






import unittest
from dataclasses import dataclass
from typing import Optional

from transformers.utils import ModelOutput


@dataclass
class        lowercase__       (     _UpperCAmelCase		):
	a_             =42
	a_             =None
	a_             =None





class        lowercase__       (     unittest.TestCase		):

	def 						UpperCAmelCase					(							self    )->   Optional[int]:







							'''simple docstring'''





							lowerCAmelCase__	 =  ModelOutputTest(a=30    )
							self.assertEqual(x.a						,      30    )
							self.assertIsNone(x.b    )
							self.assertIsNone(x.c    )
							with self.assertRaises(__UpperCAmelCase    ):
													lowerCAmelCase__	 =  x.d

	def 						UpperCAmelCase					(							self    )->   List[Any]:







							'''simple docstring'''





							lowerCAmelCase__	 =  ModelOutputTest(a=30						,      b=10    )
							self.assertEqual(x[0]						,      30    )
							self.assertEqual(x[1]						,      10    )
							self.assertEqual(x[:2]						,      (30, 10)    )
							self.assertEqual(x[:]						,      (30, 10)    )

							lowerCAmelCase__	 =  ModelOutputTest(a=30						,      c=10    )
							self.assertEqual(x[0]						,      30    )
							self.assertEqual(x[1]						,      10    )
							self.assertEqual(x[:2]						,      (30, 10)    )
							self.assertEqual(x[:]						,      (30, 10)    )

	def 						UpperCAmelCase					(							self    )->   List[Any]:







							'''simple docstring'''





							lowerCAmelCase__	 =  ModelOutputTest(a=30						,      b=10    )
							self.assertEqual(x["a"]						,      30    )
							self.assertEqual(x["b"]						,      10    )
							with self.assertRaises(__UpperCAmelCase    ):
													lowerCAmelCase__	 =  x["c"]

							lowerCAmelCase__	 =  ModelOutputTest(a=30						,      c=10    )
							self.assertEqual(x["a"]						,      30    )
							self.assertEqual(x["c"]						,      10    )
							with self.assertRaises(__UpperCAmelCase    ):
													lowerCAmelCase__	 =  x["b"]

	def 						UpperCAmelCase					(							self    )->   Dict:







							'''simple docstring'''





							lowerCAmelCase__	 =  ModelOutputTest(a=30    )
							self.assertEqual(list(x.keys()    )						,      ["a"]    )
							self.assertEqual(list(x.values()    )						,      [30]    )
							self.assertEqual(list(x.items()    )						,      [("a", 30)]    )
							self.assertEqual(list(__UpperCAmelCase    )						,      ["a"]    )

							lowerCAmelCase__	 =  ModelOutputTest(a=30						,      b=10    )
							self.assertEqual(list(x.keys()    )						,      ["a", "b"]    )
							self.assertEqual(list(x.values()    )						,      [30, 10]    )
							self.assertEqual(list(x.items()    )						,      [("a", 30), ("b", 10)]    )
							self.assertEqual(list(__UpperCAmelCase    )						,      ["a", "b"]    )

							lowerCAmelCase__	 =  ModelOutputTest(a=30						,      c=10    )
							self.assertEqual(list(x.keys()    )						,      ["a", "c"]    )
							self.assertEqual(list(x.values()    )						,      [30, 10]    )
							self.assertEqual(list(x.items()    )						,      [("a", 30), ("c", 10)]    )
							self.assertEqual(list(__UpperCAmelCase    )						,      ["a", "c"]    )

							with self.assertRaises(__UpperCAmelCase    ):
													lowerCAmelCase__	 =  x.update({"d": 20}    )
							with self.assertRaises(__UpperCAmelCase    ):
													del x["a"]
							with self.assertRaises(__UpperCAmelCase    ):
													lowerCAmelCase__	 =  x.pop("a"    )
							with self.assertRaises(__UpperCAmelCase    ):
													lowerCAmelCase__	 =  x.setdefault("d"						,      32    )

	def 						UpperCAmelCase					(							self    )->   Tuple:







							'''simple docstring'''





							lowerCAmelCase__	 =  ModelOutputTest(a=30    )
							lowerCAmelCase__	 =  10
							self.assertEqual(x.a						,      10    )
							self.assertEqual(x["a"]						,      10    )

	def 						UpperCAmelCase					(							self    )->   List[Any]:







							'''simple docstring'''





							lowerCAmelCase__	 =  ModelOutputTest(a=30    )
							lowerCAmelCase__	 =  10
							self.assertEqual(x.a						,      10    )
							self.assertEqual(x["a"]						,      10    )

	def 						UpperCAmelCase					(							self    )->   str:







							'''simple docstring'''





							lowerCAmelCase__	 =  ModelOutputTest({"a": 30, "b": 10}    )
							self.assertEqual(list(x.keys()    )						,      ["a", "b"]    )
							self.assertEqual(x.a						,      30    )
							self.assertEqual(x.b						,      10    )


	def 						UpperCAmelCase					(							self    )->   int:







							'''simple docstring'''





							lowerCAmelCase__	 =  ModelOutputTest([("a", 30), ("b", 10)]    )
							self.assertEqual(list(x.keys()    )						,      ["a", "b"]    )
							self.assertEqual(x.a						,      30    )
							self.assertEqual(x.b						,      10    )

							with self.assertRaises(__UpperCAmelCase    ):
													lowerCAmelCase__	 =  ModelOutputTest([("a", 30), (10, 10)]    )

							lowerCAmelCase__	 =  ModelOutputTest(a=(30, 30)    )
							self.assertEqual(list(x.keys()    )						,      ["a"]    )
							self.assertEqual(x.a						,      (30, 30)    )














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
a_							=      {
    '''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     _a					(       UpperCamelCase_   :			dict[str, list[str]]				)	->				set[tuple[str, str]]:
						"""simple docstring"""







						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))






