
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
__SCREAMING_SNAKE_CASE			:   List[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__							(       __magic_name__						:     dict[str, list[str]]  ):


     '''simple docstring'''

     lowerCAmelCase		:					List[Any]  	=     {node: {node} for node in graph}

     lowerCAmelCase		:					List[Any]  	=     {node: graph[node][:] for node in graph}

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

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

          lowerCAmelCase		:					str  	=     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(__magic_name__  )
               if v in graph_copy[neighbor]:
                    graph_copy[neighbor].remove(__magic_name__  )

    # Find cutset.
     lowerCAmelCase		:					Optional[int]  	=     [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 ..utils import requires_backends


__SCREAMING_SNAKE_CASE			:   Union[str, Any]         =     None


class 		__magic_name__   :





		def __init__(							self    :	Optional[int]						,  *lowerCamelCase__    :	List[str]						,  **lowerCamelCase__    :	Optional[Any]				):
							requires_backends(self						,  ['''detectron2''']				)





		@classmethod
		def       _A							(							cls    :	Dict						,  *lowerCamelCase__    :	List[str]						,  **lowerCamelCase__    :	Optional[Any]				):
							requires_backends(cls						,  ['''detectron2''']				)
