




# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

import math
from typing import Union

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import randn_tensor
from .scheduling_utils import SchedulerMixin



class       a					(       _A     ,       _A      ):

     '''simple docstring'''





     lowerCAmelCase    :	Dict 		=  1
     @register_to_config
     def __init__(     self       :      List[Any] ,   __snake_case       :      List[Any]=20_00 ,   __snake_case       :      Tuple=0.1 ,   __snake_case       :      Union[str, Any]=20 ,   __snake_case       :      Dict=1E-3    ):
         UpperCAmelCase_										=					None
         UpperCAmelCase_										=					None
         UpperCAmelCase_										=					None
     def   lowerCamelCase_       (     self       :      Optional[int] ,   __snake_case       :      Optional[int] ,   __snake_case       :      Union[str, torch.device] = None    ):
         UpperCAmelCase_										=					torch.linspace(1 ,   self.config.sampling_eps ,   __snake_case ,   device=__snake_case    )
     def   lowerCamelCase_       (     self       :      Any ,   __snake_case       :      Union[str, Any] ,   __snake_case       :      Union[str, Any] ,   __snake_case       :      Dict ,   __snake_case       :      List[Any]=None    ):
         if self.timesteps is None:
             raise ValueError(
                 '''`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler'''    )

         # TODO(Patrick) better comments + non-PyTorch
         # postprocess model score
         UpperCAmelCase_										=					(
             -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
         )
         UpperCAmelCase_										=					torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff    )    )
         UpperCAmelCase_										=					std.flatten()
         while len(std.shape    ) < len(score.shape    ):
             UpperCAmelCase_										=					std.unsqueeze(-1    )
         UpperCAmelCase_										=					-score / std

         # compute
         UpperCAmelCase_										=					-1.0 / len(self.timesteps    )

         UpperCAmelCase_										=					self.config.beta_min + t * (self.config.beta_max - self.config.beta_min)
         UpperCAmelCase_										=					beta_t.flatten()
         while len(beta_t.shape    ) < len(x.shape    ):
             UpperCAmelCase_										=					beta_t.unsqueeze(-1    )
         UpperCAmelCase_										=					-0.5 * beta_t * x

         UpperCAmelCase_										=					torch.sqrt(__snake_case    )
         UpperCAmelCase_										=					drift - diffusion**2 * score
         UpperCAmelCase_										=					x + drift * dt

         # add noise
         UpperCAmelCase_										=					randn_tensor(x.shape ,   layout=x.layout ,   generator=__snake_case ,   device=x.device ,   dtype=x.dtype    )
         UpperCAmelCase_										=					x_mean + diffusion * math.sqrt(-dt    ) * noise

         return x, x_mean




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











from __future__ import annotations

_lowerCamelCase      			=						list[list[int]]

# assigning initial values to the grid
_lowerCamelCase      			=						[
    [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
_lowerCamelCase      			=						[
    [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  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						Matrix	,					__UpperCamelCase      :						int	,					__UpperCamelCase      :						int	,					__UpperCamelCase      :						int				)  ->							bool:
    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  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						Matrix				)  ->							tuple[int, int] | None:
    for i in range(9				):
        for j in range(9				):
            if grid[i][j] == 0:
                return i, j
    return None




def  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						Matrix				)  ->							Matrix | None:
    if location := find_empty_location(__UpperCamelCase				):
        UpperCAmelCase_			,							UpperCAmelCase_										=					location
    else:
        # If the location is ``None``, then the grid is solved.
        return grid

    for digit in range(1	,					10				):
        if is_safe(__UpperCamelCase	,					__UpperCamelCase	,					__UpperCamelCase	,					__UpperCamelCase				):
            UpperCAmelCase_										=					digit

            if sudoku(__UpperCamelCase				) is not None:
                return grid

            UpperCAmelCase_										=					0

    return None




def  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						Matrix				)  ->							None:
    for row in grid:
        for cell in row:
            print(__UpperCamelCase	,					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:')
  _lowerCamelCase      			=						sudoku(example_grid)
  if solution is not None:
   print_solution(solution)
  else:
   print('Cannot find a solution.')





