from __future__ import annotations

_lowerCamelCase   :				Optional[int]     			=						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 		__lowerCamelCase							(UpperCAmelCase__       :							Matrix ,	UpperCAmelCase__       :							int ,	UpperCAmelCase__       :							int ,	UpperCAmelCase__       :							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							(UpperCAmelCase__       :							Matrix					):
					for i in range(9					):
										for j in range(9					):
															if grid[i][j] == 0:
																				return i, j
					return None





def 		__lowerCamelCase							(UpperCAmelCase__       :							Matrix					):
					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 ,	1_0					):
										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 		__lowerCamelCase							(UpperCAmelCase__       :							Matrix					):
					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   :				int     			=						sudoku(example_grid)
														if solution is not None:
																					print_solution(solution)
														else:
																					print('''Cannot find a solution.''')





import contextlib
from multiprocessing import Pool, RLock

from tqdm.auto import tqdm

from ..utils import experimental, logging


_lowerCamelCase   :				Union[str, Any]     			=						logging.get_logger(__name__)


class   lowercase      :
							lowercase__  :    str									=							None





@experimental
def 		__lowerCamelCase							(UpperCAmelCase__       :							Any ,	UpperCAmelCase__       :							int ,	UpperCAmelCase__       :							Optional[int] ,	UpperCAmelCase__       :							List[Any] ,	UpperCAmelCase__       :							Union[str, Any] ,	UpperCAmelCase__       :							List[str] ,	UpperCAmelCase__       :							Any					):
					if ParallelBackendConfig.backend_name is None:
										return _map_with_multiprocessing_pool(
										    UpperCAmelCase__ ,	UpperCAmelCase__ ,	UpperCAmelCase__ ,	UpperCAmelCase__ ,	UpperCAmelCase__ ,	UpperCAmelCase__ ,	UpperCAmelCase__					)

					return _map_with_joblib(UpperCAmelCase__ ,	UpperCAmelCase__ ,	UpperCAmelCase__ ,	UpperCAmelCase__ ,	UpperCAmelCase__ ,	UpperCAmelCase__ ,	UpperCAmelCase__					)





def 		__lowerCamelCase							(UpperCAmelCase__       :							Optional[Any] ,	UpperCAmelCase__       :							List[Any] ,	UpperCAmelCase__       :							int ,	UpperCAmelCase__       :							Union[str, Any] ,	UpperCAmelCase__       :							Any ,	UpperCAmelCase__       :							int ,	UpperCAmelCase__       :							Optional[Any]					):
					SCREAMING_SNAKE_CASE           =    num_proc if num_proc <= len(UpperCAmelCase__					) else len(UpperCAmelCase__					)
					SCREAMING_SNAKE_CASE           =    []  # We organize the splits ourselve (contiguous splits)
					for index in range(UpperCAmelCase__					):
										SCREAMING_SNAKE_CASE           =    len(UpperCAmelCase__					) // num_proc
										SCREAMING_SNAKE_CASE           =    len(UpperCAmelCase__					) % num_proc
										SCREAMING_SNAKE_CASE           =    div * index + min(UpperCAmelCase__ ,	UpperCAmelCase__					)
										SCREAMING_SNAKE_CASE           =    start + div + (1 if index < mod else 0)
										split_kwds.append((function, iterable[start:end], types, index, disable_tqdm, desc)					)

					if len(UpperCAmelCase__					) != sum(len(i[1]					) for i in split_kwds					):
										raise ValueError(
										    F"Error dividing inputs iterable among processes. "
										    F"Total number of objects {len(UpperCAmelCase__					)}, "
										    F"length: {sum(len(i[1]					) for i in split_kwds					)}"					)

					logger.info(
					    F"Spawning {num_proc} processes for {len(UpperCAmelCase__					)} objects in slices of {[len(i[1]					) for i in split_kwds]}"					)
					SCREAMING_SNAKE_CASE     ,				SCREAMING_SNAKE_CASE           =    None, None
					if not disable_tqdm:
										SCREAMING_SNAKE_CASE     ,				SCREAMING_SNAKE_CASE           =    (RLock(),), tqdm.set_lock
					with Pool(UpperCAmelCase__ ,	initargs=UpperCAmelCase__ ,	initializer=UpperCAmelCase__					) as pool:
										SCREAMING_SNAKE_CASE           =    pool.map(UpperCAmelCase__ ,	UpperCAmelCase__					)
					logger.info(F"Finished {num_proc} processes"					)
					SCREAMING_SNAKE_CASE           =    [obj for proc_res in mapped for obj in proc_res]
					logger.info(F"Unpacked {len(UpperCAmelCase__					)} objects"					)

					return mapped





def 		__lowerCamelCase							(UpperCAmelCase__       :							Tuple ,	UpperCAmelCase__       :							Dict ,	UpperCAmelCase__       :							Any ,	UpperCAmelCase__       :							Optional[int] ,	UpperCAmelCase__       :							Tuple ,	UpperCAmelCase__       :							Tuple ,	UpperCAmelCase__       :							Any					):
					# progress bar is not yet supported for _map_with_joblib, because tqdm couldn't accurately be applied to joblib,
					# and it requires monkey-patching joblib internal classes which is subject to change
					import joblib

					with joblib.parallel_backend(ParallelBackendConfig.backend_name ,	n_jobs=UpperCAmelCase__					):
										return joblib.Parallel()(
										    joblib.delayed(UpperCAmelCase__					)((function, obj, types, None, True, None)					) for obj in iterable					)





@experimental
@contextlib.contextmanager
def 		__lowerCamelCase							(UpperCAmelCase__       :							str					):
					SCREAMING_SNAKE_CASE           =    backend_name

					if backend_name == "spark":
										from joblibspark import register_spark

										register_spark()

										# TODO: call create_cache_and_write_probe if "download" in steps
										# TODO: raise NotImplementedError when Dataset.map etc is called

					try:
										yield
					finally:
										SCREAMING_SNAKE_CASE           =    None




