"""simple docstring"""


from __future__ import annotations

import random
from collections.abc import Iterable






class    __UpperCAmelCase						:

				def __init__(      self	, _lowerCamelCase      ):
										lowerCamelCase__					={literal: None for literal in literals}

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

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

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






				def 		_a	(      self	, _lowerCamelCase      ):
										for literal in self.literals:
																lowerCamelCase__					=literal.rstrip("'"      ) if literal.endswith("'"      ) else literal + "'"
																if symbol in self.literals:
																						return True

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






class    __UpperCAmelCase						:

				def __init__(      self	, _lowerCamelCase      ):
										lowerCamelCase__					=list(_lowerCamelCase      )






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





def 			lowerCamelCase_ (					)							->					Clause:




						'''simple docstring'''



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





def 			lowerCamelCase_ (					)							->					Formula:




						'''simple docstring'''



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





def 			lowerCamelCase_ (					__lowerCAmelCase				)							->					tuple[list[Clause], list[str]]:




						'''simple docstring'''



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





def 			lowerCamelCase_ (					__lowerCAmelCase   ,    __lowerCAmelCase   ,    __lowerCAmelCase				)							->					tuple[list[str], dict[str, bool | None]]:




						'''simple docstring'''



						lowerCamelCase__					=[]
						lowerCamelCase__					={}
						lowerCamelCase__					=[]

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

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





def 			lowerCamelCase_ (					__lowerCAmelCase   ,    __lowerCAmelCase				)							->					tuple[list[str], dict[str, bool | None]]:




						'''simple docstring'''



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

						return unit_symbols, assignment





def 			lowerCamelCase_ (					__lowerCAmelCase   ,    __lowerCAmelCase   ,    __lowerCAmelCase				)							->					tuple[bool | None, dict[str, bool | None] | None]:




						'''simple docstring'''



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

						if check_clause_all_true:
												return True, model

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

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

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

						return dpll_algorithm(__lowerCAmelCase   ,    __lowerCAmelCase   ,    __lowerCAmelCase				) or dpll_algorithm(__lowerCAmelCase   ,    __lowerCAmelCase   ,    __lowerCAmelCase				)


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	a							=generate_formula()
	print(F'''The formula {formula} is''', end=' ')

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

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








'''simple docstring'''



from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available


UpperCAmelCase_				:     Dict     			=						{
    '''configuration_markuplm''': ['''MARKUPLM_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''MarkupLMConfig'''],
    '''feature_extraction_markuplm''': ['''MarkupLMFeatureExtractor'''],
    '''processing_markuplm''': ['''MarkupLMProcessor'''],
    '''tokenization_markuplm''': ['''MarkupLMTokenizer'''],
}

try:
     if not is_tokenizers_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     UpperCAmelCase_				:     List[Any]     			=						['''MarkupLMTokenizerFast''']

try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     UpperCAmelCase_				:     int     			=						[
         '''MARKUPLM_PRETRAINED_MODEL_ARCHIVE_LIST''',
         '''MarkupLMForQuestionAnswering''',
         '''MarkupLMForSequenceClassification''',
         '''MarkupLMForTokenClassification''',
         '''MarkupLMModel''',
         '''MarkupLMPreTrainedModel''',
     ]


if TYPE_CHECKING:
     from .configuration_markuplm import MARKUPLM_PRETRAINED_CONFIG_ARCHIVE_MAP, MarkupLMConfig
     from .feature_extraction_markuplm import MarkupLMFeatureExtractor
     from .processing_markuplm import MarkupLMProcessor
     from .tokenization_markuplm import MarkupLMTokenizer

     try:
          if not is_tokenizers_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .tokenization_markuplm_fast import MarkupLMTokenizerFast

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_markuplm import (
              MARKUPLM_PRETRAINED_MODEL_ARCHIVE_LIST,
              MarkupLMForQuestionAnswering,
              MarkupLMForSequenceClassification,
              MarkupLMForTokenClassification,
              MarkupLMModel,
              MarkupLMPreTrainedModel,
          )


else:
     import sys

     UpperCAmelCase_				:     Dict     			=						_LazyModule(__name__, globals()['''__file__'''], _import_structure)






