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
_snake_case			=						{
    '''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   (			snake_case__							)						->   set[tuple[str, str]]:
							__UpperCAmelCase						:			int         =   {node: {node} for node in graph}

							__UpperCAmelCase						:			List[Any]         =   {node: graph[node][:] for node in graph}

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

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

														__UpperCAmelCase						:			Optional[Any]         =   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(snake_case__							)
																					if v in graph_copy[neighbor]:
																												graph_copy[neighbor].remove(snake_case__							)

    # Find cutset.
							__UpperCAmelCase						:			str         =   [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))





import unittest
from dataclasses import dataclass
from typing import Optional

from transformers.utils import ModelOutput




@dataclass
class 					_snake_case						(						_lowercase				):
					lowerCamelCase__:		float
					lowerCamelCase__:		Optional[float]  =     None
					lowerCamelCase__:		Optional[float]  =     None




class 					_snake_case						(						unittest.TestCase				):
					def    _lowerCamelCase (  self:				Union[str, Any]     )    ->				List[Any]:
												__UpperCAmelCase						:			str         =   ModelOutputTest(a=30     )
												self.assertEqual(x.a	,  30     )
												self.assertIsNone(x.b     )
												self.assertIsNone(x.c     )
												with self.assertRaises(__lowerCamelCase     ):
																			__UpperCAmelCase						:			List[Any]         =   x.d
					def    _lowerCamelCase (  self:				Optional[int]     )    ->				str:
												__UpperCAmelCase						:			Union[str, Any]         =   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)     )

												__UpperCAmelCase						:			Optional[Any]         =   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    _lowerCamelCase (  self:				Tuple     )    ->				List[str]:
												__UpperCAmelCase						:			str         =   ModelOutputTest(a=30	,  b=10     )
												self.assertEqual(x["a"]	,  30     )
												self.assertEqual(x["b"]	,  10     )
												with self.assertRaises(__lowerCamelCase     ):
																			__UpperCAmelCase						:			Dict         =   x["c"]

												__UpperCAmelCase						:			Tuple         =   ModelOutputTest(a=30	,  c=10     )
												self.assertEqual(x["a"]	,  30     )
												self.assertEqual(x["c"]	,  10     )
												with self.assertRaises(__lowerCamelCase     ):
																			__UpperCAmelCase						:			Optional[Any]         =   x["b"]
					def    _lowerCamelCase (  self:				str     )    ->				Any:
												__UpperCAmelCase						:			Union[str, Any]         =   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(__lowerCamelCase     )	,  ["a"]     )

												__UpperCAmelCase						:			str         =   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(__lowerCamelCase     )	,  ["a", "b"]     )

												__UpperCAmelCase						:			Any         =   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(__lowerCamelCase     )	,  ["a", "c"]     )

												with self.assertRaises(__lowerCamelCase     ):
																			__UpperCAmelCase						:			Dict         =   x.update({"d": 20}     )
												with self.assertRaises(__lowerCamelCase     ):
																			del x["a"]
												with self.assertRaises(__lowerCamelCase     ):
																			__UpperCAmelCase						:			List[Any]         =   x.pop("a"     )
												with self.assertRaises(__lowerCamelCase     ):
																			__UpperCAmelCase						:			str         =   x.setdefault("d"	,  32     )
					def    _lowerCamelCase (  self:				List[str]     )    ->				str:
												__UpperCAmelCase						:			Optional[Any]         =   ModelOutputTest(a=30     )
												__UpperCAmelCase						:			Tuple         =   10
												self.assertEqual(x.a	,  10     )
												self.assertEqual(x["a"]	,  10     )
					def    _lowerCamelCase (  self:				Optional[int]     )    ->				Dict:
												__UpperCAmelCase						:			str         =   ModelOutputTest(a=30     )
												__UpperCAmelCase						:			Optional[int]         =   10
												self.assertEqual(x.a	,  10     )
												self.assertEqual(x["a"]	,  10     )
					def    _lowerCamelCase (  self:				List[Any]     )    ->				Optional[int]:
												__UpperCAmelCase						:			Tuple         =   ModelOutputTest({"a": 30, "b": 10}     )
												self.assertEqual(list(x.keys()     )	,  ["a", "b"]     )
												self.assertEqual(x.a	,  30     )
												self.assertEqual(x.b	,  10     )





					def    _lowerCamelCase (  self:				Optional[int]     )    ->				Union[str, Any]:
												__UpperCAmelCase						:			Dict         =   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(__lowerCamelCase     ):
																			__UpperCAmelCase						:			Any         =   ModelOutputTest([("a", 30), (10, 10)]     )

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




