





def  __UpperCAmelCase(   lowercase_   ):
       return [
           {
               0: [1, 2],
               1: [0, 2],
               2: [0, 1, 3, 5],
               3: [2, 4],
               4: [3],
               5: [2, 6, 8],
               6: [5, 7],
               7: [6, 8],
               8: [5, 7],
           },
           {
               0: [6],
               1: [9],
               2: [4, 5],
               3: [4],
               4: [2, 3],
               5: [2],
               6: [0, 7],
               7: [6],
               8: [],
               9: [1],
           },
           {
               0: [4],
               1: [6],
               2: [],
               3: [5, 6, 7],
               4: [0, 6],
               5: [3, 8, 9],
               6: [1, 3, 4, 7],
               7: [3, 6, 8, 9],
               8: [5, 7],
               9: [5, 7],
           },
           {
               0: [1, 3],
               1: [0, 2, 4],
               2: [1, 3, 4],
               3: [0, 2, 4],
               4: [1, 2, 3],
           },
       ][index]




def  __UpperCAmelCase(   lowercase_   ):
       _lowerCamelCase				:  int						=		0
       _lowerCamelCase				:  Optional[int]						=		len(lowercase_   )  # No of vertices in graph
       _lowerCamelCase				:  Any						=		[0] * n
       _lowerCamelCase				:  str						=		[False] * n

       def dfs(lowercase_			,     lowercase_			,     lowercase_			,     lowercase_   ):
              _lowerCamelCase				:  Optional[Any]						=		True
              _lowerCamelCase				:  List[str]						=		id_
              id_ += 1
              for to in graph[at]:
                     if to == parent:
                            pass
                     elif not visited[to]:
                            dfs(lowercase_			,     lowercase_			,     lowercase_			,     id_   )
                            _lowerCamelCase				:  str						=		min(low[at]			,     low[to]   )
                            if id_ <= low[to]:
                                   bridges.append((at, to) if at < to else (to, at)   )
                     else:
                            # This edge is a back edge and cannot be a bridge
                            _lowerCamelCase				:  Tuple						=		min(low[at]			,     low[to]   )

       _lowerCamelCase				:  list[tuple[int, int]]						=		[]
       for i in range(lowercase_   ):
              if not visited[i]:
                     dfs(lowercase_			,     -1			,     lowercase_			,     id_   )
       return bridges


if __name__ == "__main__":
       import doctest

       doctest.testmod()








import inspect
from typing import List, Optional, Tuple, Union

import torch

from ...models import UNetaDModel, VQModel
from ...schedulers import DDIMScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput







class       __A							(   lowerCamelCase__	):




      """simple docstring"""







      def __init__(		self   ,				a__   ,				a__   ,				a__):



             """simple docstring"""





             super().__init__()
             self.register_modules(vqvae=a__   ,				unet=a__   ,				scheduler=a__)



      @torch.no_grad()
      def __call__(		self   ,				a__ = 1   ,				a__ = None   ,				a__ = 0.0   ,				a__ = 50   ,				a__ = "pil"   ,				a__ = True   ,				**a__   ,				):



             """simple docstring"""





             _lowerCamelCase				:  Tuple						=		randn_tensor(
                 (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)   ,				generator=a__   ,				)
             _lowerCamelCase				:  Optional[int]						=		latents.to(self.device)

             # scale the initial noise by the standard deviation required by the scheduler
             _lowerCamelCase				:  Tuple						=		latents * self.scheduler.init_noise_sigma

             self.scheduler.set_timesteps(a__)

             # prepare extra kwargs for the scheduler step, since not all schedulers have the same signature
             _lowerCamelCase				:  Optional[int]						=		'''eta''' in set(inspect.signature(self.scheduler.step).parameters.keys())

             _lowerCamelCase				:  Union[str, Any]						=		{}
             if accepts_eta:
                    _lowerCamelCase				:  List[Any]						=		eta

             for t in self.progress_bar(self.scheduler.timesteps):
                    _lowerCamelCase				:  List[Any]						=		self.scheduler.scale_model_input(a__   ,				a__)
                    # predict the noise residual
                    _lowerCamelCase				:  Optional[int]						=		self.unet(a__   ,				a__).sample
                    # compute the previous noisy sample x_t -> x_t-1
                    _lowerCamelCase				:  List[str]						=		self.scheduler.step(a__   ,				a__   ,				a__   ,				**a__).prev_sample

             # decode the image latents with the VAE
             _lowerCamelCase				:  Optional[int]						=		self.vqvae.decode(a__).sample

             _lowerCamelCase				:  Dict						=		(image / 2 + 0.5).clamp(0   ,				1)
             _lowerCamelCase				:  List[str]						=		image.cpu().permute(0   ,				2   ,				3   ,				1).numpy()
             if output_type == "pil":
                    _lowerCamelCase				:  List[Any]						=		self.numpy_to_pil(a__)

             if not return_dict:
                    return (image,)

             return ImagePipelineOutput(images=a__)

