code: 
  
  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
  __A   :     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 		SCREAMING_SNAKE_CASE__				(							_UpperCAmelCase				)					-> List[Any]:
  
  
  
  				'''simple docstring'''
  
  
  
  
  
  
  				lowerCAmelCase				:			Any    			=      {node: {node} for node in graph}
  
  				lowerCAmelCase				:			Optional[int]    			=      {node: graph[node][:] for node in graph}
  
  				while len(_UpperCAmelCase				) > 2:
  								# Choose a random edge.
  								lowerCAmelCase				:			Tuple    			=      random.choice(list(graph_copy.keys()				)				)
  								lowerCAmelCase				:			Union[str, Any]    			=      random.choice(graph_copy[u]				)
  
  								# Contract edge (u, v) to new node uv
  								lowerCAmelCase				:			List[str]    			=      u + v
  								lowerCAmelCase				:			int    			=      list(set(graph_copy[u] + graph_copy[v]				)				)
  								uv_neighbors.remove(_UpperCAmelCase				)
  								uv_neighbors.remove(_UpperCAmelCase				)
  								lowerCAmelCase				:			Tuple    			=      uv_neighbors
  								for neighbor in uv_neighbors:
  												graph_copy[neighbor].append(_UpperCAmelCase				)
  
  								lowerCAmelCase				:			Optional[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.
  				lowerCAmelCase				:			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))
  
  
  
  
  
  
style_context: 
  
  import torch
  
  from diffusers import KDPMaAncestralDiscreteScheduler
  from diffusers.utils import torch_device
  
  from .test_schedulers import SchedulerCommonTest
  
  
  
  
  
  
  class    __A				(							lowerCAmelCase ):
      lowerCAmelCase_							:		List[str]						=							(KDPMaAncestralDiscreteScheduler,)
      lowerCAmelCase_							:		Dict						=							10
  
  
  
  
  
  
      def 	lowercase__ (	self			:    Any    ,				**UpperCAmelCase_			:    List[Any]    ):
          lowerCAmelCase				:			int    			=      {
              'num_train_timesteps': 1100,
              'beta_start': 0.00_01,
              'beta_end': 0.02,
              'beta_schedule': 'linear',
          }
  
          config.update(**UpperCAmelCase_    )
          return config
  
  
  
  
  
  
      def 	lowercase__ (	self			:    Optional[Any]    ):
          for timesteps in [10, 50, 100, 1000]:
              self.check_over_configs(num_train_timesteps=UpperCAmelCase_    )
  
  
  
  
  
  
      def 	lowercase__ (	self			:    List[str]    ):
          for beta_start, beta_end in zip([0.0_00_01, 0.00_01, 0.0_01]    ,				[0.00_02, 0.0_02, 0.02]    ):
              self.check_over_configs(beta_start=UpperCAmelCase_    ,				beta_end=UpperCAmelCase_    )
  
  
  
  
  
  
      def 	lowercase__ (	self			:    Optional[int]    ):
          for schedule in ["linear", "scaled_linear"]:
              self.check_over_configs(beta_schedule=UpperCAmelCase_    )
  
  
  
  
  
  
      def 	lowercase__ (	self			:    int    ):
          if torch_device == "mps":
              return
          lowerCAmelCase				:			Any    			=      self.scheduler_classes[0]
          lowerCAmelCase				:			Optional[int]    			=      self.get_scheduler_config()
          lowerCAmelCase				:			List[str]    			=      scheduler_class(**UpperCAmelCase_    )
  
          scheduler.set_timesteps(self.num_inference_steps    )
  
          lowerCAmelCase				:			Any    			=      torch.manual_seed(0    )
  
          lowerCAmelCase				:			List[Any]    			=      self.dummy_model()
          lowerCAmelCase				:			List[Any]    			=      self.dummy_sample_deter * scheduler.init_noise_sigma
          lowerCAmelCase				:			Optional[int]    			=      sample.to(UpperCAmelCase_    )
  
          for i, t in enumerate(scheduler.timesteps    ):
              lowerCAmelCase				:			str    			=      scheduler.scale_model_input(UpperCAmelCase_    ,				UpperCAmelCase_    )
  
              lowerCAmelCase				:			Any    			=      model(UpperCAmelCase_    ,				UpperCAmelCase_    )
  
              lowerCAmelCase				:			Optional[Any]    			=      scheduler.step(UpperCAmelCase_    ,				UpperCAmelCase_    ,				UpperCAmelCase_    ,				generator=UpperCAmelCase_    )
              lowerCAmelCase				:			Union[str, Any]    			=      output.prev_sample
  
          lowerCAmelCase				:			List[Any]    			=      torch.sum(torch.abs(UpperCAmelCase_    )    )
          lowerCAmelCase				:			Any    			=      torch.mean(torch.abs(UpperCAmelCase_    )    )
  
          assert abs(result_sum.item() - 1_38_49.38_77    ) < 1E-2
          assert abs(result_mean.item() - 18.03_31    ) < 5E-3
  
  
  
  
  
  
      def 	lowercase__ (	self			:    Tuple    ):
          for prediction_type in ["epsilon", "v_prediction"]:
              self.check_over_configs(prediction_type=UpperCAmelCase_    )
  
  
  
  
  
  
      def 	lowercase__ (	self			:    List[str]    ):
          if torch_device == "mps":
              return
          lowerCAmelCase				:			Optional[Any]    			=      self.scheduler_classes[0]
          lowerCAmelCase				:			List[Any]    			=      self.get_scheduler_config(prediction_type='v_prediction'    )
          lowerCAmelCase				:			Any    			=      scheduler_class(**UpperCAmelCase_    )
  
          scheduler.set_timesteps(self.num_inference_steps    )
  
          lowerCAmelCase				:			Optional[int]    			=      self.dummy_model()
          lowerCAmelCase				:			Any    			=      self.dummy_sample_deter * scheduler.init_noise_sigma
          lowerCAmelCase				:			Optional[int]    			=      sample.to(UpperCAmelCase_    )
  
          lowerCAmelCase				:			Optional[int]    			=      torch.manual_seed(0    )
  
          for i, t in enumerate(scheduler.timesteps    ):
              lowerCAmelCase				:			Dict    			=      scheduler.scale_model_input(UpperCAmelCase_    ,				UpperCAmelCase_    )
  
              lowerCAmelCase				:			Optional[int]    			=      model(UpperCAmelCase_    ,				UpperCAmelCase_    )
  
              lowerCAmelCase				:			Optional[int]    			=      scheduler.step(UpperCAmelCase_    ,				UpperCAmelCase_    ,				UpperCAmelCase_    ,				generator=UpperCAmelCase_    )
              lowerCAmelCase				:			str    			=      output.prev_sample
  
          lowerCAmelCase				:			str    			=      torch.sum(torch.abs(UpperCAmelCase_    )    )
          lowerCAmelCase				:			Tuple    			=      torch.mean(torch.abs(UpperCAmelCase_    )    )
  
          assert abs(result_sum.item() - 3_28.99_70    ) < 1E-2
          assert abs(result_mean.item() - 0.42_84    ) < 1E-3
  
  
  
  
  
  
      def 	lowercase__ (	self			:    Tuple    ):
          if torch_device == "mps":
              return
          lowerCAmelCase				:			str    			=      self.scheduler_classes[0]
          lowerCAmelCase				:			Dict    			=      self.get_scheduler_config()
          lowerCAmelCase				:			List[str]    			=      scheduler_class(**UpperCAmelCase_    )
  
          scheduler.set_timesteps(self.num_inference_steps    ,				device=UpperCAmelCase_    )
          lowerCAmelCase				:			int    			=      torch.manual_seed(0    )
  
          lowerCAmelCase				:			Tuple    			=      self.dummy_model()
          lowerCAmelCase				:			Optional[Any]    			=      self.dummy_sample_deter.to(UpperCAmelCase_    ) * scheduler.init_noise_sigma
  
          for t in scheduler.timesteps:
              lowerCAmelCase				:			str    			=      scheduler.scale_model_input(UpperCAmelCase_    ,				UpperCAmelCase_    )
  
              lowerCAmelCase				:			List[Any]    			=      model(UpperCAmelCase_    ,				UpperCAmelCase_    )
  
              lowerCAmelCase				:			Dict    			=      scheduler.step(UpperCAmelCase_    ,				UpperCAmelCase_    ,				UpperCAmelCase_    ,				generator=UpperCAmelCase_    )
              lowerCAmelCase				:			Dict    			=      output.prev_sample
  
          lowerCAmelCase				:			Union[str, Any]    			=      torch.sum(torch.abs(UpperCAmelCase_    )    )
          lowerCAmelCase				:			str    			=      torch.mean(torch.abs(UpperCAmelCase_    )    )
  
          assert abs(result_sum.item() - 1_38_49.38_18    ) < 1E-1
          assert abs(result_mean.item() - 18.03_31    ) < 1E-3
  
  
  
  
  
  