


'''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											=					8


def       a				(      __a			, __a=BITS       )  ->     Any:



					'''simple docstring'''






					UpperCamelCase__       :List[str]							 =			x.device

					UpperCamelCase__       :Any							 =			(x * 255).int().clamp(0			, 255       )

					UpperCamelCase__       :str							 =			2 ** torch.arange(bits - 1			, -1			, -1			, device=UpperCAmelCase_       )
					UpperCamelCase__       :str							 =			rearrange(UpperCAmelCase_			, '''d -> d 1 1'''       )
					UpperCamelCase__       :int							 =			rearrange(UpperCAmelCase_			, '''b c h w -> b c 1 h w'''       )

					UpperCamelCase__       :List[str]							 =			((x & mask) != 0).float()
					UpperCamelCase__       :int							 =			rearrange(UpperCAmelCase_			, '''b c d h w -> b (c d) h w'''       )
					UpperCamelCase__       :Optional[int]							 =			bits * 2 - 1
					return bits


def       a				(      __a			, __a=BITS       )  ->     Any:



					'''simple docstring'''






					UpperCamelCase__       :Optional[int]							 =			x.device

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

					UpperCamelCase__       :int							 =			rearrange(UpperCAmelCase_			, '''d -> d 1 1'''       )
					UpperCamelCase__       :str							 =			rearrange(UpperCAmelCase_			, '''b (c d) h w -> b c d h w'''			, d=8       )
					UpperCamelCase__       :Tuple							 =			reduce(x * mask			, '''b c d h w -> b c h w'''			, '''sum'''       )
					return (dec / 255).clamp(0.0			, 1.0       )


def       a				(      self			, __a			, __a			, __a			, __a = 0.0			, __a = True			, __a=None			, __a = True			, )  ->     Dict:



					'''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__       :Any							 =			timestep - self.config.num_train_timesteps // self.num_inference_steps

					# 2. compute alphas, betas
					UpperCamelCase__       :Optional[Any]							 =			self.alphas_cumprod[timestep]
					UpperCamelCase__       :Tuple							 =			self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod

					UpperCamelCase__       :List[Any]							 =			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__       :Optional[Any]							 =			(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5

					# 4. Clip "predicted x_0"
					UpperCamelCase__       :int							 =			self.bit_scale
					if self.config.clip_sample:
										UpperCamelCase__       :str							 =			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)
					UpperCamelCase__       :Any							 =			self._get_variance(UpperCAmelCase_			, UpperCAmelCase_       )
					UpperCamelCase__       :Optional[int]							 =			eta * variance ** 0.5

					if use_clipped_model_output:
										# the model_output is always re-derived from the clipped x_0 in Glide
										UpperCamelCase__       :Any							 =			(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__       :List[Any]							 =			(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__       :Dict							 =			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__       :Any							 =			model_output.device if torch.is_tensor(UpperCAmelCase_       ) else '''cpu'''
										UpperCamelCase__       :Tuple							 =			torch.randn(model_output.shape			, dtype=model_output.dtype			, generator=UpperCAmelCase_       ).to(UpperCAmelCase_       )
										UpperCamelCase__       :Optional[Any]							 =			self._get_variance(UpperCAmelCase_			, UpperCAmelCase_       ) ** 0.5 * eta * noise

										UpperCamelCase__       :Optional[int]							 =			prev_sample + variance

					if not return_dict:
										return (prev_sample,)

					return DDIMSchedulerOutput(prev_sample=UpperCAmelCase_			, pred_original_sample=UpperCAmelCase_       )


def       a				(      self			, __a			, __a			, __a			, __a="epsilon"			, __a=None			, __a = True			, )  ->     Union[str, Any]:



					'''simple docstring'''






					UpperCamelCase__       :List[str]							 =			timestep

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

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

					# 3. Clip "predicted x_0"
					UpperCamelCase__       :int							 =			self.bit_scale
					if self.config.clip_sample:
										UpperCamelCase__       :List[str]							 =			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
					UpperCamelCase__       :Optional[int]							 =			(alpha_prod_t_prev ** 0.5 * self.betas[t]) / beta_prod_t
					UpperCamelCase__       :Dict							 =			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__       :Dict							 =			pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

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

					UpperCamelCase__       :Optional[int]							 =			pred_prev_sample + variance

					if not return_dict:
										return (pred_prev_sample,)

					return DDPMSchedulerOutput(prev_sample=UpperCAmelCase_			, pred_original_sample=UpperCAmelCase_       )







class        lowercase     (							_lowerCamelCase ):

		"""simple docstring"""

		def __init__(		self   ,       UpperCamelCase_   ,       UpperCamelCase_   ,       UpperCamelCase_ = 1.0   ,       ):

							'''simple docstring'''


							super().__init__()
							UpperCamelCase__       :Dict							 =			bit_scale
							UpperCamelCase__       :str							 =			(
							    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   ,       UpperCamelCase_ = 256   ,       UpperCamelCase_ = 256   ,       UpperCamelCase_ = 50   ,       UpperCamelCase_ = None   ,       UpperCamelCase_ = 1   ,       UpperCamelCase_ = "pil"   ,       UpperCamelCase_ = True   ,       **UpperCamelCase_   ,       ):

							'''simple docstring'''


							UpperCamelCase__       :Optional[int]							 =			torch.randn(
							    (batch_size, self.unet.config.in_channels, height, width)   ,       generator=UpperCamelCase_   ,       )
							UpperCamelCase__       :Dict							 =			decimal_to_bits(UpperCamelCase_							) * self.bit_scale
							UpperCamelCase__       :Optional[int]							 =			latents.to(self.device							)

							self.scheduler.set_timesteps(UpperCamelCase_							)

							for t in self.progress_bar(self.scheduler.timesteps							):
												# predict the noise residual
												UpperCamelCase__       :List[Any]							 =			self.unet(UpperCamelCase_   ,       UpperCamelCase_							).sample

												# compute the previous noisy sample x_t -> x_t-1
												UpperCamelCase__       :str							 =			self.scheduler.step(UpperCamelCase_   ,       UpperCamelCase_   ,       UpperCamelCase_							).prev_sample

							UpperCamelCase__       :Optional[Any]							 =			bits_to_decimal(UpperCamelCase_							)

							if output_type == "pil":
												UpperCamelCase__       :List[Any]							 =			self.numpy_to_pil(UpperCamelCase_							)

							if not return_dict:
												return (image,)

							return ImagePipelineOutput(images=UpperCamelCase_							)



'''simple docstring'''
from __future__ import annotations

__snake_case											=					list[list[int]]

# assigning initial values to the grid
__snake_case											=					[
    [3, 0, 6, 5, 0, 8, 4, 0, 0],
    [5, 2, 0, 0, 0, 0, 0, 0, 0],
    [0, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]

# a grid with no solution
__snake_case											=					[
    [5, 0, 6, 5, 0, 8, 4, 0, 3],
    [5, 2, 0, 0, 0, 0, 0, 0, 2],
    [1, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]


def       a				(      __a			, __a			, __a			, __a       )  ->     bool:



					'''simple docstring'''






					for i in range(9       ):
										if grid[row][i] == n or grid[i][column] == n:
															return False

					for i in range(3       ):
										for j in range(3       ):
															if grid[(row - row % 3) + i][(column - column % 3) + j] == n:
																				return False

					return True


def       a				(      __a       )  ->     tuple[int, int] | None:



					'''simple docstring'''






					for i in range(9       ):
										for j in range(9       ):
															if grid[i][j] == 0:
																				return i, j
					return None


def       a				(      __a       )  ->     Matrix | None:



					'''simple docstring'''






					if location := find_empty_location(__a       ):
										UpperCamelCase__ ,    UpperCamelCase__       :Optional[int]							 =			location
					else:
										# If the location is ``None``, then the grid is solved.
										return grid

					for digit in range(1			, 10       ):
										if is_safe(__a			, __a			, __a			, __a       ):
															UpperCamelCase__       :Tuple							 =			digit

															if sudoku(__a       ) is not None:
																				return grid

															UpperCamelCase__       :Union[str, Any]							 =			0

					return None


def       a				(      __a       )  ->     None:



					'''simple docstring'''






					for row in grid:
										for cell in row:
															print(__a			, end=''' '''       )
										print()


if __name__ == "__main__":
		# make a copy of grid so that you can compare with the unmodified grid
		for example_grid in (initial_grid, no_solution):
				print('''\nExample grid:\n''' + '''=''' * 20)
				print_solution(example_grid)
				print('''\nExample grid solution:''')
				__snake_case											=					sudoku(example_grid)
				if solution is not None:
						print_solution(solution)
				else:
						print('''Cannot find a solution.''')