






from __future__ import annotations







def       lowercase__	(					A_:						list[int]  ,      A_:						list[int]  ,      A_:						list[int]  ,      A_:						list[list[str]]  ,      A_:						int  ,      )	->				None:







       """simple docstring"""






       __UpperCAmelCase     				=len(A_		)

       # 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(A_		):
              # 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]  ,      A_  ,      A_  ,      )







def       lowercase__	(					A_:						int		)	->				None:







       """simple docstring"""






       __UpperCAmelCase     				=[]
       depth_first_search([]  ,      []  ,      []  ,      A_  ,      A_		)

       # Print all the boards
       for board in boards:
              for column in board:
                     print(A_		)
              print(""""""		)

       print(len(A_		)  ,      """solutions were found."""		)


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   n_queens_solution(4)






import unittest

import numpy as np
import torch

from diffusers import PNDMPipeline, PNDMScheduler, UNetaDModel
from diffusers.utils.testing_utils import enable_full_determinism, require_torch, slow, torch_device


enable_full_determinism()







class 							lowerCAmelCase__   ( unittest.TestCase						):

						@property
						def 			A_					(      self					)       ->   int:


								'''simple docstring'''

								torch.manual_seed(0					)
								_UpperCamelCase         =						UNetaDModel(
								    block_out_channels=(32, 64)							,				layers_per_block=2							,				sample_size=32							,				in_channels=3							,				out_channels=3							,				down_block_types=("""DownBlock2D""", """AttnDownBlock2D""")							,				up_block_types=("""AttnUpBlock2D""", """UpBlock2D""")							,				)
								return model







						def 			A_					(      self					)       ->   Any:


								'''simple docstring'''

								_UpperCamelCase         =						self.dummy_uncond_unet
								_UpperCamelCase         =						PNDMScheduler()

								_UpperCamelCase         =						PNDMPipeline(unet=a							,				scheduler=a					)
								pndm.to(a					)
								pndm.set_progress_bar_config(disable=a					)

								_UpperCamelCase         =						torch.manual_seed(0					)
								_UpperCamelCase         =						pndm(generator=a							,				num_inference_steps=20							,				output_type="""numpy"""					).images

								_UpperCamelCase         =						torch.manual_seed(0					)
								_UpperCamelCase         =						pndm(generator=a							,				num_inference_steps=20							,				output_type="""numpy"""							,				return_dict=a					)[0]

								_UpperCamelCase         =						image[0, -3:, -3:, -1]
								_UpperCamelCase         =						image_from_tuple[0, -3:, -3:, -1]

								assert image.shape == (1, 32, 32, 3)
								_UpperCamelCase         =						np.array([1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0]					)

								assert np.abs(image_slice.flatten() - expected_slice					).max() < 1e-2
								assert np.abs(image_from_tuple_slice.flatten() - expected_slice					).max() < 1e-2







@slow
@require_torch
class 							lowerCAmelCase__   ( unittest.TestCase						):

						def 			A_					(      self					)       ->   Optional[Any]:


								'''simple docstring'''

								_UpperCamelCase         =						"""google/ddpm-cifar10-32"""

								_UpperCamelCase         =						UNetaDModel.from_pretrained(a					)
								_UpperCamelCase         =						PNDMScheduler()

								_UpperCamelCase         =						PNDMPipeline(unet=a							,				scheduler=a					)
								pndm.to(a					)
								pndm.set_progress_bar_config(disable=a					)
								_UpperCamelCase         =						torch.manual_seed(0					)
								_UpperCamelCase         =						pndm(generator=a							,				output_type="""numpy"""					).images

								_UpperCamelCase         =						image[0, -3:, -3:, -1]

								assert image.shape == (1, 32, 32, 3)
								_UpperCamelCase         =						np.array([0.1564, 0.1_4645, 0.1406, 0.1_4715, 0.1_2425, 0.1_4045, 0.1_3115, 0.1_2175, 0.125]					)

								assert np.abs(image_slice.flatten() - expected_slice					).max() < 1e-2



