

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        _lowercase  (					a_					:       dict[str, list[str]]					)					->						set[tuple[str, str]]:




					'''simple docstring'''







					__magic_name__				=     {node: {node} for node in graph}

					__magic_name__				=     {node: graph[node][:] for node in graph}

					while len(a_					) > 2:
										# Choose a random edge.
										__magic_name__				=     random.choice(list(graph_copy.keys()					)					)
										__magic_name__				=     random.choice(graph_copy[u]					)

										# Contract edge (u, v) to new node uv
										__magic_name__				=     u + v
										__magic_name__				=     list(set(graph_copy[u] + graph_copy[v]					)					)
										uv_neighbors.remove(a_					)
										uv_neighbors.remove(a_					)
										__magic_name__				=     uv_neighbors
										for neighbor in uv_neighbors:
															graph_copy[neighbor].append(a_					)

										__magic_name__				=     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.
					__magic_name__				=     [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))







from __future__ import annotations

from collections.abc import Iterator
from typing import Any

class 					__UpperCamelCase					:







	def __init__( self:			Optional[Any]	,			__UpperCamelCase:			Any   ):

						'''simple docstring'''





						__magic_name__				=     data
						__magic_name__				=     None







	def __str__( self:			Optional[int]   ):

						'''simple docstring'''





						return F'{self.data}'




class 					__UpperCamelCase					:







	def __init__( self:			List[Any]   ):

						'''simple docstring'''





						__magic_name__				=     None
						__magic_name__				=     None







	def __iter__( self:			str   ):

						'''simple docstring'''





						__magic_name__				=     self.front
						while node:
											yield node.data
											__magic_name__				=     node.next







	def __len__( self:			Any   ):

						'''simple docstring'''





						return len(tuple(iter(self   )   )   )







	def __str__( self:			List[str]   ):

						'''simple docstring'''





						return " <- ".join(str(__UpperCamelCase   ) for item in self   )







	def 						_SCREAMING_SNAKE_CASE				( self:			Any   ):

						'''simple docstring'''





						return len(self   ) == 0







	def 						_SCREAMING_SNAKE_CASE				( self:			Any	,			__UpperCamelCase:			Any   ):

						'''simple docstring'''





						__magic_name__				=     Node(__UpperCamelCase   )
						if self.is_empty():
											__magic_name__				=     __magic_name__				=     node
						else:
											assert isinstance(self.rear	,			__UpperCamelCase   )
											__magic_name__				=     node
											__magic_name__				=     node







	def 						_SCREAMING_SNAKE_CASE				( self:			Any   ):

						'''simple docstring'''





						if self.is_empty():
											raise IndexError('dequeue from empty queue'   )
						assert isinstance(self.front	,			__UpperCamelCase   )
						__magic_name__				=     self.front
						__magic_name__				=     self.front.next
						if self.front is None:
											__magic_name__				=     None
						return node.data







	def 						_SCREAMING_SNAKE_CASE				( self:			Tuple   ):

						'''simple docstring'''





						__magic_name__				=     __magic_name__				=     None


if __name__ == "__main__":
						from doctest import testmod

						testmod()




