


from __future__ import annotations
def 				UpperCAmelCase_					(							__snake_case     ,						__snake_case     ,						__snake_case     ,						__snake_case     ,						__snake_case     ,						)     ->			None:







 """simple docstring"""


 _lowercase							      =len(__snake_case						)

 # If row is equal to the size of the board it means there are a queen in each row in
 # the current board (possible_board)
 if row == n:
  # We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
  # this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
  boards.append(['''. ''' * i + '''Q ''' + '''. ''' * (n - 1 - i) for i in possible_board]						)
  return

 # We iterate each column in the row to find all possible results in each row
 for col in range(__snake_case						):
  # We apply that we learned previously. First we check that in the current board
  # (possible_board) there are not other same value because if there is it means
  # that there are a collision in vertical. Then we apply the two formulas we
  # learned before:
  #
  # 45º: y - x = b or 45: row - col = b
  # 135º: y + x = b or row + col = b.
  #
  # And we verify if the results of this two formulas not exist in their variables
  # respectively.  (diagonal_right_collisions, diagonal_left_collisions)
  #
  # If any or these are True it means there is a collision so we continue to the
  # next value in the for loop.
  if (
      col in possible_board
      or row - col in diagonal_right_collisions
      or row + col in diagonal_left_collisions
  ):
   continue

  # If it is False we call dfs function again and we update the inputs
  depth_first_search(
      [*possible_board, col]     ,						[*diagonal_right_collisions, row - col]     ,						[*diagonal_left_collisions, row + col]     ,						__snake_case     ,						__snake_case     ,						)
def 				UpperCAmelCase_					(							__snake_case						)     ->			None:







 """simple docstring"""


 _lowercase							      =[]
 depth_first_search([]     ,						[]     ,						[]     ,						__snake_case     ,						__snake_case						)

 # Print all the boards
 for board in boards:
  for column in board:
   print(__snake_case						)
  print(''''''						)

 print(len(__snake_case						)     ,						'''solutions were found.'''						)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  n_queens_solution(4)





# 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       lowerCamelCase__   (       lowerCAmelCase   ,							lowerCAmelCase):
     SCREAMING_SNAKE_CASE__      			=			1





     @register_to_config
     def __init__(self		,     UpperCAmelCase=2_0_0_0		,     UpperCAmelCase=0.1		,     UpperCAmelCase=2_0		,     UpperCAmelCase=1e-3       )     ->   List[str]:
      _lowercase							      =None
      _lowercase							      =None
      _lowercase							      =None





     def      __A					(self		,     UpperCAmelCase		,     UpperCAmelCase = None       )     ->   str:
      _lowercase							      =torch.linspace(1		,     self.config.sampling_eps		,     UpperCAmelCase		,     device=UpperCAmelCase       )





     def      __A					(self		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase=None       )     ->   Optional[int]:
      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
      _lowercase							      =(
          -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
      )
      _lowercase							      =torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff       )       )
      _lowercase							      =std.flatten()
      while len(std.shape       ) < len(score.shape       ):
       _lowercase							      =std.unsqueeze(-1       )
      _lowercase							      =-score / std

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

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

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

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

      return x, x_mean





     def __len__(self       )     ->   str:
      return self.config.num_train_timesteps

