

# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
# and https://github.com/hojonathanho/diffusion
import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.schedulers.scheduling_utils import SchedulerMixin
from diffusers.utils import BaseOutput, deprecate


@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->DDIM
class       SCREAMING_SNAKE_CASE__					(__snake_case     ):
    __lowerCamelCase						:       int														=     42
    __lowerCamelCase						:       int														=     None



def 	snake_case__			(    SCREAMING_SNAKE_CASE_		:    Optional[Any]	,     SCREAMING_SNAKE_CASE_		:    Any=0.999	,     SCREAMING_SNAKE_CASE_		:    Dict="cosine"	,     ):



     '''simple docstring'''





     if alpha_transform_type == "cosine":

          def alpha_bar_fn(SCREAMING_SNAKE_CASE_		:    Optional[int]			):
               return math.cos((t + 0.008) / 1.008 * math.pi / 2			) ** 2

     elif alpha_transform_type == "exp":

          def alpha_bar_fn(SCREAMING_SNAKE_CASE_		:    Any			):
               return math.exp(t * -12.0			)

     else:
          raise ValueError(f"""Unsupported alpha_tranform_type: {alpha_transform_type}"""			)

     lowercase__    :   Any      =       []
     for i in range(SCREAMING_SNAKE_CASE_			):
          lowercase__    :   Optional[int]      =       i / num_diffusion_timesteps
          lowercase__    :   Any      =       (i + 1) / num_diffusion_timesteps
          betas.append(min(1 - alpha_bar_fn(SCREAMING_SNAKE_CASE_			) / alpha_bar_fn(SCREAMING_SNAKE_CASE_			)	,     SCREAMING_SNAKE_CASE_			)			)
     return torch.tensor(SCREAMING_SNAKE_CASE_	,     dtype=torch.floataa			)


class       SCREAMING_SNAKE_CASE__					(__snake_case		,       __snake_case     ):
    __lowerCamelCase						:       Tuple														=     1





    @register_to_config
    def __init__(      self						,   a = 1000						,   a = 0.0_001						,   a = 0.02						,   a = "linear"						,   a = None						,   a = True						,   a = True						,   a = 0						,   a = "epsilon"						,   a = 1.0						,   **a						,   ):

         if kwargs.get('set_alpha_to_one'						,   lowerCamelCase_) is not None:
              lowercase__    :   List[Any]      =       (
                  'The `set_alpha_to_one` argument is deprecated. Please use `set_alpha_to_zero` instead.'
              )
              deprecate('set_alpha_to_one'						,   '1.0.0'						,   lowerCamelCase_						,   standard_warn=lowerCamelCase_)
              lowercase__    :   Dict      =       kwargs['set_alpha_to_one']
         if trained_betas is not None:
              lowercase__    :   Union[str, Any]      =       torch.tensor(lowerCamelCase_						,   dtype=torch.floataa)
         elif beta_schedule == "linear":
              lowercase__    :   Dict      =       torch.linspace(lowerCamelCase_						,   lowerCamelCase_						,   lowerCamelCase_						,   dtype=torch.floataa)
         elif beta_schedule == "scaled_linear":
              # this schedule is very specific to the latent diffusion model.
              lowercase__    :   Tuple      =       (
                  torch.linspace(beta_start**0.5						,   beta_end**0.5						,   lowerCamelCase_						,   dtype=torch.floataa) ** 2
              )
         elif beta_schedule == "squaredcos_cap_v2":
              # Glide cosine schedule
              lowercase__    :   Optional[int]      =       betas_for_alpha_bar(lowerCamelCase_)
         else:
              raise NotImplementedError(f"""{beta_schedule} does is not implemented for {self.__class__}""")

         lowercase__    :   str      =       1.0 - self.betas
         lowercase__    :   Any      =       torch.cumprod(self.alphas						,   dim=0)

         # At every step in inverted ddim, we are looking into the next alphas_cumprod
         # For the final step, there is no next alphas_cumprod, and the index is out of bounds
         # `set_alpha_to_zero` decides whether we set this parameter simply to zero
         # in this case, self.step() just output the predicted noise
         # or whether we use the final alpha of the "non-previous" one.
         lowercase__    :   Any      =       torch.tensor(0.0) if set_alpha_to_zero else self.alphas_cumprod[-1]

         # standard deviation of the initial noise distribution
         lowercase__    :   str      =       1.0

         # setable values
         lowercase__    :   Optional[Any]      =       None
         lowercase__    :   str      =       torch.from_numpy(np.arange(0						,   lowerCamelCase_).copy().astype(np.intaa))





    def       snake_case_				(      self						,   a						,   a = None):
         return sample





    def       snake_case_				(      self						,   a						,   a = None):

         if num_inference_steps > self.config.num_train_timesteps:
              raise ValueError(
                  f"""`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:"""
                  f""" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle"""
                  f""" maximal {self.config.num_train_timesteps} timesteps.""")

         lowercase__    :   Optional[Any]      =       num_inference_steps
         lowercase__    :   List[Any]      =       self.config.num_train_timesteps // self.num_inference_steps
         # creates integer timesteps by multiplying by ratio
         # casting to int to avoid issues when num_inference_step is power of 3
         lowercase__    :   str      =       (np.arange(0						,   lowerCamelCase_) * step_ratio).round().copy().astype(np.intaa)
         lowercase__    :   Optional[Any]      =       torch.from_numpy(lowerCamelCase_).to(lowerCamelCase_)
         self.timesteps += self.config.steps_offset





    def       snake_case_				(      self						,   a						,   a						,   a						,   a = 0.0						,   a = False						,   a = None						,   a = True						,   ):
         lowercase__    :   Optional[Any]      =       timestep + self.config.num_train_timesteps // self.num_inference_steps

         # 2. compute alphas, betas
         # change original implementation to exactly match noise levels for analogous forward process
         lowercase__    :   int      =       self.alphas_cumprod[timestep]
         lowercase__    :   Union[str, Any]      =       (
             self.alphas_cumprod[prev_timestep]
             if prev_timestep < self.config.num_train_timesteps
             else self.final_alpha_cumprod
         )

         lowercase__    :   str      =       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
         if self.config.prediction_type == "epsilon":
              lowercase__    :   Tuple      =       (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
              lowercase__    :   Union[str, Any]      =       model_output
         elif self.config.prediction_type == "sample":
              lowercase__    :   Dict      =       model_output
              lowercase__    :   List[Any]      =       (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
         elif self.config.prediction_type == "v_prediction":
              lowercase__    :   Optional[int]      =       (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
              lowercase__    :   int      =       (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
         else:
              raise ValueError(
                  f"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"""
                  ' `v_prediction`')

         # 4. Clip or threshold "predicted x_0"
         if self.config.clip_sample:
              lowercase__    :   Optional[Any]      =       pred_original_sample.clamp(
                  -self.config.clip_sample_range						,   self.config.clip_sample_range)

         # 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
         lowercase__    :   str      =       (1 - alpha_prod_t_prev) ** 0.5 * pred_epsilon

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

         if not return_dict:
              return (prev_sample, pred_original_sample)
         return DDIMSchedulerOutput(prev_sample=lowerCamelCase_						,   pred_original_sample=lowerCamelCase_)





    def __len__(      self):
         return self.config.num_train_timesteps






from __future__ import annotations

_lowercase: Tuple      			=		list[list[int]]

# assigning initial values to the grid
_lowercase: Matrix      			=		[
    [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
_lowercase: Matrix      			=		[
    [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       :    Matrix ,     A       :    int ,     A       :    int ,     A       :    int       )		->       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       :    Matrix       )		->       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       )		->       Matrix | None:
					"""simple docstring"""





					if location := find_empty_location(A       ):
										a     ,				a					     =   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       ):
															a					     =   digit

															if sudoku(A       ) is not None:
																				return grid

															a					     =   0

					return None






def     a(      A       :    Matrix       )		->       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:")
								_lowercase: List[str]      			=		sudoku(example_grid)
								if solution is not None:
												print_solution(solution)
								else:
												print("Cannot find a solution.")
