



"""simple docstring"""







from __future__ import annotations

import random
from collections.abc import Iterable





class    UpperCamelCase     :




	"""simple docstring"""






	def __init__(			self							,UpperCAmelCase_					):
			_lowercase							:      dict[str, bool | None]			=					{literal: None for literal in literals}






	def __str__(			self					):
			return "{" + " , ".join(self.literals					) + "}"






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






	def 					lowerCamelCase__ (			self							,UpperCAmelCase_					):
			for literal in self.literals:
					_lowercase							:      Dict			=					literal[:2]
					if symbol in model:
							_lowercase							:      Tuple			=					model[symbol]
					else:
							continue
					if value is not None:
							# Complement assignment if literal is in complemented form
							if literal.endswith("""'"""					):
									_lowercase							:      List[str]			=					not value
					_lowercase							:      Dict			=					value






	def 					lowerCamelCase__ (			self							,UpperCAmelCase_					):
			for literal in self.literals:
					_lowercase							:      int			=					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    UpperCamelCase     :




	"""simple docstring"""






	def __init__(			self							,UpperCAmelCase_					):
			_lowercase							:      List[Any]			=					list(UpperCAmelCase_					)






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







def       __SCREAMING_SNAKE_CASE      (   ):
		_lowercase							:      Any			=					[]
		_lowercase							:      List[str]			=					random.randint(1					,							5	)
		_lowercase							:      Union[str, Any]			=					"""A"""
		_lowercase							:      Tuple			=					0
		while i < no_of_literals:
				_lowercase							:      int			=					random.randint(1					,							5	)
				_lowercase							:      Union[str, Any]			=					base_var + str(__UpperCAmelCase	)
				_lowercase							:      Optional[int]			=					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      (   ):
		_lowercase							:      set[Clause]			=					set()
		_lowercase							:      List[Any]			=					random.randint(1					,							10	)
		while len(__UpperCAmelCase	) < no_of_clauses:
				clauses.add(generate_clause()	)
		return Formula(__UpperCAmelCase	)


def       __SCREAMING_SNAKE_CASE      (   __UpperCAmelCase	):
		_lowercase							:      Optional[int]			=					formula.clauses
		_lowercase							:      Any			=					[]
		for clause in formula.clauses:
				for literal in clause.literals:
						_lowercase							:      Dict			=					literal[:2]
						if symbol not in symbols_set:
								symbols_set.append(__UpperCAmelCase	)
		return clauses, symbols_set


def       __SCREAMING_SNAKE_CASE      (   __UpperCAmelCase					,							__UpperCAmelCase					,							__UpperCAmelCase	):
		_lowercase							:      Union[str, Any]			=					[]
		_lowercase							:      dict[str, bool | None]			=					{}
		_lowercase							:      Optional[int]			=					[]

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

		for s in symbols:
				_lowercase							:      Union[str, Any]			=					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:
				_lowercase							:      List[Any]			=					None
		for s in pure_symbols:
				_lowercase							:      Optional[Any]			=					s + """'"""
				if s in literals:
						_lowercase							:      Tuple			=					True
				elif sym in literals:
						_lowercase							:      Dict			=					False
		return pure_symbols, assignment


def       __SCREAMING_SNAKE_CASE      (   __UpperCAmelCase					,							__UpperCAmelCase	):
		_lowercase							:      Union[str, Any]			=					[]
		for clause in clauses:
				if len(__UpperCAmelCase	) == 1:
						unit_symbols.append(list(clause.literals.keys()	)[0]	)
				else:
						_lowercase			,   _lowercase							:      int			=					0, 0
						for literal, value in clause.literals.items():
								if value is False:
										f_count += 1
								elif value is None:
										_lowercase							:      Dict			=					literal
										n_count += 1
						if f_count == len(__UpperCAmelCase	) - 1 and n_count == 1:
								unit_symbols.append(__UpperCAmelCase	)
		_lowercase							:      dict[str, bool | None]			=					{}
		for i in unit_symbols:
				_lowercase							:      str			=					i[:2]
				_lowercase							:      Tuple			=					len(__UpperCAmelCase	) == 2
		_lowercase							:      Optional[int]			=					[i[:2] for i in unit_symbols]

		return unit_symbols, assignment


def       __SCREAMING_SNAKE_CASE      (   __UpperCAmelCase					,							__UpperCAmelCase					,							__UpperCAmelCase	):
		_lowercase							:      str			=					True
		for clause in clauses:
				_lowercase							:      List[Any]			=					clause.evaluate(__UpperCAmelCase	)
				if clause_check is False:
						return False, None
				elif clause_check is None:
						_lowercase							:      List[Any]			=					False
						continue

		if check_clause_all_true:
				return True, model

		try:
				_lowercase			,   _lowercase							:      Union[str, Any]			=					find_pure_symbols(__UpperCAmelCase					,							__UpperCAmelCase					,							__UpperCAmelCase	)
		except RecursionError:
				print("""raises a RecursionError and is"""	)
				return None, {}
		_lowercase							:      Optional[int]			=					None
		if len(__UpperCAmelCase	) > 0:
				_lowercase			,   _lowercase							:      Tuple			=					pure_symbols[0], assignment[pure_symbols[0]]

		if p:
				_lowercase							:      List[str]			=					model
				_lowercase							:      List[Any]			=					value
				_lowercase							:      Any			=					list(__UpperCAmelCase	)
				if p in tmp_symbols:
						tmp_symbols.remove(__UpperCAmelCase	)
				return dpll_algorithm(__UpperCAmelCase					,							__UpperCAmelCase					,							__UpperCAmelCase	)

		_lowercase			,   _lowercase							:      str			=					find_unit_clauses(__UpperCAmelCase					,							__UpperCAmelCase	)
		_lowercase							:      str			=					None
		if len(__UpperCAmelCase	) > 0:
				_lowercase			,   _lowercase							:      Optional[int]			=					unit_symbols[0], assignment[unit_symbols[0]]
		if p:
				_lowercase							:      Any			=					model
				_lowercase							:      List[Any]			=					value
				_lowercase							:      List[str]			=					list(__UpperCAmelCase	)
				if p in tmp_symbols:
						tmp_symbols.remove(__UpperCAmelCase	)
				return dpll_algorithm(__UpperCAmelCase					,							__UpperCAmelCase					,							__UpperCAmelCase	)
		_lowercase							:      Any			=					symbols[0]
		_lowercase							:      Dict			=					symbols[1:]
		_lowercase			,   _lowercase							:      Tuple			=					model, model
		_lowercase			,   _lowercase							:      List[Any]			=					True, False

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


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		UpperCAmelCase:   Optional[int]       			=							generate_formula()
		print(F'The formula {formula} is', end=""" """)

		UpperCAmelCase			,      UpperCAmelCase:   List[str]       			=							generate_parameters(formula)
		UpperCAmelCase			,      UpperCAmelCase:   int       			=							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}



