



from typing import Optional, Tuple, Union

import torch
from einops import rearrange, reduce

from diffusers import DDIMScheduler, DDPMScheduler, DiffusionPipeline, ImagePipelineOutput, UNetaDConditionModel
from diffusers.schedulers.scheduling_ddim import DDIMSchedulerOutput
from diffusers.schedulers.scheduling_ddpm import DDPMSchedulerOutput


__A       =						8



def 	__a					(   lowerCAmelCase_       : Any      ,lowerCAmelCase_       : Any=BITS    )				->			Optional[Any]:






						'''simple docstring'''



						UpperCAmelCase_=       x.device

						UpperCAmelCase_=       (x * 2_55).int().clamp(0      ,2_55    )

						UpperCAmelCase_=       2 ** torch.arange(bits - 1      ,-1      ,-1      ,device=lowerCAmelCase_    )
						UpperCAmelCase_=       rearrange(lowerCAmelCase_      ,"""d -> d 1 1"""    )
						UpperCAmelCase_=       rearrange(lowerCAmelCase_      ,"""b c h w -> b c 1 h w"""    )

						UpperCAmelCase_=       ((x & mask) != 0).float()
						UpperCAmelCase_=       rearrange(lowerCAmelCase_      ,"""b c d h w -> b (c d) h w"""    )
						UpperCAmelCase_=       bits * 2 - 1
						return bits



def 	__a					(   lowerCAmelCase_       : Tuple      ,lowerCAmelCase_       : List[Any]=BITS    )				->			str:






						'''simple docstring'''



						UpperCAmelCase_=       x.device

						UpperCAmelCase_=       (x > 0).int()
						UpperCAmelCase_=       2 ** torch.arange(bits - 1      ,-1      ,-1      ,device=lowerCAmelCase_      ,dtype=torch.intaa    )

						UpperCAmelCase_=       rearrange(lowerCAmelCase_      ,"""d -> d 1 1"""    )
						UpperCAmelCase_=       rearrange(lowerCAmelCase_      ,"""b (c d) h w -> b c d h w"""      ,d=8    )
						UpperCAmelCase_=       reduce(x * mask      ,"""b c d h w -> b c h w"""      ,"""sum"""    )
						return (dec / 2_55).clamp(0.0      ,1.0    )



def 	__a					(   self       : Dict      ,lowerCAmelCase_       : torch.FloatTensor      ,lowerCAmelCase_       : int      ,lowerCAmelCase_       : torch.FloatTensor      ,lowerCAmelCase_       : float = 0.0      ,lowerCAmelCase_       : bool = True      ,lowerCAmelCase_       : Optional[int]=None      ,lowerCAmelCase_       : bool = True      ,)				->			Union[DDIMSchedulerOutput, Tuple]:






						'''simple docstring'''



						if self.num_inference_steps is None:
												raise ValueError(
												    """Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"""    )

						# See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
						# Ideally, read DDIM paper in-detail understanding

						# Notation (<variable name> -> <name in paper>
						# - pred_noise_t -> e_theta(x_t, t)
						# - pred_original_sample -> f_theta(x_t, t) or x_0
						# - std_dev_t -> sigma_t
						# - eta -> η
						# - pred_sample_direction -> "direction pointing to x_t"
						# - pred_prev_sample -> "x_t-1"

						# 1. get previous step value (=t-1)
						UpperCAmelCase_=       timestep - self.config.num_train_timesteps // self.num_inference_steps

						# 2. compute alphas, betas
						UpperCAmelCase_=       self.alphas_cumprod[timestep]
						UpperCAmelCase_=       self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod

						UpperCAmelCase_=       1 - alpha_prod_t

						# 3. compute predicted original sample from predicted noise also called
						# "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
						UpperCAmelCase_=       (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5

						# 4. Clip "predicted x_0"
						UpperCAmelCase_=       self.bit_scale
						if self.config.clip_sample:
												UpperCAmelCase_=       torch.clamp(lowerCAmelCase_      ,-scale      ,lowerCAmelCase_    )

						# 5. compute variance: "sigma_t(η)" -> see formula (16)
						# σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
						UpperCAmelCase_=       self._get_variance(lowerCAmelCase_      ,lowerCAmelCase_    )
						UpperCAmelCase_=       eta * variance ** 0.5

						if use_clipped_model_output:
												# the model_output is always re-derived from the clipped x_0 in Glide
												UpperCAmelCase_=       (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5

						# 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
						UpperCAmelCase_=       (1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * model_output

						# 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
						UpperCAmelCase_=       alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

						if eta > 0:
												# randn_like does not support generator https://github.com/pytorch/pytorch/issues/27072
												UpperCAmelCase_=       model_output.device if torch.is_tensor(lowerCAmelCase_    ) else """cpu"""
												UpperCAmelCase_=       torch.randn(model_output.shape      ,dtype=model_output.dtype      ,generator=lowerCAmelCase_    ).to(lowerCAmelCase_    )
												UpperCAmelCase_=       self._get_variance(lowerCAmelCase_      ,lowerCAmelCase_    ) ** 0.5 * eta * noise

												UpperCAmelCase_=       prev_sample + variance

						if not return_dict:
												return (prev_sample,)

						return DDIMSchedulerOutput(prev_sample=lowerCAmelCase_      ,pred_original_sample=lowerCAmelCase_    )



def 	__a					(   self       : Dict      ,lowerCAmelCase_       : torch.FloatTensor      ,lowerCAmelCase_       : int      ,lowerCAmelCase_       : torch.FloatTensor      ,lowerCAmelCase_       : Any="epsilon"      ,lowerCAmelCase_       : Tuple=None      ,lowerCAmelCase_       : bool = True      ,)				->			Union[DDPMSchedulerOutput, Tuple]:






						'''simple docstring'''



						UpperCAmelCase_=       timestep

						if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type in ["learned", "learned_range"]:
												UpperCAmelCase_,       UpperCAmelCase_=       torch.split(lowerCAmelCase_      ,sample.shape[1]      ,dim=1    )
						else:
												UpperCAmelCase_=       None

						# 1. compute alphas, betas
						UpperCAmelCase_=       self.alphas_cumprod[t]
						UpperCAmelCase_=       self.alphas_cumprod[t - 1] if t > 0 else self.one
						UpperCAmelCase_=       1 - alpha_prod_t
						UpperCAmelCase_=       1 - alpha_prod_t_prev

						# 2. compute predicted original sample from predicted noise also called
						# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
						if prediction_type == "epsilon":
												UpperCAmelCase_=       (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
						elif prediction_type == "sample":
												UpperCAmelCase_=       model_output
						else:
												raise ValueError(F"""Unsupported prediction_type {prediction_type}."""    )

						# 3. Clip "predicted x_0"
						UpperCAmelCase_=       self.bit_scale
						if self.config.clip_sample:
												UpperCAmelCase_=       torch.clamp(lowerCAmelCase_      ,-scale      ,lowerCAmelCase_    )

						# 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
						# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
						UpperCAmelCase_=       (alpha_prod_t_prev ** 0.5 * self.betas[t]) / beta_prod_t
						UpperCAmelCase_=       self.alphas[t] ** 0.5 * beta_prod_t_prev / beta_prod_t

						# 5. Compute predicted previous sample µ_t
						# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
						UpperCAmelCase_=       pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

						# 6. Add noise
						UpperCAmelCase_=       0
						if t > 0:
												UpperCAmelCase_=       torch.randn(
												    model_output.size()      ,dtype=model_output.dtype      ,layout=model_output.layout      ,generator=lowerCAmelCase_    ).to(model_output.device    )
												UpperCAmelCase_=       (self._get_variance(lowerCAmelCase_      ,predicted_variance=lowerCAmelCase_    ) ** 0.5) * noise

						UpperCAmelCase_=       pred_prev_sample + variance

						if not return_dict:
												return (pred_prev_sample,)

						return DDPMSchedulerOutput(prev_sample=lowerCAmelCase_      ,pred_original_sample=lowerCAmelCase_    )






class 		lowercase						(			snake_case__):






	"""simple docstring"""


	def __init__(     self     :						str						,  __UpperCAmelCase     :						UNetaDConditionModel						,  __UpperCAmelCase     :						Union[DDIMScheduler, DDPMScheduler]						,  __UpperCAmelCase     :						Optional[float] = 1.0						,  )      ->			int:
							super().__init__()
							UpperCAmelCase_=       bit_scale
							UpperCAmelCase_=       (
							    ddim_bit_scheduler_step if isinstance(__UpperCAmelCase						,  __UpperCAmelCase					) else ddpm_bit_scheduler_step
							)

							self.register_modules(unet=__UpperCAmelCase						,  scheduler=__UpperCAmelCase					)




	@torch.no_grad()
	def __call__(     self     :						Any						,  __UpperCAmelCase     :						Optional[int] = 256						,  __UpperCAmelCase     :						Optional[int] = 256						,  __UpperCAmelCase     :						Optional[int] = 50						,  __UpperCAmelCase     :						Optional[torch.Generator] = None						,  __UpperCAmelCase     :						Optional[int] = 1						,  __UpperCAmelCase     :						Optional[str] = "pil"						,  __UpperCAmelCase     :						bool = True						,  **__UpperCAmelCase     :						List[Any]						,  )      ->			Union[Tuple, ImagePipelineOutput]:
							UpperCAmelCase_=       torch.randn(
							    (batch_size, self.unet.config.in_channels, height, width)						,  generator=__UpperCAmelCase						,  )
							UpperCAmelCase_=       decimal_to_bits(__UpperCAmelCase					) * self.bit_scale
							UpperCAmelCase_=       latents.to(self.device					)

							self.scheduler.set_timesteps(__UpperCAmelCase					)

							for t in self.progress_bar(self.scheduler.timesteps					):
													# predict the noise residual
													UpperCAmelCase_=       self.unet(__UpperCAmelCase						,  __UpperCAmelCase					).sample

													# compute the previous noisy sample x_t -> x_t-1
													UpperCAmelCase_=       self.scheduler.step(__UpperCAmelCase						,  __UpperCAmelCase						,  __UpperCAmelCase					).prev_sample

							UpperCAmelCase_=       bits_to_decimal(__UpperCAmelCase					)

							if output_type == "pil":
													UpperCAmelCase_=       self.numpy_to_pil(__UpperCAmelCase					)

							if not return_dict:
													return (image,)

							return ImagePipelineOutput(images=__UpperCAmelCase					)









def 	__a					(   lowerCAmelCase_       : Dict    )				->			Dict:






						'''simple docstring'''



						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 	__a					(   lowerCAmelCase_       : dict[int, list[int]]    )				->			list[tuple[int, int]]:






						'''simple docstring'''



						UpperCAmelCase_=       0
						UpperCAmelCase_=       len(lowerCAmelCase_    )  # No of vertices in graph
						UpperCAmelCase_=       [0] * n
						UpperCAmelCase_=       [False] * n

						def dfs(lowerCAmelCase_       : Optional[int]      ,lowerCAmelCase_       : Dict      ,lowerCAmelCase_       : Any      ,lowerCAmelCase_       : int    ):
												UpperCAmelCase_=       True
												UpperCAmelCase_=       id_
												id_ += 1
												for to in graph[at]:
																		if to == parent:
																								pass
																		elif not visited[to]:
																								dfs(lowerCAmelCase_      ,lowerCAmelCase_      ,lowerCAmelCase_      ,id_    )
																								UpperCAmelCase_=       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
																								UpperCAmelCase_=       min(low[at]      ,low[to]    )

						UpperCAmelCase_=       []
						for i in range(lowerCAmelCase_    ):
												if not visited[i]:
																		dfs(lowerCAmelCase_      ,-1      ,lowerCAmelCase_      ,id_    )
						return bridges


if __name__ == "__main__":
	import doctest

	doctest.testmod()




