code: 
  
  
  
  
  
  
  """simple docstring"""
  
  from typing import List, Optional, Tuple, Union
  
  import torch
  
  from ...utils import randn_tensor
  from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput
  
  
  class 	__lowerCamelCase       (				UpperCamelCase_    ):
  
  
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  		def __init__(     self							:			Optional[Any]		,    a_							:			Optional[int]		,    a_							:			Union[str, Any]			):
  				super().__init__()
  				self.register_modules(unet=__SCREAMING_SNAKE_CASE		,    scheduler=__SCREAMING_SNAKE_CASE			)
  
  
  
  
  
  		@torch.no_grad()
  		def __call__(     self							:			Tuple		,    a_							:			Tuple = 1		,    a_							:			Optional[Any] = None		,    a_							:			int = 10_00		,    a_							:			Any = "pil"		,    a_							:			List[Any] = True		,    ):
  				# Sample gaussian noise to begin loop
  				if isinstance(self.unet.config.sample_size		,    __SCREAMING_SNAKE_CASE			):
  						lowerCAmelCase_     :							Union[str, Any]             =    (
  						    batch_size,
  						    self.unet.config.in_channels,
  						    self.unet.config.sample_size,
  						    self.unet.config.sample_size,
  						)
  				else:
  						lowerCAmelCase_     :							Optional[Any]             =    (batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)
  
  				if self.device.type == "mps":
  						# randn does not work reproducibly on mps
  						lowerCAmelCase_     :							Any             =    randn_tensor(__SCREAMING_SNAKE_CASE		,    generator=__SCREAMING_SNAKE_CASE			)
  						lowerCAmelCase_     :							str             =    image.to(self.device			)
  				else:
  						lowerCAmelCase_     :							Tuple             =    randn_tensor(__SCREAMING_SNAKE_CASE		,    generator=__SCREAMING_SNAKE_CASE		,    device=self.device			)
  
  				# set step values
  				self.scheduler.set_timesteps(__SCREAMING_SNAKE_CASE			)
  
  				for t in self.progress_bar(self.scheduler.timesteps			):
  						# 1. predict noise model_output
  						lowerCAmelCase_     :							Tuple             =    self.unet(__SCREAMING_SNAKE_CASE		,    __SCREAMING_SNAKE_CASE			).sample
  
  						# 2. compute previous image: x_t -> x_t-1
  						lowerCAmelCase_     :							Any             =    self.scheduler.step(__SCREAMING_SNAKE_CASE		,    __SCREAMING_SNAKE_CASE		,    __SCREAMING_SNAKE_CASE		,    generator=__SCREAMING_SNAKE_CASE			).prev_sample
  
  				lowerCAmelCase_     :							Union[str, Any]             =    (image / 2 + 0.5).clamp(0		,    1			)
  				lowerCAmelCase_     :							str             =    image.cpu().permute(0		,    2		,    3		,    1			).numpy()
  				if output_type == "pil":
  						lowerCAmelCase_     :							List[Any]             =    self.numpy_to_pil(__SCREAMING_SNAKE_CASE			)
  
  				if not return_dict:
  						return (image,)
  
  				return ImagePipelineOutput(images=__SCREAMING_SNAKE_CASE			)
  
style_context: 
  
  
  
  
  
  
  """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
  lowercase__      =				{
      """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			(						__UpperCamelCase )		->					set[tuple[str, str]]:
  
  		"""simple docstring"""
  
  
  
  
  
  
  
  		lowerCAmelCase_     :							Union[str, Any]             =    {node: {node} for node in graph}
  
  		lowerCAmelCase_     :							List[str]             =    {node: graph[node][:] for node in graph}
  
  		while len(__UpperCamelCase ) > 2:
  				# Choose a random edge.
  				lowerCAmelCase_     :							int             =    random.choice(list(graph_copy.keys() ) )
  				lowerCAmelCase_     :							Any             =    random.choice(graph_copy[u] )
  
  				# Contract edge (u, v) to new node uv
  				lowerCAmelCase_     :							Union[str, Any]             =    u + v
  				lowerCAmelCase_     :							List[Any]             =    list(set(graph_copy[u] + graph_copy[v] ) )
  				uv_neighbors.remove(__UpperCamelCase )
  				uv_neighbors.remove(__UpperCamelCase )
  				lowerCAmelCase_     :							str             =    uv_neighbors
  				for neighbor in uv_neighbors:
  						graph_copy[neighbor].append(__UpperCamelCase )
  
  				lowerCAmelCase_     :							Optional[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(__UpperCamelCase )
  						if v in graph_copy[neighbor]:
  								graph_copy[neighbor].remove(__UpperCamelCase )
  
      # Find cutset.
  		lowerCAmelCase_     :							Union[str, 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))
  