

"""simple docstring"""


from __future__ import annotations

a					:Dict    = list[list[int]]

# assigning initial values to the grid
a					: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
a					: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  _lowercase					(    __lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase							)       ->				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  _lowercase					(    __lowerCAmelCase							)       ->				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  _lowercase					(    __lowerCAmelCase							)       ->				Matrix | None:
      if location := find_empty_location(__lowerCAmelCase							):
            SCREAMING_SNAKE_CASE__		,		SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	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__   :      List[Any]      		=	digit

                  if sudoku(__lowerCAmelCase							) is not None:
                        return grid

                  SCREAMING_SNAKE_CASE__   :      str      		=	0

      return None




def  _lowercase					(    __lowerCAmelCase							)       ->				None:
      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:")
    a					:Any    = sudoku(example_grid)
    if solution is not None:
      print_solution(solution)
    else:
      print("Cannot find a solution.")







"""simple docstring"""


import torch

from diffusers import DDPMScheduler

from .test_schedulers import SchedulerCommonTest

class      __a							(UpperCamelCase_):






     '''simple docstring'''
     _SCREAMING_SNAKE_CASE						:Tuple       = (DDPMScheduler,)

     def 					_a			(						self	,    **_a  )  ->      List[str]:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      int      		=	{
               """num_train_timesteps""": 1_000,
               """beta_start""": 0.0_001,
               """beta_end""": 0.02,
               """beta_schedule""": """linear""",
               """variance_type""": """fixed_small""",
               """clip_sample""": True,
           }

           config.update(**_a  )
           return config

     def 					_a			(						self  )  ->      str:


           """simple docstring"""


           for timesteps in [1, 5, 100, 1_000]:
                 self.check_over_configs(num_train_timesteps=_a  )

     def 					_a			(						self  )  ->      str:


           """simple docstring"""


           for beta_start, beta_end in zip([0.0_001, 0.001, 0.01, 0.1]	,    [0.002, 0.02, 0.2, 2]  ):
                 self.check_over_configs(beta_start=_a	,    beta_end=_a  )

     def 					_a			(						self  )  ->      Union[str, Any]:


           """simple docstring"""


           for schedule in ["linear", "squaredcos_cap_v2"]:
                 self.check_over_configs(beta_schedule=_a  )

     def 					_a			(						self  )  ->      Any:


           """simple docstring"""


           for variance in ["fixed_small", "fixed_large", "other"]:
                 self.check_over_configs(variance_type=_a  )

     def 					_a			(						self  )  ->      Optional[int]:


           """simple docstring"""


           for clip_sample in [True, False]:
                 self.check_over_configs(clip_sample=_a  )

     def 					_a			(						self  )  ->      int:


           """simple docstring"""


           self.check_over_configs(thresholding=_a  )
           for threshold in [0.5, 1.0, 2.0]:
                 for prediction_type in ["epsilon", "sample", "v_prediction"]:
                       self.check_over_configs(
                           thresholding=_a	,    prediction_type=_a	,    sample_max_value=_a	,    )

     def 					_a			(						self  )  ->      str:


           """simple docstring"""


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

     def 					_a			(						self  )  ->      str:


           """simple docstring"""


           for t in [0, 500, 999]:
                 self.check_over_forward(time_step=_a  )

     def 					_a			(						self  )  ->      str:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Tuple      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      int      		=	self.get_scheduler_config()
           SCREAMING_SNAKE_CASE__   :      Dict      		=	scheduler_class(**_a  )

           assert torch.sum(torch.abs(scheduler._get_variance(0  ) - 0.0  )  ) < 1E-5
           assert torch.sum(torch.abs(scheduler._get_variance(487  ) - 0.00_979  )  ) < 1E-5
           assert torch.sum(torch.abs(scheduler._get_variance(999  ) - 0.02  )  ) < 1E-5

     def 					_a			(						self  )  ->      List[Any]:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      List[Any]      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	self.get_scheduler_config()
           SCREAMING_SNAKE_CASE__   :      int      		=	scheduler_class(**_a  )

           SCREAMING_SNAKE_CASE__   :      Any      		=	len(_a  )

           SCREAMING_SNAKE_CASE__   :      List[Any]      		=	self.dummy_model()
           SCREAMING_SNAKE_CASE__   :      str      		=	self.dummy_sample_deter
           SCREAMING_SNAKE_CASE__   :      str      		=	torch.manual_seed(0  )

           for t in reversed(range(_a  )  ):
                 # 1. predict noise residual
                 SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	model(_a	,    _a  )

                 # 2. predict previous mean of sample x_t-1
                 SCREAMING_SNAKE_CASE__   :      int      		=	scheduler.step(_a	,    _a	,    _a	,    generator=_a  ).prev_sample

                 # if t > 0:
                 #     noise = self.dummy_sample_deter
                 #     variance = scheduler.get_variance(t) ** (0.5) * noise
                 #
                 # sample = pred_prev_sample + variance
                 SCREAMING_SNAKE_CASE__   :      str      		=	pred_prev_sample

           SCREAMING_SNAKE_CASE__   :      str      		=	torch.sum(torch.abs(_a  )  )
           SCREAMING_SNAKE_CASE__   :      Any      		=	torch.mean(torch.abs(_a  )  )

           assert abs(result_sum.item() - 258.9_606  ) < 1E-2
           assert abs(result_mean.item() - 0.3_372  ) < 1E-3

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


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      Tuple      		=	self.get_scheduler_config(prediction_type="""v_prediction"""  )
           SCREAMING_SNAKE_CASE__   :      List[str]      		=	scheduler_class(**_a  )

           SCREAMING_SNAKE_CASE__   :      Dict      		=	len(_a  )

           SCREAMING_SNAKE_CASE__   :      List[str]      		=	self.dummy_model()
           SCREAMING_SNAKE_CASE__   :      List[str]      		=	self.dummy_sample_deter
           SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	torch.manual_seed(0  )

           for t in reversed(range(_a  )  ):
                 # 1. predict noise residual
                 SCREAMING_SNAKE_CASE__   :      int      		=	model(_a	,    _a  )

                 # 2. predict previous mean of sample x_t-1
                 SCREAMING_SNAKE_CASE__   :      List[str]      		=	scheduler.step(_a	,    _a	,    _a	,    generator=_a  ).prev_sample

                 # if t > 0:
                 #     noise = self.dummy_sample_deter
                 #     variance = scheduler.get_variance(t) ** (0.5) * noise
                 #
                 # sample = pred_prev_sample + variance
                 SCREAMING_SNAKE_CASE__   :      Tuple      		=	pred_prev_sample

           SCREAMING_SNAKE_CASE__   :      Any      		=	torch.sum(torch.abs(_a  )  )
           SCREAMING_SNAKE_CASE__   :      int      		=	torch.mean(torch.abs(_a  )  )

           assert abs(result_sum.item() - 202.0_296  ) < 1E-2
           assert abs(result_mean.item() - 0.2_631  ) < 1E-3

     def 					_a			(						self  )  ->      Union[str, Any]:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	self.get_scheduler_config()
           SCREAMING_SNAKE_CASE__   :      Dict      		=	scheduler_class(**_a  )

           SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	[100, 87, 50, 1, 0]

           scheduler.set_timesteps(timesteps=_a  )

           SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	scheduler.timesteps

           for i, timestep in enumerate(_a  ):
                 if i == len(_a  ) - 1:
                       SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	-1
                 else:
                       SCREAMING_SNAKE_CASE__   :      Tuple      		=	timesteps[i + 1]

                 SCREAMING_SNAKE_CASE__   :      int      		=	scheduler.previous_timestep(_a  )
                 SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	prev_t.item()

                 self.assertEqual(_a	,    _a  )

     def 					_a			(						self  )  ->      Union[str, Any]:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Tuple      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      int      		=	self.get_scheduler_config()
           SCREAMING_SNAKE_CASE__   :      List[str]      		=	scheduler_class(**_a  )

           SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	[100, 87, 50, 51, 0]

           with self.assertRaises(_a	,    msg="""`custom_timesteps` must be in descending order."""  ):
                 scheduler.set_timesteps(timesteps=_a  )

     def 					_a			(						self  )  ->      List[Any]:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      List[Any]      		=	self.get_scheduler_config()
           SCREAMING_SNAKE_CASE__   :      List[str]      		=	scheduler_class(**_a  )

           SCREAMING_SNAKE_CASE__   :      int      		=	[100, 87, 50, 1, 0]
           SCREAMING_SNAKE_CASE__   :      List[str]      		=	len(_a  )

           with self.assertRaises(_a	,    msg="""Can only pass one of `num_inference_steps` or `custom_timesteps`."""  ):
                 scheduler.set_timesteps(num_inference_steps=_a	,    timesteps=_a  )





     def 					_a			(						self  )  ->      Tuple:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      List[Any]      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	self.get_scheduler_config()
           SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	scheduler_class(**_a  )

           SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	[scheduler.config.num_train_timesteps]

           with self.assertRaises(
               _a	,    msg="""`timesteps` must start before `self.config.train_timesteps`: {scheduler.config.num_train_timesteps}}"""	,    ):
                 scheduler.set_timesteps(timesteps=_a  )




