from sklearn.metrics import fa_score

import datasets


__lowerCamelCase      :			Dict							       =		'''
The F1 score is the harmonic mean of the precision and recall. It can be computed with the equation:
F1 = 2 * (precision * recall) / (precision + recall)
'''


__lowerCamelCase      :			Any							       =		'''
Args:
    predictions (`list` of `int`): Predicted labels.
    references (`list` of `int`): Ground truth labels.
    labels (`list` of `int`): The set of labels to include when `average` is not set to `\'binary\'`, and the order of the labels if `average` is `None`. Labels present in the data can be excluded, for example to calculate a multiclass average ignoring a majority negative class. Labels not present in the data will result in 0 components in a macro average. For multilabel targets, labels are column indices. By default, all labels in `predictions` and `references` are used in sorted order. Defaults to None.
    pos_label (`int`): The class to be considered the positive class, in the case where `average` is set to `binary`. Defaults to 1.
    average (`string`): This parameter is required for multiclass/multilabel targets. If set to `None`, the scores for each class are returned. Otherwise, this determines the type of averaging performed on the data. Defaults to `\'binary\'`.

        - \'binary\': Only report results for the class specified by `pos_label`. This is applicable only if the classes found in `predictions` and `references` are binary.
        - \'micro\': Calculate metrics globally by counting the total true positives, false negatives and false positives.
        - \'macro\': Calculate metrics for each label, and find their unweighted mean. This does not take label imbalance into account.
        - \'weighted\': Calculate metrics for each label, and find their average weighted by support (the number of true instances for each label). This alters `\'macro\'` to account for label imbalance. This option can result in an F-score that is not between precision and recall.
        - \'samples\': Calculate metrics for each instance, and find their average (only meaningful for multilabel classification).
    sample_weight (`list` of `float`): Sample weights Defaults to None.

Returns:
    f1 (`float` or `array` of `float`): F1 score or list of f1 scores, depending on the value passed to `average`. Minimum possible value is 0. Maximum possible value is 1. Higher f1 scores are better.

Examples:

    Example 1-A simple binary example
        >>> f1_metric = datasets.load_metric("f1")
        >>> results = f1_metric.compute(references=[0, 1, 0, 1, 0], predictions=[0, 0, 1, 1, 0])
        >>> print(results)
        {\'f1\': 0.5}

    Example 2-The same simple binary example as in Example 1, but with `pos_label` set to `0`.
        >>> f1_metric = datasets.load_metric("f1")
        >>> results = f1_metric.compute(references=[0, 1, 0, 1, 0], predictions=[0, 0, 1, 1, 0], pos_label=0)
        >>> print(round(results[\'f1\'], 2))
        0.67

    Example 3-The same simple binary example as in Example 1, but with `sample_weight` included.
        >>> f1_metric = datasets.load_metric("f1")
        >>> results = f1_metric.compute(references=[0, 1, 0, 1, 0], predictions=[0, 0, 1, 1, 0], sample_weight=[0.9, 0.5, 3.9, 1.2, 0.3])
        >>> print(round(results[\'f1\'], 2))
        0.35

    Example 4-A multiclass example, with different values for the `average` input.
        >>> predictions = [0, 2, 1, 0, 0, 1]
        >>> references = [0, 1, 2, 0, 1, 2]
        >>> results = f1_metric.compute(predictions=predictions, references=references, average="macro")
        >>> print(round(results[\'f1\'], 2))
        0.27
        >>> results = f1_metric.compute(predictions=predictions, references=references, average="micro")
        >>> print(round(results[\'f1\'], 2))
        0.33
        >>> results = f1_metric.compute(predictions=predictions, references=references, average="weighted")
        >>> print(round(results[\'f1\'], 2))
        0.27
        >>> results = f1_metric.compute(predictions=predictions, references=references, average=None)
        >>> print(results)
        {\'f1\': array([0.8, 0. , 0. ])}
'''


__lowerCamelCase      :			List[str]							       =		'''
@article{scikit-learn,
    title={Scikit-learn: Machine Learning in {P}ython},
    author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V.
           and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P.
           and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and
           Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.},
    journal={Journal of Machine Learning Research},
    volume={12},
    pages={2825--2830},
    year={2011}
}
'''







@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION       ,		_KWARGS_DESCRIPTION		)
class __snake_case    (						datasets.Metric		):




   def      __a						(   self      :    Union[str, Any]				):



     """simple docstring"""






     return datasets.MetricInfo(
         description=_DESCRIPTION	,     citation=_CITATION	,     inputs_description=_KWARGS_DESCRIPTION	,     features=datasets.Features(
             {
                 """predictions""": datasets.Sequence(datasets.Value("""int32"""				)				),
                 """references""": datasets.Sequence(datasets.Value("""int32"""				)				),
             }
             if self.config_name == """multilabel"""
             else {
                 """predictions""": datasets.Value("""int32"""				),
                 """references""": datasets.Value("""int32"""				),
             }				)	,     reference_urls=["""https://scikit-learn.org/stable/modules/generated/sklearn.metrics.f1_score.html"""]	,     )




   def      __a						(   self      :    List[str]	,     _lowercase      :    List[Any]	,     _lowercase      :    Union[str, Any]	,     _lowercase      :    Dict=None	,     _lowercase      :    Dict=1	,     _lowercase      :    Any="binary"	,     _lowercase      :    int=None				):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__      							=				fa_score(
         _lowercase	,     _lowercase	,     labels=_lowercase	,     pos_label=_lowercase	,     average=_lowercase	,     sample_weight=_lowercase				)
     return {"f1": float(_lowercase				) if score.size == 1 else score}

from __future__ import annotations

__lowerCamelCase      :			Tuple							       =		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      __SCREAMING_SNAKE_CASE  ( __UpperCamelCase   :	Matrix			,					__UpperCamelCase   :	int			,					__UpperCamelCase   :	int			,					__UpperCamelCase   :	int     )							-> bool:







  """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      __SCREAMING_SNAKE_CASE  ( __UpperCamelCase   :	Matrix     )							-> tuple[int, int] | None:







  """simple docstring"""





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



def      __SCREAMING_SNAKE_CASE  ( __UpperCamelCase   :	Matrix     )							-> Matrix | None:







  """simple docstring"""





  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			,					10     ):
    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      __SCREAMING_SNAKE_CASE  ( __UpperCamelCase   :	Matrix     )							-> None:







  """simple docstring"""





  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      :			str							       =		sudoku(example_grid)
      if solution is not None:
         print_solution(solution)
      else:
         print('''Cannot find a solution.''')
