




from __future__ import annotations

import random
from collections.abc import Iterable

class        _lowerCamelCase  :

      """simple docstring"""

      def __init__(   self    :       int       ,				snake_case    :       Tuple ):
          __UpperCamelCase     						=  {literal: None for literal in literals}







      def __str__(   self    :       List[str] ):
          return "{" + " , ".join(self.literals ) + "}"







      def __len__(   self    :       int ):
          return len(self.literals )







      def 					snake_case		(   self    :       Optional[int]       ,				snake_case    :       Tuple ):
          for literal in self.literals:
              __UpperCamelCase     						=  literal[:2]
              if symbol in model:
                  __UpperCamelCase     						=  model[symbol]
              else:
                  continue
              if value is not None:
                  # Complement assignment if literal is in complemented form
                  if literal.endswith('''\'''' ):
                      __UpperCamelCase     						=  not value
              __UpperCamelCase     						=  value







      def 					snake_case		(   self    :       Optional[int]       ,				snake_case    :       Optional[Any] ):
          for literal in self.literals:
              __UpperCamelCase     						=  literal.rstrip('''\'''' ) if literal.endswith('''\'''' ) else literal + """'"""
              if symbol in self.literals:
                  return True

          self.assign(UpperCAmelCase_ )
          for value in self.literals.values():
              if value in (True, None):
                  return value
          return any(self.literals.values() )







class        _lowerCamelCase  :

      """simple docstring"""

      def __init__(   self    :       Dict       ,				snake_case    :       int ):
          __UpperCamelCase     						=  list(UpperCAmelCase_ )







      def __str__(   self    :       Any ):
          return "{" + " , ".join(str(UpperCAmelCase_ ) for clause in self.clauses ) + "}"







def     __SCREAMING_SNAKE_CASE      (     )				->		Any:

    """simple docstring"""


    __UpperCamelCase     						=  []
    __UpperCamelCase     						=  random.randint(1    ,   5					)
    __UpperCamelCase     						=  """A"""
    __UpperCamelCase     						=  0
    while i < no_of_literals:
        __UpperCamelCase     						=  random.randint(1    ,   5					)
        __UpperCamelCase     						=  base_var + str(__UpperCAmelCase					)
        __UpperCamelCase     						=  random.randint(0    ,   1					)
        if var_complement == 1:
            var_name += "'"
        if var_name in literals:
            i -= 1
        else:
            literals.append(__UpperCAmelCase					)
        i += 1
    return Clause(__UpperCAmelCase					)




def     __SCREAMING_SNAKE_CASE      (     )				->		Optional[int]:

    """simple docstring"""


    __UpperCamelCase     						=  set()
    __UpperCamelCase     						=  random.randint(1    ,   10					)
    while len(__UpperCAmelCase					) < no_of_clauses:
        clauses.add(generate_clause()					)
    return Formula(__UpperCAmelCase					)




def     __SCREAMING_SNAKE_CASE      (     lowercase_					)				->		List[Any]:

    """simple docstring"""


    __UpperCamelCase     						=  formula.clauses
    __UpperCamelCase     						=  []
    for clause in formula.clauses:
        for literal in clause.literals:
            __UpperCamelCase     						=  literal[:2]
            if symbol not in symbols_set:
                symbols_set.append(__UpperCAmelCase					)
    return clauses, symbols_set




def     __SCREAMING_SNAKE_CASE      (     lowercase_    ,   lowercase_    ,   lowercase_					)				->		int:

    """simple docstring"""


    __UpperCamelCase     						=  []
    __UpperCamelCase     						=  {}
    __UpperCamelCase     						=  []

    for clause in clauses:
        if clause.evaluate(__UpperCAmelCase					):
            continue
        for literal in clause.literals:
            literals.append(__UpperCAmelCase					)

    for s in symbols:
        __UpperCamelCase     						=  s + """'"""
        if (s in literals and sym not in literals) or (
            s not in literals and sym in literals
        ):
            pure_symbols.append(__UpperCAmelCase					)
    for p in pure_symbols:
        __UpperCamelCase     						=  None
    for s in pure_symbols:
        __UpperCamelCase     						=  s + """'"""
        if s in literals:
            __UpperCamelCase     						=  True
        elif sym in literals:
            __UpperCamelCase     						=  False
    return pure_symbols, assignment




def     __SCREAMING_SNAKE_CASE      (     lowercase_    ,   lowercase_					)				->		Optional[int]:

    """simple docstring"""


    __UpperCamelCase     						=  []
    for clause in clauses:
        if len(__UpperCAmelCase					) == 1:
            unit_symbols.append(list(clause.literals.keys()					)[0]					)
        else:
            __UpperCamelCase     						=  0, 0
            for literal, value in clause.literals.items():
                if value is False:
                    f_count += 1
                elif value is None:
                    __UpperCamelCase     						=  literal
                    n_count += 1
            if f_count == len(__UpperCAmelCase					) - 1 and n_count == 1:
                unit_symbols.append(__UpperCAmelCase					)
    __UpperCamelCase     						=  {}
    for i in unit_symbols:
        __UpperCamelCase     						=  i[:2]
        __UpperCamelCase     						=  len(__UpperCAmelCase					) == 2
    __UpperCamelCase     						=  [i[:2] for i in unit_symbols]

    return unit_symbols, assignment




def     __SCREAMING_SNAKE_CASE      (     lowercase_    ,   lowercase_    ,   lowercase_					)				->		Dict:

    """simple docstring"""


    __UpperCamelCase     						=  True
    for clause in clauses:
        __UpperCamelCase     						=  clause.evaluate(__UpperCAmelCase					)
        if clause_check is False:
            return False, None
        elif clause_check is None:
            __UpperCamelCase     						=  False
            continue

    if check_clause_all_true:
        return True, model

    try:
        __UpperCamelCase     						=  find_pure_symbols(__UpperCAmelCase    ,   __UpperCAmelCase    ,   __UpperCAmelCase					)
    except RecursionError:
        print('''raises a RecursionError and is'''					)
        return None, {}
    __UpperCamelCase     						=  None
    if len(__UpperCAmelCase					) > 0:
        __UpperCamelCase     						=  pure_symbols[0], assignment[pure_symbols[0]]

    if p:
        __UpperCamelCase     						=  model
        __UpperCamelCase     						=  value
        __UpperCamelCase     						=  list(__UpperCAmelCase					)
        if p in tmp_symbols:
            tmp_symbols.remove(__UpperCAmelCase					)
        return dpll_algorithm(__UpperCAmelCase    ,   __UpperCAmelCase    ,   __UpperCAmelCase					)

    __UpperCamelCase     						=  find_unit_clauses(__UpperCAmelCase    ,   __UpperCAmelCase					)
    __UpperCamelCase     						=  None
    if len(__UpperCAmelCase					) > 0:
        __UpperCamelCase     						=  unit_symbols[0], assignment[unit_symbols[0]]
    if p:
        __UpperCamelCase     						=  model
        __UpperCamelCase     						=  value
        __UpperCamelCase     						=  list(__UpperCAmelCase					)
        if p in tmp_symbols:
            tmp_symbols.remove(__UpperCAmelCase					)
        return dpll_algorithm(__UpperCAmelCase    ,   __UpperCAmelCase    ,   __UpperCAmelCase					)
    __UpperCamelCase     						=  symbols[0]
    __UpperCamelCase     						=  symbols[1:]
    __UpperCamelCase     						=  model, model
    __UpperCamelCase     						=  True, False

    return dpll_algorithm(__UpperCAmelCase    ,   __UpperCAmelCase    ,   __UpperCAmelCase					) or dpll_algorithm(__UpperCAmelCase    ,   __UpperCAmelCase    ,   __UpperCAmelCase					)


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 a_      						=   generate_formula()
 print(f"""The formula {formula} is""", end=" ")

 a_      						=   generate_parameters(formula)
 a_      						=   dpll_algorithm(clauses, symbols, {})

 if solution:
  print(f"""satisfiable with the assignment {model}.""")
 else:
  print("not satisfiable.")











"""simple docstring"""







from sklearn.metrics import precision_score

import datasets


UpperCAmelCase:   Optional[Any]       			=							"""
Precision is the fraction of correctly labeled positive examples out of all of the examples that were labeled as positive. It is computed via the equation:
Precision = TP / (TP + FP)
where TP is the True positives (i.e. the examples correctly labeled as positive) and FP is the False positive examples (i.e. the examples incorrectly labeled as positive).
"""


UpperCAmelCase:   Union[str, Any]       			=							"""
Args:
    predictions (`list` of `int`): Predicted class labels.
    references (`list` of `int`): Actual class labels.
    labels (`list` of `int`): The set of labels to include when `average` is not set to `'binary'`. If `average` is `None`, it should be the label order. 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.
    zero_division (`int` or `string`): Sets the value to return when there is a zero division. Defaults to 'warn'.

        - 0: Returns 0 when there is a zero division.
        - 1: Returns 1 when there is a zero division.
        - 'warn': Raises warnings and then returns 0 when there is a zero division.

Returns:
    precision (`float` or `array` of `float`): Precision score or list of precision scores, depending on the value passed to `average`. Minimum possible value is 0. Maximum possible value is 1. Higher values indicate that fewer negative examples were incorrectly labeled as positive, which means that, generally, higher scores are better.

Examples:

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

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

    Example 3-The same simple binary example as in Example 1, but with `sample_weight` included.
        >>> precision_metric = datasets.load_metric(\"precision\")
        >>> results = precision_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(results)
        {'precision': 0.23529411764705882}

    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 = precision_metric.compute(predictions=predictions, references=references, average='macro')
        >>> print(results)
        {'precision': 0.2222222222222222}
        >>> results = precision_metric.compute(predictions=predictions, references=references, average='micro')
        >>> print(results)
        {'precision': 0.3333333333333333}
        >>> results = precision_metric.compute(predictions=predictions, references=references, average='weighted')
        >>> print(results)
        {'precision': 0.2222222222222222}
        >>> results = precision_metric.compute(predictions=predictions, references=references, average=None)
        >>> print([round(res, 2) for res in results['precision']])
        [0.67, 0.0, 0.0]
"""


UpperCAmelCase:   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    UpperCamelCase     (			datasets.Metric    ):




	"""simple docstring"""






	def 					lowerCamelCase__ (			self					):
			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.precision_score.html"""]							,)






	def 					lowerCamelCase__ (			self							,UpperCAmelCase_							,UpperCAmelCase_							,UpperCAmelCase_=None							,UpperCAmelCase_=1							,UpperCAmelCase_="binary"							,UpperCAmelCase_=None							,UpperCAmelCase_="warn"							,):
			_lowercase							:      int			=					precision_score(
			    UpperCAmelCase_							,UpperCAmelCase_							,labels=UpperCAmelCase_							,pos_label=UpperCAmelCase_							,average=UpperCAmelCase_							,sample_weight=UpperCAmelCase_							,zero_division=UpperCAmelCase_							,)
			return {"precision": float(UpperCAmelCase_					) if score.size == 1 else score}



