





'''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
UpperCAmelCase			:			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   _A (	SCREAMING_SNAKE_CASE  :     List[Any]		):





  """simple docstring"""



  a__			:      Tuple            ={node: {node} for node in graph}

  a__			:      Optional[int]            ={node: graph[node][:] for node in graph}

  while len(_A		) > 2:
    # Choose a random edge.
    a__			:      List[Any]            =random.choice(list(graph_copy.keys()		)		)
    a__			:      Tuple            =random.choice(graph_copy[u]		)

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

    a__			:      Dict            =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.
  a__			:      Tuple            =[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))













def   _A (	SCREAMING_SNAKE_CASE  :     int		):





  """simple docstring"""



  if not isinstance(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE		) or number < 0:
    raise ValueError("Input must be a non-negative integer"		)

  a__			:      List[str]            =number & ~(number - 1)
  a__			:      Optional[int]            =0
  while intermediate:
    intermediate >>= 1
    index += 1
  return index - 1


if __name__ == "__main__":
     import doctest

     doctest.testmod(verbose=True)






