code: 
  
  
  
  
  
  '''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))
  
  
  
  
  
  
  
style_context: 
  
  
  
  
  
  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)
  
  
  
  
  
  
  