

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       :     int           =							{
    "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__  (	UpperCAmelCase							:    dict[str, list[str]]    )						->		set[tuple[str, str]]:
  UpperCAmelCase :							Optional[Any]								=				{node: {node} for node in graph}

  UpperCAmelCase :							List[str]								=				{node: graph[node][:] for node in graph}

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

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

    UpperCAmelCase :							Union[str, Any]								=				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(UpperCAmelCase    )
      if v in graph_copy[neighbor]:
        graph_copy[neighbor].remove(UpperCAmelCase    )

    # Find cutset.
  UpperCAmelCase :							List[Any]								=				[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 typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available, is_tokenizers_available


_lowerCamelCase       :     int           =							{}

try:
     if not is_sentencepiece_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     _lowerCamelCase       :     Tuple           =							["MBart50Tokenizer"]

try:
     if not is_tokenizers_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     _lowerCamelCase       :     List[Any]           =							["MBart50TokenizerFast"]


if TYPE_CHECKING:
     try:
          if not is_sentencepiece_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .tokenization_mbartaa import MBartaaTokenizer

     try:
          if not is_tokenizers_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .tokenization_mbartaa_fast import MBartaaTokenizerFast

else:
     import sys

     _lowerCamelCase       :     Optional[int]           =							_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)





