:
					from .configuration_videomae import VIDEOMAE_PRETRAINED_CONFIG_ARCHIVE_MAP, VideoMAEConfig

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_videomae import (
										    VIDEOMAE_PRETRAINED_MODEL_ARCHIVE_LIST,
										    VideoMAEForPreTraining,
										    VideoMAEForVideoClassification,
										    VideoMAEModel,
										    VideoMAEPreTrainedModel,
										)

					try:
										if not is_vision_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .feature_extraction_videomae import VideoMAEFeatureExtractor
										from .image_processing_videomae import VideoMAEImageProcessor

else:
					import sys

					lowercase__      =				_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
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 )		->					set[tuple[str, str]]:

		"""simple docstring"""







		lowerCAmelCase_     :							Union[str, Any]             =    {node: {node} for node in graph}

		lowerCAmelCase_     :							List[str]             =    {node: graph[node][:] for node in graph}

		while len(__UpperCamelCase ) > 2:
				# Choose a random edge.
				lowerCAmelCase_     :							int             =    random.choice(list(graph_copy.keys() ) )
				lowerCAmelCase_     :							Any             =    random.choice(graph_copy[u] )

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

				lowerCAmelCase_     :							Optional[int]             =    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_     :							Union[str, 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))
