




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    : 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     lowerCAmelCase		(		_lowerCAmelCase				: dict[str, list[str]]						):




 """simple docstring"""







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

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

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

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

  UpperCAmelCase__							=    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.
 UpperCAmelCase__							=    [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 os
from typing import List, Union

import tensorflow as tf
from tensorflow_text import BertTokenizer as BertTokenizerLayer
from tensorflow_text import FastBertTokenizer, ShrinkLongestTrimmer, case_fold_utfa, combine_segments, pad_model_inputs

from .tokenization_bert import BertTokenizer
class       _UpperCamelCase   (					tf.keras.layers.Layer		):
      def __init__(      self :int			,   lowerCamelCase :List			,   lowerCamelCase :bool			,   lowerCamelCase :int = None			,   lowerCamelCase :int = None			,   lowerCamelCase :int = None			,   lowerCamelCase :str = "longest"			,   lowerCamelCase :bool = True			,   lowerCamelCase :int = 512			,   lowerCamelCase :int = None			,   lowerCamelCase :bool = True			,   lowerCamelCase :bool = True			,   lowerCamelCase :bool = True			,   **lowerCamelCase :Optional[Any]			,   )  ->      List[str]:
       super().__init__()
       if use_fast_bert_tokenizer:
        UpperCAmelCase__							=    FastBertTokenizer(
            lowerCamelCase			,   token_out_type=tf.intaa			,   lower_case_nfd_strip_accents=lowerCamelCase			,   **lowerCamelCase   )
       else:
        UpperCAmelCase__							=    tf.lookup.StaticVocabularyTable(
            tf.lookup.KeyValueTensorInitializer(
                keys=lowerCamelCase			,   key_dtype=tf.string			,   values=tf.range(tf.size(lowerCamelCase			,   out_type=tf.intaa   )			,   dtype=tf.intaa   )			,   value_dtype=tf.intaa			,   )			,   num_oov_buckets=1			,   )
        UpperCAmelCase__							=    BertTokenizerLayer(
            lowerCamelCase			,   token_out_type=tf.intaa			,   lower_case=lowerCamelCase			,   **lowerCamelCase   )

       UpperCAmelCase__							=    vocab_list
       UpperCAmelCase__							=    do_lower_case
       UpperCAmelCase__							=    cls_token_id or vocab_list.index("[CLS]"   )
       UpperCAmelCase__							=    sep_token_id or vocab_list.index("[SEP]"   )
       UpperCAmelCase__							=    pad_token_id or vocab_list.index("[PAD]"   )
       UpperCAmelCase__							=    ShrinkLongestTrimmer(max_length - 3			,   axis=1   )  # Allow room for special tokens
       UpperCAmelCase__							=    max_length
       UpperCAmelCase__							=    padding
       UpperCAmelCase__							=    truncation
       UpperCAmelCase__							=    pad_to_multiple_of
       UpperCAmelCase__							=    return_token_type_ids
       UpperCAmelCase__							=    return_attention_mask
      @classmethod
      def 						UpperCAmelCase_    (      cls :List[str]			,   lowerCamelCase :"PreTrainedTokenizerBase"			,   **lowerCamelCase :Dict   )  ->      Dict:  # noqa: F821
       UpperCAmelCase__							=    kwargs.pop("do_lower_case"			,   lowerCamelCase   )
       UpperCAmelCase__							=    tokenizer.do_lower_case if do_lower_case is None else do_lower_case
       UpperCAmelCase__							=    kwargs.pop("cls_token_id"			,   lowerCamelCase   )
       UpperCAmelCase__							=    tokenizer.cls_token_id if cls_token_id is None else cls_token_id
       UpperCAmelCase__							=    kwargs.pop("sep_token_id"			,   lowerCamelCase   )
       UpperCAmelCase__							=    tokenizer.sep_token_id if sep_token_id is None else sep_token_id
       UpperCAmelCase__							=    kwargs.pop("pad_token_id"			,   lowerCamelCase   )
       UpperCAmelCase__							=    tokenizer.pad_token_id if pad_token_id is None else pad_token_id

       UpperCAmelCase__							=    tokenizer.get_vocab()
       UpperCAmelCase__							=    sorted([(wordpiece, idx) for wordpiece, idx in vocab.items()]			,   key=lambda lowerCamelCase   : x[1]   )
       UpperCAmelCase__							=    [entry[0] for entry in vocab]
       return cls(
           vocab_list=lowerCamelCase			,   do_lower_case=lowerCamelCase			,   cls_token_id=lowerCamelCase			,   sep_token_id=lowerCamelCase			,   pad_token_id=lowerCamelCase			,   **lowerCamelCase			,   )
      @classmethod
      def 						UpperCAmelCase_    (      cls :Any			,   lowerCamelCase :Union[str, os.PathLike]			,   *lowerCamelCase :str			,   **lowerCamelCase :List[str]   )  ->      Tuple:
       try:
        UpperCAmelCase__							=    BertTokenizer.from_pretrained(lowerCamelCase			,   *lowerCamelCase			,   **lowerCamelCase   )
       except:  # noqa: E722
        from .tokenization_bert_fast import BertTokenizerFast

        UpperCAmelCase__							=    BertTokenizerFast.from_pretrained(lowerCamelCase			,   *lowerCamelCase			,   **lowerCamelCase   )
       return cls.from_tokenizer(lowerCamelCase			,   **lowerCamelCase   )
      def 						UpperCAmelCase_    (      self :int			,   lowerCamelCase :Optional[int]   )  ->      List[str]:
       if self.do_lower_case:
        UpperCAmelCase__							=    case_fold_utfa(lowerCamelCase   )
       UpperCAmelCase__							=    self.tf_tokenizer.tokenize(lowerCamelCase   )
       return tokens.merge_dims(1			,   -1   )
      def 						UpperCAmelCase_    (      self :Optional[Any]			,   lowerCamelCase :Tuple			,   lowerCamelCase :str=None			,   lowerCamelCase :Tuple=None			,   lowerCamelCase :Any=None			,   lowerCamelCase :Optional[int]=None			,   lowerCamelCase :Optional[Any]=None			,   lowerCamelCase :Optional[Any]=None			,   lowerCamelCase :Tuple=None			,   )  ->      str:
       if padding is None:
        UpperCAmelCase__							=    self.padding
       if padding not in ("longest", "max_length"):
        raise ValueError("Padding must be either 'longest' or 'max_length'!"   )
       if max_length is not None and text_pair is not None:
        # Because we have to instantiate a Trimmer to do it properly
        raise ValueError("max_length cannot be overridden at call time when truncating paired texts!"   )
       if max_length is None:
        UpperCAmelCase__							=    self.max_length
       if truncation is None:
        UpperCAmelCase__							=    self.truncation
       if pad_to_multiple_of is None:
        UpperCAmelCase__							=    self.pad_to_multiple_of
       if return_token_type_ids is None:
        UpperCAmelCase__							=    self.return_token_type_ids
       if return_attention_mask is None:
        UpperCAmelCase__							=    self.return_attention_mask
       if not isinstance(lowerCamelCase			,   tf.Tensor   ):
        UpperCAmelCase__							=    tf.convert_to_tensor(lowerCamelCase   )
       if text_pair is not None and not isinstance(lowerCamelCase			,   tf.Tensor   ):
        UpperCAmelCase__							=    tf.convert_to_tensor(lowerCamelCase   )
       if text_pair is not None:
        if text.shape.rank > 1:
         raise ValueError("text argument should not be multidimensional when a text pair is supplied!"   )
        if text_pair.shape.rank > 1:
         raise ValueError("text_pair should not be multidimensional!"   )
       if text.shape.rank == 2:
        UpperCAmelCase__			,			UpperCAmelCase__							=    text[:, 0], text[:, 1]
       UpperCAmelCase__							=    self.unpaired_tokenize(lowerCamelCase   )
       if text_pair is None:  # Unpaired text
        if truncation:
         UpperCAmelCase__							=    text[:, : max_length - 2]  # Allow room for special tokens
        UpperCAmelCase__			,			UpperCAmelCase__							=    combine_segments(
            (text,)			,   start_of_sequence_id=self.cls_token_id			,   end_of_segment_id=self.sep_token_id   )
       else:  # Paired text
        UpperCAmelCase__							=    self.unpaired_tokenize(lowerCamelCase   )
        if truncation:
         UpperCAmelCase__			,			UpperCAmelCase__							=    self.paired_trimmer.trim([text, text_pair]   )
        UpperCAmelCase__			,			UpperCAmelCase__							=    combine_segments(
            (text, text_pair)			,   start_of_sequence_id=self.cls_token_id			,   end_of_segment_id=self.sep_token_id   )
       if padding == "longest":
        UpperCAmelCase__							=    input_ids.bounding_shape(axis=1   )
        if pad_to_multiple_of is not None:
         # No ceiling division in tensorflow, so we negate floordiv instead
         UpperCAmelCase__							=    pad_to_multiple_of * (-tf.math.floordiv(-pad_length			,   lowerCamelCase   ))
       else:
        UpperCAmelCase__							=    max_length

       UpperCAmelCase__			,			UpperCAmelCase__							=    pad_model_inputs(lowerCamelCase			,   max_seq_length=lowerCamelCase			,   pad_value=self.pad_token_id   )
       UpperCAmelCase__							=    {"input_ids": input_ids}
       if return_attention_mask:
        UpperCAmelCase__							=    attention_mask
       if return_token_type_ids:
        UpperCAmelCase__			,			UpperCAmelCase__							=    pad_model_inputs(
            lowerCamelCase			,   max_seq_length=lowerCamelCase			,   pad_value=self.pad_token_id   )
        UpperCAmelCase__							=    token_type_ids
       return output







      def 						UpperCAmelCase_    (      self :Tuple   )  ->      Tuple:
       return {
           "vocab_list": self.vocab_list,
           "do_lower_case": self.do_lower_case,
           "cls_token_id": self.cls_token_id,
           "sep_token_id": self.sep_token_id,
           "pad_token_id": self.pad_token_id,
       }





