




import posixpath
from pathlib import Path
from unittest.mock import patch

import pytest
from fsspec.implementations.local import AbstractFileSystem, LocalFileSystem, stringify_path
from fsspec.registry import _registry as _fsspec_registry





class 			__snake_case  (      SCREAMING_SNAKE_CASE_     ):
					__lowerCamelCase	 =       "mock"




					def __init__(       self   ,	*__UpperCamelCase   ,	__UpperCamelCase   ,	**__UpperCamelCase		)					->  Union[str, Any]:



									'''simple docstring'''







									super().__init__()
									snake_case__ :     Union[str, Any] 							=				LocalFileSystem(*lowercase_   ,	**lowercase_		)
									snake_case__ :     Optional[int] 							=				Path(lowercase_		).resolve().as_posix() + '/'




					def       __a      (       self   ,	__UpperCamelCase   ,	*__UpperCamelCase   ,	**__UpperCamelCase		)					->  List[str]:



									'''simple docstring'''







									snake_case__ :     Optional[int] 							=				posixpath.join(self.local_root_dir   ,	self._strip_protocol(lowercase_		)		)
									return self._fs.mkdir(lowercase_   ,	*lowercase_   ,	**lowercase_		)




					def       __a      (       self   ,	__UpperCamelCase   ,	*__UpperCamelCase   ,	**__UpperCamelCase		)					->  List[str]:



									'''simple docstring'''







									snake_case__ :     str 							=				posixpath.join(self.local_root_dir   ,	self._strip_protocol(lowercase_		)		)
									return self._fs.makedirs(lowercase_   ,	*lowercase_   ,	**lowercase_		)




					def       __a      (       self   ,	__UpperCamelCase		)					->  Optional[Any]:



									'''simple docstring'''







									snake_case__ :     str 							=				posixpath.join(self.local_root_dir   ,	self._strip_protocol(lowercase_		)		)
									return self._fs.rmdir(lowercase_		)




					def       __a      (       self   ,	__UpperCamelCase   ,	__UpperCamelCase=True   ,	*__UpperCamelCase   ,	**__UpperCamelCase		)					->  Tuple:



									'''simple docstring'''







									snake_case__ :     int 							=				posixpath.join(self.local_root_dir   ,	self._strip_protocol(lowercase_		)		)
									snake_case__ :     str 							=				self._fs.ls(lowercase_   ,	detail=lowercase_   ,	*lowercase_   ,	**lowercase_		)
									if detail:
													return [{**info, "name": info["name"][len(self.local_root_dir		) :]} for info in out]
									else:
													return [name[len(self.local_root_dir		) :] for name in out]




					def       __a      (       self   ,	__UpperCamelCase   ,	*__UpperCamelCase   ,	**__UpperCamelCase		)					->  Tuple:



									'''simple docstring'''







									snake_case__ :     str 							=				posixpath.join(self.local_root_dir   ,	self._strip_protocol(lowercase_		)		)
									snake_case__ :     Optional[int] 							=				dict(self._fs.info(lowercase_   ,	*lowercase_   ,	**lowercase_		)		)
									snake_case__ :     str 							=				out['name'][len(self.local_root_dir		) :]
									return out




					def       __a      (       self   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	*__UpperCamelCase   ,	**__UpperCamelCase		)					->  Optional[int]:



									'''simple docstring'''







									snake_case__ :     int 							=				posixpath.join(self.local_root_dir   ,	self._strip_protocol(lowercase_		)		)
									snake_case__ :     Union[str, Any] 							=				posixpath.join(self.local_root_dir   ,	self._strip_protocol(lowercase_		)		)
									return self._fs.cp_file(lowercase_   ,	lowercase_   ,	*lowercase_   ,	**lowercase_		)




					def       __a      (       self   ,	__UpperCamelCase   ,	*__UpperCamelCase   ,	**__UpperCamelCase		)					->  int:



									'''simple docstring'''







									snake_case__ :     Union[str, Any] 							=				posixpath.join(self.local_root_dir   ,	self._strip_protocol(lowercase_		)		)
									return self._fs.rm_file(lowercase_   ,	*lowercase_   ,	**lowercase_		)




					def       __a      (       self   ,	__UpperCamelCase   ,	*__UpperCamelCase   ,	**__UpperCamelCase		)					->  List[str]:



									'''simple docstring'''







									snake_case__ :     int 							=				posixpath.join(self.local_root_dir   ,	self._strip_protocol(lowercase_		)		)
									return self._fs.rm(lowercase_   ,	*lowercase_   ,	**lowercase_		)




					def       __a      (       self   ,	__UpperCamelCase   ,	*__UpperCamelCase   ,	**__UpperCamelCase		)					->  Any:



									'''simple docstring'''







									snake_case__ :     Any 							=				posixpath.join(self.local_root_dir   ,	self._strip_protocol(lowercase_		)		)
									return self._fs._open(lowercase_   ,	*lowercase_   ,	**lowercase_		)




					def       __a      (       self   ,	__UpperCamelCase		)					->  int:



									'''simple docstring'''







									snake_case__ :     Dict 							=				posixpath.join(self.local_root_dir   ,	self._strip_protocol(lowercase_		)		)
									return self._fs.created(lowercase_		)




					def       __a      (       self   ,	__UpperCamelCase		)					->  Optional[int]:



									'''simple docstring'''







									snake_case__ :     Union[str, Any] 							=				posixpath.join(self.local_root_dir   ,	self._strip_protocol(lowercase_		)		)
									return self._fs.modified(lowercase_		)




					@classmethod
					def       __a      (       cls   ,	__UpperCamelCase		)					->  List[Any]:



									'''simple docstring'''







									snake_case__ :     Optional[int] 							=				stringify_path(lowercase_		)
									if path.startswith('mock://'		):
													snake_case__ :     int 							=				path[7:]
									return path





class 			__snake_case  (      SCREAMING_SNAKE_CASE_     ):
					__lowerCamelCase	 =       "tmp"
					__lowerCamelCase	 =       None




					def __init__(       self   ,	*__UpperCamelCase   ,	**__UpperCamelCase		)					->  Union[str, Any]:



									'''simple docstring'''







									assert self.tmp_dir is not None, "TmpDirFileSystem.tmp_dir is not set"
									super().__init__(*lowercase_   ,	**lowercase_   ,	local_root_dir=self.tmp_dir   ,	auto_mkdir=lowercase_		)




					@classmethod
					def       __a      (       cls   ,	__UpperCamelCase		)					->  Optional[int]:



									'''simple docstring'''







									snake_case__ :     Union[str, Any] 							=				stringify_path(lowercase_		)
									if path.startswith('tmp://'		):
													snake_case__ :     Union[str, Any] 							=				path[6:]
									return path




@pytest.fixture
def 			UpperCamelCase__						(    )       -> Dict:
				snake_case__ :     List[str] 							=				MockFileSystem
				snake_case__ :     int 							=				TmpDirFileSystem
				yield
				del _fsspec_registry["mock"]
				del _fsspec_registry["tmp"]
@pytest.fixture
def 			UpperCamelCase__						(    A__      ,			A__   )       -> str:
				snake_case__ :     Union[str, Any] 							=				tmp_path_factory.mktemp('mockfs'   )
				return MockFileSystem(local_root_dir=A__      ,			auto_mkdir=A__   )

@pytest.fixture
def 			UpperCamelCase__						(    A__      ,			A__   )       -> Union[str, Any]:
				snake_case__ :     str 							=				tmp_path_factory.mktemp('tmpfs'   )
				with patch.object(A__      ,			'tmp_dir'      ,			A__   ):
								yield TmpDirFileSystem()



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__					:       Dict		=       {
    '''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 			UpperCamelCase__						(    A__   )       -> set[tuple[str, str]]:
				snake_case__ :     Tuple 							=				{node: {node} for node in graph}

				snake_case__ :     Tuple 							=				{node: graph[node][:] for node in graph}

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

								# Contract edge (u, v) to new node uv
								snake_case__ :     Tuple 							=				u + v
								snake_case__ :     Dict 							=				list(set(graph_copy[u] + graph_copy[v]   )   )
								uv_neighbors.remove(A__   )
								uv_neighbors.remove(A__   )
								snake_case__ :     Optional[Any] 							=				uv_neighbors
								for neighbor in uv_neighbors:
												graph_copy[neighbor].append(A__   )

								snake_case__ :     Tuple 							=				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__ :     Tuple 							=				[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))


