
'''simple docstring'''

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  (    lowerCAmelCase_       ):
     _UpperCAmelCase					:  Optional[Any]         =    {node: {node} for node in graph}

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

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

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

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

    # Find cutset.
     _UpperCAmelCase					:  Tuple         =    [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))









"""simple docstring"""
from ...configuration_utils import PretrainedConfig
from ...utils import is_detectrona_available, logging


__UpperCamelCase			:		List[Any]		    =   logging.get_logger(__name__)

__UpperCamelCase			:		Union[str, Any]		    =   {
    '''layoutlmv2-base-uncased''': '''https://huggingface.co/microsoft/layoutlmv2-base-uncased/resolve/main/config.json''',
    '''layoutlmv2-large-uncased''': '''https://huggingface.co/microsoft/layoutlmv2-large-uncased/resolve/main/config.json''',
    # See all LayoutLMv2 models at https://huggingface.co/models?filter=layoutlmv2
}

# soft dependency
if is_detectrona_available():
       import detectrona







class 	a				(					a__   ):
 snake_case__    	=    '''layoutlmv2'''



 def __init__(			self							,    _snake_case=3_05_22							,    _snake_case=7_68							,    _snake_case=12							,    _snake_case=12							,    _snake_case=30_72							,    _snake_case="gelu"							,    _snake_case=0.1							,    _snake_case=0.1							,    _snake_case=5_12							,    _snake_case=2							,    _snake_case=0.02							,    _snake_case=1E-12							,    _snake_case=0							,    _snake_case=10_24							,    _snake_case=1_28							,    _snake_case=32							,    _snake_case=True							,    _snake_case=2_56							,    _snake_case=64							,    _snake_case=True							,    _snake_case=[7, 7, 2_56]							,    _snake_case=1_28							,    _snake_case=1_28							,    _snake_case=True							,    _snake_case=True							,    _snake_case=False							,    _snake_case=None							,    **_snake_case							,    ):







  """simple docstring"""






  super().__init__(
      vocab_size=_snake_case							,    hidden_size=_snake_case							,    num_hidden_layers=_snake_case							,    num_attention_heads=_snake_case							,    intermediate_size=_snake_case							,    hidden_act=_snake_case							,    hidden_dropout_prob=_snake_case							,    attention_probs_dropout_prob=_snake_case							,    max_position_embeddings=_snake_case							,    type_vocab_size=_snake_case							,    initializer_range=_snake_case							,    layer_norm_eps=_snake_case							,    pad_token_id=_snake_case							,    **_snake_case							,    )
  lowerCAmelCase  							=      max_ad_position_embeddings
  lowerCAmelCase  							=      max_rel_pos
  lowerCAmelCase  							=      rel_pos_bins
  lowerCAmelCase  							=      fast_qkv
  lowerCAmelCase  							=      max_rel_ad_pos
  lowerCAmelCase  							=      rel_ad_pos_bins
  lowerCAmelCase  							=      convert_sync_batchnorm
  lowerCAmelCase  							=      image_feature_pool_shape
  lowerCAmelCase  							=      coordinate_size
  lowerCAmelCase  							=      shape_size
  lowerCAmelCase  							=      has_relative_attention_bias
  lowerCAmelCase  							=      has_spatial_attention_bias
  lowerCAmelCase  							=      has_visual_segment_embedding
  lowerCAmelCase  							=      (
      detectrona_config_args if detectrona_config_args is not None else self.get_default_detectrona_config()
  )



 @classmethod
 def 					UpperCamelCase__   (			self			):







  """simple docstring"""






  return {
      "MODEL.MASK_ON": True,
      "MODEL.PIXEL_STD": [57.375, 57.120, 58.395],
      "MODEL.BACKBONE.NAME": "build_resnet_fpn_backbone",
      "MODEL.FPN.IN_FEATURES": ["res2", "res3", "res4", "res5"],
      "MODEL.ANCHOR_GENERATOR.SIZES": [[32], [64], [1_28], [2_56], [5_12]],
      "MODEL.RPN.IN_FEATURES": ["p2", "p3", "p4", "p5", "p6"],
      "MODEL.RPN.PRE_NMS_TOPK_TRAIN": 20_00,
      "MODEL.RPN.PRE_NMS_TOPK_TEST": 10_00,
      "MODEL.RPN.POST_NMS_TOPK_TRAIN": 10_00,
      "MODEL.POST_NMS_TOPK_TEST": 10_00,
      "MODEL.ROI_HEADS.NAME": "StandardROIHeads",
      "MODEL.ROI_HEADS.NUM_CLASSES": 5,
      "MODEL.ROI_HEADS.IN_FEATURES": ["p2", "p3", "p4", "p5"],
      "MODEL.ROI_BOX_HEAD.NAME": "FastRCNNConvFCHead",
      "MODEL.ROI_BOX_HEAD.NUM_FC": 2,
      "MODEL.ROI_BOX_HEAD.POOLER_RESOLUTION": 14,
      "MODEL.ROI_MASK_HEAD.NAME": "MaskRCNNConvUpsampleHead",
      "MODEL.ROI_MASK_HEAD.NUM_CONV": 4,
      "MODEL.ROI_MASK_HEAD.POOLER_RESOLUTION": 7,
      "MODEL.RESNETS.DEPTH": 1_01,
      "MODEL.RESNETS.SIZES": [[32], [64], [1_28], [2_56], [5_12]],
      "MODEL.RESNETS.ASPECT_RATIOS": [[0.5, 1.0, 2.0]],
      "MODEL.RESNETS.OUT_FEATURES": ["res2", "res3", "res4", "res5"],
      "MODEL.RESNETS.NUM_GROUPS": 32,
      "MODEL.RESNETS.WIDTH_PER_GROUP": 8,
      "MODEL.RESNETS.STRIDE_IN_1X1": False,
  }



 def 					UpperCamelCase__   (			self			):







  """simple docstring"""






  lowerCAmelCase  							=      detectrona.config.get_cfg()
  for k, v in self.detectrona_config_args.items():
   lowerCAmelCase  							=      k.split('.'			)
   lowerCAmelCase  							=      detectrona_config
   for attribute in attributes[:-1]:
    lowerCAmelCase  							=      getattr(_snake_case							,    _snake_case			)
   setattr(_snake_case							,    attributes[-1]							,    _snake_case			)

  return detectrona_config





