
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
__snake_case							 =  {
    """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__  :     dict[str, list[str]]	):
    UpperCamelCase	:str     							=       {node: {node} for node in graph}

    UpperCamelCase	:int     							=       {node: graph[node][:] for node in graph}

    while len(SCREAMING_SNAKE_CASE__	) > 2:
        # Choose a random edge.
        UpperCamelCase	:Any     							=       random.choice(list(graph_copy.keys()	)	)
        UpperCamelCase	:Optional[int]     							=       random.choice(graph_copy[u]	)

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

        UpperCamelCase	:Optional[int]     							=       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(SCREAMING_SNAKE_CASE__	)
            if v in graph_copy[neighbor]:
                graph_copy[neighbor].remove(SCREAMING_SNAKE_CASE__	)

    # Find cutset.
    UpperCamelCase	: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 __future__ import annotations

from enum import Enum







class       UpperCAmelCase_						( lowercase			):



      """simple docstring"""
      UpperCamelCase_    : Optional[Any]									=24
      UpperCamelCase_    : Any									=21
      UpperCamelCase_    : Union[str, Any]									=18
      UpperCamelCase_    : Tuple									=15
      UpperCamelCase_    : List[Any]									=12
      UpperCamelCase_    : Optional[Any]									=9
      UpperCamelCase_    : List[str]									=6
      UpperCamelCase_    : List[str]									=3
      UpperCamelCase_    : Any									=2
      UpperCamelCase_    : List[str]									=1
      UpperCamelCase_    : Optional[Any]									=-1
      UpperCamelCase_    : str									=-2
      UpperCamelCase_    : Any									=-3
      UpperCamelCase_    : Optional[int]									=-6
      UpperCamelCase_    : int									=-9
      UpperCamelCase_    : Optional[int]									=-12
      UpperCamelCase_    : Optional[Any]									=-15
      UpperCamelCase_    : str									=-18
      UpperCamelCase_    : int									=-21
      UpperCamelCase_    : Union[str, Any]									=-24







class       UpperCAmelCase_						( lowercase			):



      """simple docstring"""
      UpperCamelCase_    : Tuple									=8
      UpperCamelCase_    : str									=7
      UpperCamelCase_    : List[str]									=6
      UpperCamelCase_    : List[str]									=5
      UpperCamelCase_    : int									=4
      UpperCamelCase_    : Optional[Any]									=3
      UpperCamelCase_    : Optional[Any]									=2
      UpperCamelCase_    : List[str]									=1







def   _A       (    SCREAMING_SNAKE_CASE__  :     float					,  SCREAMING_SNAKE_CASE__  :     str | SIUnit					,  SCREAMING_SNAKE_CASE__  :     str | SIUnit					,  ):
    if isinstance(SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__	):
        UpperCamelCase	:str     							=       SIUnit[known_prefix.lower()]
    if isinstance(SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__	):
        UpperCamelCase	:Any     							=       SIUnit[unknown_prefix.lower()]
    UpperCamelCase	:float     							=       known_amount * (
        10 ** (known_prefix.value - unknown_prefix.value)
    )
    return unknown_amount


def   _A       (    SCREAMING_SNAKE_CASE__  :     float					,  SCREAMING_SNAKE_CASE__  :     str | BinaryUnit					,  SCREAMING_SNAKE_CASE__  :     str | BinaryUnit					,  ):
    if isinstance(SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__	):
        UpperCamelCase	:Dict     							=       BinaryUnit[known_prefix.lower()]
    if isinstance(SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__	):
        UpperCamelCase	:List[str]     							=       BinaryUnit[unknown_prefix.lower()]
    UpperCamelCase	:float     							=       known_amount * (
        2 ** ((known_prefix.value - unknown_prefix.value) * 10)
    )
    return unknown_amount


if __name__ == "__main__":
 import doctest

 doctest.testmod()





