# 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 __snake_case    (						lowerCamelCase_       ,		lowerCamelCase_		):
   lowerCAmelCase_														=							1




   @register_to_config
   def __init__(   self      :    Union[str, Any]	,     _lowercase      :    int=20_00	,     _lowercase      :    Optional[Any]=0.1	,     _lowercase      :    Any=20	,     _lowercase      :    Dict=1E-3				):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__      							=				None
     SCREAMING_SNAKE_CASE__      							=				None
     SCREAMING_SNAKE_CASE__      							=				None




   def      __a						(   self      :    Union[str, Any]	,     _lowercase      :    Any	,     _lowercase      :    Union[str, torch.device] = None				):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__      							=				torch.linspace(1	,     self.config.sampling_eps	,     _lowercase	,     device=_lowercase				)




   def      __a						(   self      :    Dict	,     _lowercase      :    Dict	,     _lowercase      :    Optional[int]	,     _lowercase      :    Any	,     _lowercase      :    Union[str, Any]=None				):



     """simple docstring"""






     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
     SCREAMING_SNAKE_CASE__      							=				(
         -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
     )
     SCREAMING_SNAKE_CASE__      							=				torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff				)				)
     SCREAMING_SNAKE_CASE__      							=				std.flatten()
     while len(std.shape				) < len(score.shape				):
       SCREAMING_SNAKE_CASE__      							=				std.unsqueeze(-1				)
     SCREAMING_SNAKE_CASE__      							=				-score / std

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

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

     SCREAMING_SNAKE_CASE__      							=				torch.sqrt(_lowercase				)
     SCREAMING_SNAKE_CASE__      							=				drift - diffusion**2 * score
     SCREAMING_SNAKE_CASE__      							=				x + drift * dt

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

     return x, x_mean




   def __len__(   self      :    int				):



     """simple docstring"""






     return self.config.num_train_timesteps

from __future__ import annotations

__lowerCamelCase      :			Tuple							       =		list[list[int]]

# assigning initial values to the grid
__lowerCamelCase      :			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
__lowerCamelCase      :			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      __SCREAMING_SNAKE_CASE  ( __UpperCamelCase   :	Matrix			,					__UpperCamelCase   :	int			,					__UpperCamelCase   :	int			,					__UpperCamelCase   :	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      __SCREAMING_SNAKE_CASE  ( __UpperCamelCase   :	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      __SCREAMING_SNAKE_CASE  ( __UpperCamelCase   :	Matrix     )							-> Matrix | None:







  """simple docstring"""





  if location := find_empty_location(__UpperCamelCase     ):
    SCREAMING_SNAKE_CASE__							,					SCREAMING_SNAKE_CASE__      							=				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     ):
      SCREAMING_SNAKE_CASE__      							=				digit

      if sudoku(__UpperCamelCase     ) is not None:
        return grid

      SCREAMING_SNAKE_CASE__      							=				0

  return None



def      __SCREAMING_SNAKE_CASE  ( __UpperCamelCase   :	Matrix     )							-> None:







  """simple docstring"""





  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      :			str							       =		sudoku(example_grid)
      if solution is not None:
         print_solution(solution)
      else:
         print('''Cannot find a solution.''')
