code: 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_:      Any        =			{
      '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			(  _A					):
  
  
  
  							"""simple docstring"""
  
  
  							_lowercase				=	{node: {node} for node in graph}
  
  							_lowercase				=	{node: graph[node][:] for node in graph}
  
  							while len(_A					) > 2:
  														# Choose a random edge.
  														_lowercase				=	random.choice(list(graph_copy.keys()					)					)
  														_lowercase				=	random.choice(graph_copy[u]					)
  
  														# Contract edge (u, v) to new node uv
  														_lowercase				=	u + v
  														_lowercase				=	list(set(graph_copy[u] + graph_copy[v]					)					)
  														uv_neighbors.remove(_A					)
  														uv_neighbors.remove(_A					)
  														_lowercase				=	uv_neighbors
  														for neighbor in uv_neighbors:
  																					graph_copy[neighbor].append(_A					)
  
  														_lowercase				=	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.
  							_lowercase				=	[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))
  
  
  
style_context: def 					__lowerCAmelCase			(  _A					):
  
  
  
  							"""simple docstring"""
  
  
  							if len(_A					) <= 1:
  														return data
  							else:
  														return [
  														    *quick_sort([e for e in data[1:] if e <= data[0]]					),
  														    data[0],
  														    *quick_sort([e for e in data[1:] if e > data[0]]					),
  														]
  
  
  if __name__ == "__main__":
  				import doctest
  
  				doctest.testmod()
  
  
  