'''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      :				str 				=    {
    '''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_	:	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(snake_case_				) > 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(snake_case_				)
  uv_neighbors.remove(snake_case_				)
  __lowerCAmelCase    							=						uv_neighbors
  for neighbor in uv_neighbors:
   graph_copy[neighbor].append(snake_case_				)

  __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(snake_case_				)
   if v in graph_copy[neighbor]:
    graph_copy[neighbor].remove(snake_case_				)

    # 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 unittest.mock import patch

import datasets
from datasets import Dataset







def 					UpperCamelCase_						( ) ->					Dict:






 '''simple docstring'''

 __lowerCAmelCase    							=						Dataset.from_dict({"""col_1""": [3, 2, 0, 1]}				)

 with patch("""tqdm.auto.tqdm"""				) as mock_tqdm:
  datasets.disable_progress_bar()
  dset.map(lambda snake_case_				: {"col_2": x["col_1"] + 1}				)
  mock_tqdm.assert_not_called()

  mock_tqdm.reset_mock()

  datasets.enable_progress_bar()
  dset.map(lambda snake_case_				: {"col_2": x["col_1"] + 1}				)
  mock_tqdm.assert_called()






