






"""simple docstring"""







from __future__ import annotations

lowerCAmelCase_	:    str            =      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       (      lowerCAmelCase	,      lowerCAmelCase	,      lowerCAmelCase	,      lowerCAmelCase		):







       '''simple docstring'''
       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		):







       '''simple docstring'''
       for i in range(9		):
              for j in range(9		):
                     if grid[i][j] == 0:
                            return i, j
       return None






def       _lowerCAmelCase       (      lowerCAmelCase		):







       '''simple docstring'''
       if location := find_empty_location(lowerCAmelCase		):
              UpperCAmelCase    ,       UpperCAmelCase	    =			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		):
                     UpperCAmelCase	    =			digit

                     if sudoku(lowerCAmelCase		) is not None:
                            return grid

                     UpperCAmelCase	    =			0

       return None






def       _lowerCAmelCase       (      lowerCAmelCase		):







       '''simple docstring'''
       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''' + '''=''' * 2_0)
  print_solution(example_grid)
  print('''\nExample grid solution:''')
  lowerCAmelCase_	:    Optional[Any]            =      sudoku(example_grid)
  if solution is not None:
   print_solution(solution)
  else:
   print('''Cannot find a solution.''')








"""simple docstring"""







from . import __version__

# Backward compatibility imports, to make sure all those objects can be found in file_utils
from .utils import (
    CLOUDFRONT_DISTRIB_PREFIX,
    CONFIG_NAME,
    DISABLE_TELEMETRY,
    DUMMY_INPUTS,
    DUMMY_MASK,
    ENV_VARS_TRUE_AND_AUTO_VALUES,
    ENV_VARS_TRUE_VALUES,
    FEATURE_EXTRACTOR_NAME,
    FLAX_WEIGHTS_NAME,
    HF_MODULES_CACHE,
    HUGGINGFACE_CO_PREFIX,
    HUGGINGFACE_CO_RESOLVE_ENDPOINT,
    MODEL_CARD_NAME,
    MULTIPLE_CHOICE_DUMMY_INPUTS,
    PYTORCH_PRETRAINED_BERT_CACHE,
    PYTORCH_TRANSFORMERS_CACHE,
    S3_BUCKET_PREFIX,
    SENTENCEPIECE_UNDERLINE,
    SPIECE_UNDERLINE,
    TF2_WEIGHTS_NAME,
    TF_WEIGHTS_NAME,
    TORCH_FX_REQUIRED_VERSION,
    TRANSFORMERS_CACHE,
    TRANSFORMERS_DYNAMIC_MODULE_NAME,
    USE_JAX,
    USE_TF,
    USE_TORCH,
    WEIGHTS_INDEX_NAME,
    WEIGHTS_NAME,
    ContextManagers,
    DummyObject,
    EntryNotFoundError,
    ExplicitEnum,
    ModelOutput,
    PaddingStrategy,
    PushToHubMixin,
    RepositoryNotFoundError,
    RevisionNotFoundError,
    TensorType,
    _LazyModule,
    add_code_sample_docstrings,
    add_end_docstrings,
    add_start_docstrings,
    add_start_docstrings_to_model_forward,
    cached_property,
    copy_func,
    default_cache_path,
    define_sagemaker_information,
    get_cached_models,
    get_file_from_repo,
    get_full_repo_name,
    get_torch_version,
    has_file,
    http_user_agent,
    is_apex_available,
    is_bsa_available,
    is_coloredlogs_available,
    is_datasets_available,
    is_detectrona_available,
    is_faiss_available,
    is_flax_available,
    is_ftfy_available,
    is_in_notebook,
    is_ipex_available,
    is_librosa_available,
    is_offline_mode,
    is_onnx_available,
    is_pandas_available,
    is_phonemizer_available,
    is_protobuf_available,
    is_psutil_available,
    is_pyanvml_available,
    is_pyctcdecode_available,
    is_pytesseract_available,
    is_pytorch_quantization_available,
    is_rjieba_available,
    is_sagemaker_dp_enabled,
    is_sagemaker_mp_enabled,
    is_scipy_available,
    is_sentencepiece_available,
    is_seqio_available,
    is_sklearn_available,
    is_soundfile_availble,
    is_spacy_available,
    is_speech_available,
    is_tensor,
    is_tensorflow_probability_available,
    is_tfaonnx_available,
    is_tf_available,
    is_timm_available,
    is_tokenizers_available,
    is_torch_available,
    is_torch_bfaa_available,
    is_torch_cuda_available,
    is_torch_fx_available,
    is_torch_fx_proxy,
    is_torch_mps_available,
    is_torch_tfaa_available,
    is_torch_tpu_available,
    is_torchaudio_available,
    is_training_run_on_sagemaker,
    is_vision_available,
    replace_return_docstrings,
    requires_backends,
    to_numpy,
    to_py_obj,
    torch_only_method,
)
