



'''simple docstring'''




from __future__ import annotations

UpperCamelCase__ :			Optional[Any]												=				list[list[int]]

# assigning initial values to the grid
UpperCamelCase__ :			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
UpperCamelCase__ :			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        lowerCAmelCase_     (			_lowerCamelCase:     Matrix ,   _lowerCamelCase:     int ,   _lowerCamelCase:     int ,   _lowerCamelCase:     int      ):
		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        lowerCAmelCase_     (			_lowerCamelCase:     Matrix      ):
		for i in range(9      ):
				for j in range(9      ):
						if grid[i][j] == 0:
								return i, j
		return None


def        lowerCAmelCase_     (			_lowerCamelCase:     Matrix      ):
		if location := find_empty_location(_lowerCamelCase      ):
				__SCREAMING_SNAKE_CASE :	Optional[Any]					 =	location
		else:
				# If the location is ``None``, then the grid is solved.
				return grid

		for digit in range(1 ,   10      ):
				if is_safe(_lowerCamelCase ,   _lowerCamelCase ,   _lowerCamelCase ,   _lowerCamelCase      ):
						__SCREAMING_SNAKE_CASE :	Optional[int]					 =	digit

						if sudoku(_lowerCamelCase      ) is not None:
								return grid

						__SCREAMING_SNAKE_CASE :	List[Any]					 =	0

		return None


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






'''simple docstring'''




import torch

from diffusers import KDPMaDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest






class 		_UpperCamelCase						(							lowerCamelCase__					):


			'''simple docstring'''

			_A   :	Optional[int]    					=	(KDPMaDiscreteScheduler,)
			_A   :	Dict    					=	10

			def UpperCamelCase__      (							self  :				Optional[int]							,  **lowerCAmelCase__  :				List[Any]		):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE :	Any					 =	{
					    """num_train_timesteps""": 1_1_0_0,
					    """beta_start""": 0.00_01,
					    """beta_end""": 0.02,
					    """beta_schedule""": """linear""",
					}

					config.update(**lowerCAmelCase__		)
					return config

			def UpperCamelCase__      (							self  :				int		):





					"""simple docstring"""






					for timesteps in [1_0, 5_0, 1_0_0, 1_0_0_0]:
							self.check_over_configs(num_train_timesteps=lowerCAmelCase__		)

			def UpperCamelCase__      (							self  :				str		):





					"""simple docstring"""






					for beta_start, beta_end in zip([0.0_00_01, 0.00_01, 0.0_01]							,  [0.00_02, 0.0_02, 0.02]		):
							self.check_over_configs(beta_start=lowerCAmelCase__							,  beta_end=lowerCAmelCase__		)

			def UpperCamelCase__      (							self  :				Tuple		):





					"""simple docstring"""






					for schedule in ["linear", "scaled_linear"]:
							self.check_over_configs(beta_schedule=lowerCAmelCase__		)

			def UpperCamelCase__      (							self  :				int		):





					"""simple docstring"""






					for prediction_type in ["epsilon", "v_prediction"]:
							self.check_over_configs(prediction_type=lowerCAmelCase__		)

			def UpperCamelCase__      (							self  :				List[str]		):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE :	Any					 =	self.scheduler_classes[0]
					__SCREAMING_SNAKE_CASE :	Tuple					 =	self.get_scheduler_config(prediction_type="""v_prediction"""		)
					__SCREAMING_SNAKE_CASE :	Optional[int]					 =	scheduler_class(**lowerCAmelCase__		)

					scheduler.set_timesteps(self.num_inference_steps		)

					__SCREAMING_SNAKE_CASE :	Optional[int]					 =	self.dummy_model()
					__SCREAMING_SNAKE_CASE :	Optional[Any]					 =	self.dummy_sample_deter * scheduler.init_noise_sigma
					__SCREAMING_SNAKE_CASE :	Union[str, Any]					 =	sample.to(lowerCAmelCase__		)

					for i, t in enumerate(scheduler.timesteps		):
							__SCREAMING_SNAKE_CASE :	List[Any]					 =	scheduler.scale_model_input(lowerCAmelCase__							,  lowerCAmelCase__		)

							__SCREAMING_SNAKE_CASE :	Optional[Any]					 =	model(lowerCAmelCase__							,  lowerCAmelCase__		)

							__SCREAMING_SNAKE_CASE :	Dict					 =	scheduler.step(lowerCAmelCase__							,  lowerCAmelCase__							,  lowerCAmelCase__		)
							__SCREAMING_SNAKE_CASE :	List[str]					 =	output.prev_sample

					__SCREAMING_SNAKE_CASE :	List[Any]					 =	torch.sum(torch.abs(lowerCAmelCase__		)		)
					__SCREAMING_SNAKE_CASE :	List[Any]					 =	torch.mean(torch.abs(lowerCAmelCase__		)		)

					if torch_device in ["cpu", "mps"]:
							assert abs(result_sum.item() - 4.69_34E-07		) < 1E-2
							assert abs(result_mean.item() - 6.11_12E-10		) < 1E-3
					else:
							# CUDA
							assert abs(result_sum.item() - 4.6_93_42_86_50_17_09_72E-07		) < 1E-2
							assert abs(result_mean.item() - 0.00_02		) < 1E-3

			def UpperCamelCase__      (							self  :				Optional[int]		):





					"""simple docstring"""






					if torch_device == "mps":
							return
					__SCREAMING_SNAKE_CASE :	List[Any]					 =	self.scheduler_classes[0]
					__SCREAMING_SNAKE_CASE :	str					 =	self.get_scheduler_config()
					__SCREAMING_SNAKE_CASE :	Optional[Any]					 =	scheduler_class(**lowerCAmelCase__		)

					scheduler.set_timesteps(self.num_inference_steps		)

					__SCREAMING_SNAKE_CASE :	Union[str, Any]					 =	self.dummy_model()
					__SCREAMING_SNAKE_CASE :	Optional[int]					 =	self.dummy_sample_deter * scheduler.init_noise_sigma
					__SCREAMING_SNAKE_CASE :	str					 =	sample.to(lowerCAmelCase__		)

					for i, t in enumerate(scheduler.timesteps		):
							__SCREAMING_SNAKE_CASE :	Tuple					 =	scheduler.scale_model_input(lowerCAmelCase__							,  lowerCAmelCase__		)

							__SCREAMING_SNAKE_CASE :	Optional[Any]					 =	model(lowerCAmelCase__							,  lowerCAmelCase__		)

							__SCREAMING_SNAKE_CASE :	Any					 =	scheduler.step(lowerCAmelCase__							,  lowerCAmelCase__							,  lowerCAmelCase__		)
							__SCREAMING_SNAKE_CASE :	List[Any]					 =	output.prev_sample

					__SCREAMING_SNAKE_CASE :	int					 =	torch.sum(torch.abs(lowerCAmelCase__		)		)
					__SCREAMING_SNAKE_CASE :	int					 =	torch.mean(torch.abs(lowerCAmelCase__		)		)

					if torch_device in ["cpu", "mps"]:
							assert abs(result_sum.item() - 20.41_25		) < 1E-2
							assert abs(result_mean.item() - 0.02_66		) < 1E-3
					else:
							# CUDA
							assert abs(result_sum.item() - 20.41_25		) < 1E-2
							assert abs(result_mean.item() - 0.02_66		) < 1E-3



			def UpperCamelCase__      (							self  :				List[str]		):





					"""simple docstring"""






					if torch_device == "mps":
							return
					__SCREAMING_SNAKE_CASE :	Dict					 =	self.scheduler_classes[0]
					__SCREAMING_SNAKE_CASE :	Dict					 =	self.get_scheduler_config()
					__SCREAMING_SNAKE_CASE :	List[Any]					 =	scheduler_class(**lowerCAmelCase__		)

					scheduler.set_timesteps(self.num_inference_steps							,  device=lowerCAmelCase__		)

					__SCREAMING_SNAKE_CASE :	List[Any]					 =	self.dummy_model()
					__SCREAMING_SNAKE_CASE :	Optional[Any]					 =	self.dummy_sample_deter.to(lowerCAmelCase__		) * scheduler.init_noise_sigma

					for t in scheduler.timesteps:
							__SCREAMING_SNAKE_CASE :	Dict					 =	scheduler.scale_model_input(lowerCAmelCase__							,  lowerCAmelCase__		)

							__SCREAMING_SNAKE_CASE :	Any					 =	model(lowerCAmelCase__							,  lowerCAmelCase__		)

							__SCREAMING_SNAKE_CASE :	Union[str, Any]					 =	scheduler.step(lowerCAmelCase__							,  lowerCAmelCase__							,  lowerCAmelCase__		)
							__SCREAMING_SNAKE_CASE :	str					 =	output.prev_sample

					__SCREAMING_SNAKE_CASE :	Dict					 =	torch.sum(torch.abs(lowerCAmelCase__		)		)
					__SCREAMING_SNAKE_CASE :	int					 =	torch.mean(torch.abs(lowerCAmelCase__		)		)

					if str(lowerCAmelCase__		).startswith("""cpu"""		):
							# The following sum varies between 148 and 156 on mps. Why?
							assert abs(result_sum.item() - 20.41_25		) < 1E-2
							assert abs(result_mean.item() - 0.02_66		) < 1E-3
					else:
							# CUDA
							assert abs(result_sum.item() - 20.41_25		) < 1E-2
							assert abs(result_mean.item() - 0.02_66		) < 1E-3