





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 			lowerCamelCase_		(					lowerCAmelCase:		dict[str, list[str]] )->						set[tuple[str, str]]:
  _snake_case      : Dict														=		{node: {node} for node in graph}

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

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

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

    _snake_case      : 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(lowerCAmelCase )
      if v in graph_copy[neighbor]:
        graph_copy[neighbor].remove(lowerCAmelCase )

    # Find cutset.
  _snake_case      : str														=		[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 warnings
from typing import List, Optional, Union

from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding, PaddingStrategy, PreTokenizedInput, TextInput, TruncationStrategy
from ...utils import TensorType



class 				_lowerCAmelCase			(	UpperCAmelCase_							):


  '''simple docstring'''
  a_							:				List[str]					    =["""image_processor""", """tokenizer"""]
  a_							:				Optional[Any]					    ="""LayoutLMv2ImageProcessor"""
  a_							:				Any					    =("""LayoutLMv2Tokenizer""", """LayoutLMv2TokenizerFast""")







  def __init__(					self					:    Union[str, Any]					, UpperCamelCase					:    str=None					, UpperCamelCase					:    List[Any]=None					, **UpperCamelCase					:    List[str]							):


    '''simple docstring'''





    _snake_case      : Dict														=		None
    if "feature_extractor" in kwargs:
      warnings.warn(
          'The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`'
          ' instead.'					, UpperCamelCase					, )
      _snake_case      : Dict														=		kwargs.pop('feature_extractor'							)

    _snake_case      : Optional[Any]														=		image_processor if image_processor is not None else feature_extractor
    if image_processor is None:
      raise ValueError('You need to specify an `image_processor`.'							)
    if tokenizer is None:
      raise ValueError('You need to specify a `tokenizer`.'							)

    super().__init__(UpperCamelCase					, UpperCamelCase							)







  def __call__(					self					:    int					, UpperCamelCase					:    Tuple					, UpperCamelCase					:    Union[TextInput, PreTokenizedInput, List[TextInput], List[PreTokenizedInput]] = None					, UpperCamelCase					:    Optional[Union[PreTokenizedInput, List[PreTokenizedInput]]] = None					, UpperCamelCase					:    Union[List[List[int]], List[List[List[int]]]] = None					, UpperCamelCase					:    Optional[Union[List[int], List[List[int]]]] = None					, UpperCamelCase					:    bool = True					, UpperCamelCase					:    Union[bool, str, PaddingStrategy] = False					, UpperCamelCase					:    Union[bool, str, TruncationStrategy] = False					, UpperCamelCase					:    Optional[int] = None					, UpperCamelCase					:    int = 0					, UpperCamelCase					:    Optional[int] = None					, UpperCamelCase					:    Optional[bool] = None					, UpperCamelCase					:    Optional[bool] = None					, UpperCamelCase					:    bool = False					, UpperCamelCase					:    bool = False					, UpperCamelCase					:    bool = False					, UpperCamelCase					:    bool = False					, UpperCamelCase					:    bool = True					, UpperCamelCase					:    Optional[Union[str, TensorType]] = None					, **UpperCamelCase					:    Optional[Any]					, ):


    '''simple docstring'''





    if self.image_processor.apply_ocr and (boxes is not None):
      raise ValueError(
          'You cannot provide bounding boxes if you initialized the image processor with apply_ocr set to True.'							)

    if self.image_processor.apply_ocr and (word_labels is not None):
      raise ValueError(
          'You cannot provide word labels if you initialized the image processor with apply_ocr set to True.'							)

    if return_overflowing_tokens is True and return_offsets_mapping is False:
      raise ValueError('You cannot return overflowing tokens without returning the offsets mapping.'							)

    # first, apply the image processor
    _snake_case      : Optional[Any]														=		self.image_processor(images=UpperCamelCase					, return_tensors=UpperCamelCase							)

    # second, apply the tokenizer
    if text is not None and self.image_processor.apply_ocr and text_pair is None:
      if isinstance(UpperCamelCase					, UpperCamelCase							):
        _snake_case      : List[Any]														=		[text]  # add batch dimension (as the image processor always adds a batch dimension)
      _snake_case      : Dict														=		features['words']

    _snake_case      : Optional[int]														=		self.tokenizer(
        text=text if text is not None else features['words']					, text_pair=text_pair if text_pair is not None else None					, boxes=boxes if boxes is not None else features['boxes']					, word_labels=UpperCamelCase					, add_special_tokens=UpperCamelCase					, padding=UpperCamelCase					, truncation=UpperCamelCase					, max_length=UpperCamelCase					, stride=UpperCamelCase					, pad_to_multiple_of=UpperCamelCase					, return_token_type_ids=UpperCamelCase					, return_attention_mask=UpperCamelCase					, return_overflowing_tokens=UpperCamelCase					, return_special_tokens_mask=UpperCamelCase					, return_offsets_mapping=UpperCamelCase					, return_length=UpperCamelCase					, verbose=UpperCamelCase					, return_tensors=UpperCamelCase					, **UpperCamelCase					, )

    # add pixel values
    _snake_case      : Optional[int]														=		features.pop('pixel_values'							)
    if return_overflowing_tokens is True:
      _snake_case      : Any														=		self.get_overflowing_images(UpperCamelCase					, encoded_inputs['overflow_to_sample_mapping']							)
    _snake_case      : int														=		images

    return encoded_inputs







  def UpperCamelCase_       (					self					:    List[Any]					, UpperCamelCase					:    List[str]					, UpperCamelCase					:    List[str]							):


    '''simple docstring'''





    _snake_case      : Optional[Any]														=		[]
    for sample_idx in overflow_to_sample_mapping:
      images_with_overflow.append(images[sample_idx]							)

    if len(UpperCamelCase							) != len(UpperCamelCase							):
      raise ValueError(
          'Expected length of images to be the same as the length of `overflow_to_sample_mapping`, but got'
          f""" {len(UpperCamelCase							)} and {len(UpperCamelCase							)}"""							)

    return images_with_overflow







  def UpperCamelCase_       (					self					:    List[Any]					, *UpperCamelCase					:    Any					, **UpperCamelCase					:    int							):


    '''simple docstring'''





    return self.tokenizer.batch_decode(*UpperCamelCase					, **UpperCamelCase							)







  def UpperCamelCase_       (					self					:    Any					, *UpperCamelCase					:    Optional[int]					, **UpperCamelCase					:    Any							):


    '''simple docstring'''





    return self.tokenizer.decode(*UpperCamelCase					, **UpperCamelCase							)







  @property
  def UpperCamelCase_       (					self					:    str							):


    '''simple docstring'''





    return ["input_ids", "bbox", "token_type_ids", "attention_mask", "image"]







  @property
  def UpperCamelCase_       (					self					:    Dict							):


    '''simple docstring'''





    warnings.warn(
        '`feature_extractor_class` is deprecated and will be removed in v5. Use `image_processor_class` instead.'					, UpperCamelCase					, )
    return self.image_processor_class







  @property
  def UpperCamelCase_       (					self					:    Tuple							):


    '''simple docstring'''





    warnings.warn(
        '`feature_extractor` is deprecated and will be removed in v5. Use `image_processor` instead.'					, UpperCamelCase					, )
    return self.image_processor




