

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
_lowerCamelCase								={
    "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       snake_case__    (       lowerCAmelCase_      ):





     """simple docstring"""







     SCREAMING_SNAKE_CASE										={node: {node} for node in graph}

     SCREAMING_SNAKE_CASE										={node: graph[node][:] for node in graph}

     while len(lowerCAmelCase_      ) > 2:
          # Choose a random edge.
          SCREAMING_SNAKE_CASE										=random.choice(list(graph_copy.keys()      )      )
          SCREAMING_SNAKE_CASE										=random.choice(graph_copy[u]      )

          # Contract edge (u, v) to new node uv
          SCREAMING_SNAKE_CASE										=u + v
          SCREAMING_SNAKE_CASE										=list(set(graph_copy[u] + graph_copy[v]      )      )
          uv_neighbors.remove(lowerCAmelCase_      )
          uv_neighbors.remove(lowerCAmelCase_      )
          SCREAMING_SNAKE_CASE										=uv_neighbors
          for neighbor in uv_neighbors:
               graph_copy[neighbor].append(lowerCAmelCase_      )

          SCREAMING_SNAKE_CASE										=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(lowerCAmelCase_      )
               if v in graph_copy[neighbor]:
                    graph_copy[neighbor].remove(lowerCAmelCase_      )

    # Find cutset.
     SCREAMING_SNAKE_CASE										=[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))




import decimal







def       snake_case__    (       ):





     """simple docstring"""







     SCREAMING_SNAKE_CASE										=0
     SCREAMING_SNAKE_CASE										=decimal.Context(prec=105      )
     for i in range(2,   100      ):
          SCREAMING_SNAKE_CASE										=decimal.Decimal(lowerCAmelCase_      )
          SCREAMING_SNAKE_CASE										=number.sqrt(lowerCAmelCase_      )
          if len(str(lowerCAmelCase_      )      ) > 1:
               answer += int(str(lowerCAmelCase_      )[0]      )
               SCREAMING_SNAKE_CASE										=str(lowerCAmelCase_      )[2:101]
               answer += sum(int(lowerCAmelCase_      ) for x in sqrt_number_str      )
     return answer


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 print(f'{solution() = }')

