




'''simple docstring'''



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

import numpy as np
import PIL
import torch
import torch.utils.checkpoint

from ...models import UNetaDModel, VQModel
from ...schedulers import (
    DDIMScheduler,
    DPMSolverMultistepScheduler,
    EulerAncestralDiscreteScheduler,
    EulerDiscreteScheduler,
    LMSDiscreteScheduler,
    PNDMScheduler,
)
from ...utils import PIL_INTERPOLATION, randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput


def    lowerCamelCase__   ( A     :    Tuple  ):




						'''simple docstring'''






						UpperCAmelCase       ,       UpperCAmelCase         =			image.size
						UpperCAmelCase       ,       UpperCAmelCase         =			(x - x % 32 for x in (w, h))  # resize to integer multiple of 32
						UpperCAmelCase         =			image.resize((w, h)   ,     resample=PIL_INTERPOLATION['''lanczos''']  )
						UpperCAmelCase         =			np.array(A  ).astype(np.floataa  ) / 255.0
						UpperCAmelCase         =			image[None].transpose(0   ,     3   ,     1   ,     2  )
						UpperCAmelCase         =			torch.from_numpy(A  )
						return 2.0 * image - 1.0






class  UpperCamelCase__(     lowerCAmelCase ):




				def __init__(	self    :				Tuple   ,					lowerCAmelCase    :				VQModel   ,					lowerCAmelCase    :				UNetaDModel   ,					lowerCAmelCase    :				Union[
				        DDIMScheduler,
				        PNDMScheduler,
				        LMSDiscreteScheduler,
				        EulerDiscreteScheduler,
				        EulerAncestralDiscreteScheduler,
				        DPMSolverMultistepScheduler,
				    ]   ,					)->  Any:

										"""simple docstring"""




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





				@torch.no_grad()
				def __call__(	self    :				Tuple   ,					lowerCAmelCase    :				Union[torch.Tensor, PIL.Image.Image] = None   ,					lowerCAmelCase    :				Optional[int] = 1   ,					lowerCAmelCase    :				Optional[int] = 100   ,					lowerCAmelCase    :				Optional[float] = 0.0   ,					lowerCAmelCase    :				Optional[Union[torch.Generator, List[torch.Generator]]] = None   ,					lowerCAmelCase    :				Optional[str] = "pil"   ,					lowerCAmelCase    :				bool = True   ,					)->  Union[Tuple, ImagePipelineOutput]:

										"""simple docstring"""




										if isinstance(lowerCAmelCase   ,					PIL.Image.Image   ):
																UpperCAmelCase         =			1
										elif isinstance(lowerCAmelCase   ,					torch.Tensor   ):
																UpperCAmelCase         =			image.shape[0]
										else:
																raise ValueError(F"""`image` has to be of type `PIL.Image.Image` or `torch.Tensor` but is {type(lowerCAmelCase   )}"""   )

										if isinstance(lowerCAmelCase   ,					PIL.Image.Image   ):
																UpperCAmelCase         =			preprocess(lowerCAmelCase   )

										UpperCAmelCase       ,       UpperCAmelCase         =			image.shape[-2:]

										# in_channels should be 6: 3 for latents, 3 for low resolution image
										UpperCAmelCase         =			(batch_size, self.unet.config.in_channels // 2, height, width)
										UpperCAmelCase         =			next(self.unet.parameters()   ).dtype

										UpperCAmelCase         =			randn_tensor(lowerCAmelCase   ,					generator=lowerCAmelCase   ,					device=self.device   ,					dtype=lowerCAmelCase   )

										UpperCAmelCase         =			image.to(device=self.device   ,					dtype=lowerCAmelCase   )

										# set timesteps and move to the correct device
										self.scheduler.set_timesteps(lowerCAmelCase   ,					device=self.device   )
										UpperCAmelCase         =			self.scheduler.timesteps

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

										# prepare extra kwargs for the scheduler step, since not all schedulers have the same signature.
										# eta (η) is only used with the DDIMScheduler, it will be ignored for other schedulers.
										# eta corresponds to η in DDIM paper: https://arxiv.org/abs/2010.02502
										# and should be between [0, 1]
										UpperCAmelCase         =			'''eta''' in set(inspect.signature(self.scheduler.step   ).parameters.keys()   )
										UpperCAmelCase         =			{}
										if accepts_eta:
																UpperCAmelCase         =			eta

										for t in self.progress_bar(lowerCAmelCase   ):
																# concat latents and low resolution image in the channel dimension.
																UpperCAmelCase         =			torch.cat([latents, image]   ,					dim=1   )
																UpperCAmelCase         =			self.scheduler.scale_model_input(lowerCAmelCase   ,					lowerCAmelCase   )
																# predict the noise residual
																UpperCAmelCase         =			self.unet(lowerCAmelCase   ,					lowerCAmelCase   ).sample
																# compute the previous noisy sample x_t -> x_t-1
																UpperCAmelCase         =			self.scheduler.step(lowerCAmelCase   ,					lowerCAmelCase   ,					lowerCAmelCase   ,					**lowerCAmelCase   ).prev_sample

										# decode the image latents with the VQVAE
										UpperCAmelCase         =			self.vqvae.decode(lowerCAmelCase   ).sample
										UpperCAmelCase         =			torch.clamp(lowerCAmelCase   ,					-1.0   ,					1.0   )
										UpperCAmelCase         =			image / 2 + 0.5
										UpperCAmelCase         =			image.cpu().permute(0   ,					2   ,					3   ,					1   ).numpy()

										if output_type == "pil":
																UpperCAmelCase         =			self.numpy_to_pil(lowerCAmelCase   )

										if not return_dict:
																return (image,)

										return ImagePipelineOutput(images=lowerCAmelCase   )









'''simple docstring'''



import heapq


def    lowerCamelCase__   ( A     :    dict  ):




						'''simple docstring'''






						UpperCAmelCase         =			[]

						# for each node and his adjacency list add them and the rank of the node to queue
						# using heapq module the queue will be filled like a Priority Queue
						# heapq works with a min priority queue, so I used -1*len(v) to build it
						for key, value in graph.items():
												# O(log(n))
												heapq.heappush(A   ,     [-1 * len(A  ), (key, value)]  )

						# chosen_vertices = set of chosen vertices
						UpperCAmelCase         =			set()

						# while queue isn't empty and there are still edges
						#   (queue[0][0] is the rank of the node with max rank)
						while queue and queue[0][0] != 0:
												# extract vertex with max rank from queue and add it to chosen_vertices
												UpperCAmelCase         =			heapq.heappop(A  )[1][0]
												chosen_vertices.add(A  )

												# Remove all arcs adjacent to argmax
												for elem in queue:
																		# if v haven't adjacent node, skip
																		if elem[0] == 0:
																								continue
																		# if argmax is reachable from elem
																		# remove argmax from elem's adjacent list and update his rank
																		if argmax in elem[1][1]:
																								UpperCAmelCase         =			elem[1][1].index(A  )
																								del elem[1][1][index]
																								elem[0] += 1
        # re-order the queue
												heapq.heapify(A  )
						return chosen_vertices


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	_lowercase    :    Optional[int]			     =  {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
	print(F"""Minimum vertex cover:\n{greedy_min_vertex_cover(graph)}""")





