



'''simple docstring'''





from collections import defaultdict

from graphs.minimum_spanning_tree_prims import prisms_algorithm as mst




def lowerCAmelCase    ():



     """simple docstring"""



     _a    ,       _a           =    9, 14  # noqa: F841
     _a           =    [
         [0, 1, 4],
         [0, 7, 8],
         [1, 2, 8],
         [7, 8, 7],
         [7, 6, 1],
         [2, 8, 2],
         [8, 6, 6],
         [2, 3, 7],
         [2, 5, 4],
         [6, 5, 2],
         [3, 5, 14],
         [3, 4, 9],
         [5, 4, 10],
         [1, 7, 11],
     ]

     _a           =    defaultdict(__A)
     for nodea, nodea, cost in edges:
          adjancency[nodea].append([nodea, cost])
          adjancency[nodea].append([nodea, cost])

     _a           =    mst(__A)

     _a           =    [
         [7, 6, 1],
         [2, 8, 2],
         [6, 5, 2],
         [0, 1, 4],
         [2, 5, 4],
         [2, 3, 7],
         [0, 7, 8],
         [3, 4, 9],
     ]

     for answer in expected:
          _a           =    tuple(answer[:2])
          _a           =    tuple(edge[::-1])
          assert edge in result or reverse in result









'''simple docstring'''


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


_snake_case : Optional[Any]  				=						8
def 						snake_case_       (UpperCamelCase			:    List[Any]					,		UpperCamelCase			:    Dict=BITS ):





							'''simple docstring'''


							_a      	=							x.device

							_a      	=							(x * 255).int().clamp(0					,		255 )

							_a      	=							2 ** torch.arange(bits - 1					,		-1					,		-1					,		device=UpperCamelCase )
							_a      	=							rearrange(UpperCamelCase					,		'''d -> d 1 1''' )
							_a      	=							rearrange(UpperCamelCase					,		'''b c h w -> b c 1 h w''' )

							_a      	=							((x & mask) != 0).float()
							_a      	=							rearrange(UpperCamelCase					,		'''b c d h w -> b (c d) h w''' )
							_a      	=							bits * 2 - 1
							return bits
def 						snake_case_       (UpperCamelCase			:    List[Any]					,		UpperCamelCase			:    Any=BITS ):





							'''simple docstring'''


							_a      	=							x.device

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

							_a      	=							rearrange(UpperCamelCase					,		'''d -> d 1 1''' )
							_a      	=							rearrange(UpperCamelCase					,		'''b (c d) h w -> b c d h w'''					,		d=8 )
							_a      	=							reduce(x * mask					,		'''b c d h w -> b c h w'''					,		'''sum''' )
							return (dec / 255).clamp(0.0					,		1.0 )
def 						snake_case_       (self			:    Union[str, Any]					,		UpperCamelCase			:    torch.FloatTensor					,		UpperCamelCase			:    int					,		UpperCamelCase			:    torch.FloatTensor					,		UpperCamelCase			:    float = 0.0					,		UpperCamelCase			:    bool = True					,		UpperCamelCase			:    Any=None					,		UpperCamelCase			:    bool = True					,		):





							'''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)
							_a      	=							timestep - self.config.num_train_timesteps // self.num_inference_steps

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

							_a      	=							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
							_a      	=							(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5

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

							# 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)
							_a      	=							self._get_variance(UpperCamelCase					,		UpperCamelCase )
							_a      	=							eta * variance ** 0.5

							if use_clipped_model_output:
														# the model_output is always re-derived from the clipped x_0 in Glide
														_a      	=							(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
							_a      	=							(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
							_a      	=							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
														_a      	=							model_output.device if torch.is_tensor(UpperCamelCase ) else '''cpu'''
														_a      	=							torch.randn(model_output.shape					,		dtype=model_output.dtype					,		generator=UpperCamelCase ).to(UpperCamelCase )
														_a      	=							self._get_variance(UpperCamelCase					,		UpperCamelCase ) ** 0.5 * eta * noise

														_a      	=							prev_sample + variance

							if not return_dict:
														return (prev_sample,)

							return DDIMSchedulerOutput(prev_sample=UpperCamelCase					,		pred_original_sample=UpperCamelCase )
def 						snake_case_       (self			:    Any					,		UpperCamelCase			:    torch.FloatTensor					,		UpperCamelCase			:    int					,		UpperCamelCase			:    torch.FloatTensor					,		UpperCamelCase			:    str="epsilon"					,		UpperCamelCase			:    Dict=None					,		UpperCamelCase			:    bool = True					,		):





							'''simple docstring'''


							_a      	=							timestep

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

							# 1. compute alphas, betas
							_a      	=							self.alphas_cumprod[t]
							_a      	=							self.alphas_cumprod[t - 1] if t > 0 else self.one
							_a      	=							1 - alpha_prod_t
							_a      	=							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":
														_a      	=							(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
							elif prediction_type == "sample":
														_a      	=							model_output
							else:
														raise ValueError(f'Unsupported prediction_type {prediction_type}.' )

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

							# 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
							_a      	=							(alpha_prod_t_prev ** 0.5 * self.betas[t]) / beta_prod_t
							_a      	=							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
							_a      	=							pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

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

							_a      	=							pred_prev_sample + variance

							if not return_dict:
														return (pred_prev_sample,)

							return DDPMSchedulerOutput(prev_sample=UpperCamelCase					,		pred_original_sample=UpperCamelCase )

class      A       (						_a       ):







							def __init__(    self			:    Any				,     lowerCAmelCase_			:    UNetaDConditionModel				,     lowerCAmelCase_			:    Union[DDIMScheduler, DDPMScheduler]				,     lowerCAmelCase_			:    Optional[float] = 1.0				,     )     ->				int:


														"""simple docstring"""


														super().__init__()
														_a      	=							bit_scale
														_a      	=							(
														    ddim_bit_scheduler_step if isinstance(lowerCAmelCase_				,     lowerCAmelCase_   ) else ddpm_bit_scheduler_step
														)

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







							@torch.no_grad()
							def __call__(    self			:    List[Any]				,     lowerCAmelCase_			:    Optional[int] = 2_56				,     lowerCAmelCase_			:    Optional[int] = 2_56				,     lowerCAmelCase_			:    Optional[int] = 50				,     lowerCAmelCase_			:    Optional[torch.Generator] = None				,     lowerCAmelCase_			:    Optional[int] = 1				,     lowerCAmelCase_			:    Optional[str] = "pil"				,     lowerCAmelCase_			:    bool = True				,     **lowerCAmelCase_			:    Any				,     )     ->				Union[Tuple, ImagePipelineOutput]:


														"""simple docstring"""


														_a      	=							torch.randn(
														    (batch_size, self.unet.config.in_channels, height, width)				,     generator=lowerCAmelCase_				,     )
														_a      	=							decimal_to_bits(lowerCAmelCase_   ) * self.bit_scale
														_a      	=							latents.to(self.device   )

														self.scheduler.set_timesteps(lowerCAmelCase_   )

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

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

														_a      	=							bits_to_decimal(lowerCAmelCase_   )

														if output_type == "pil":
																					_a      	=							self.numpy_to_pil(lowerCAmelCase_   )

														if not return_dict:
																					return (image,)

														return ImagePipelineOutput(images=lowerCAmelCase_   )

