
"""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
__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     _lowerCamelCase(__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))






'''simple docstring'''
from transformers import PretrainedConfig
class  _snake_case						(__SCREAMING_SNAKE_CASE):
			__A   :     Optional[Any]          ="custom"






			def __init__(   self       ,_snake_case=1       ,**_snake_case			):
				UpperCAmelCase_			:	Optional[int]      =   attribute
				super().__init__(**_snake_case			)




class  _snake_case						(__SCREAMING_SNAKE_CASE):
			__A   :     Dict          ="custom"






			def __init__(   self       ,_snake_case=1       ,**_snake_case			):
				UpperCAmelCase_			:	Optional[int]      =   attribute




