






"""simple docstring"""







from __future__ import annotations

import random
from collections.abc import Iterable







class 							_SCREAMING_SNAKE_CASE    :





							"""simple docstring"""





							def __init__( self:  Union[str, Any]					,		__A:  list[str]     ):

												'''simple docstring'''

												a__ 							=	{literal: None for literal in literals}




							def __str__( self:  int     ):

												'''simple docstring'''

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




							def __len__( self:  Optional[Any]     ):

												'''simple docstring'''

												return len(self.literals     )




							def 			lowercase		( self:  List[str]					,		__A:  dict[str, bool | None]     ):

												'''simple docstring'''

												for literal in self.literals:
																	a__ 							=	literal[:2]
																	if symbol in model:
																						a__ 							=	model[symbol]
																	else:
																						continue
																	if value is not None:
																						# Complement assignment if literal is in complemented form
																						if literal.endswith('''\''''     ):
																											a__ 							=	not value
																	a__ 							=	value





							def 			lowercase		( self:  Any					,		__A:  dict[str, bool | None]     ):

												'''simple docstring'''

												for literal in self.literals:
																	a__ 							=	literal.rstrip('''\''''     ) if literal.endswith('''\''''     ) else literal + '''\''''
																	if symbol in self.literals:
																						return True

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







class 							_SCREAMING_SNAKE_CASE    :





							"""simple docstring"""





							def __init__( self:  List[Any]					,		__A:  Iterable[Clause]     ):

												'''simple docstring'''

												a__ 							=	list(__A     )





							def __str__( self:  Optional[Any]     ):

												'''simple docstring'''

												return "{" + " , ".join(str(__A     ) for clause in self.clauses     ) + "}"





def 							SCREAMING_SNAKE_CASE							(   ):
					a__ 							=	[]
					a__ 							=	random.randint(1			,  5)
					a__ 							=	'''A'''
					a__ 							=	0
					while i < no_of_literals:
										a__ 							=	random.randint(1			,  5)
										a__ 							=	base_var + str(lowerCamelCase_)
										a__ 							=	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 							SCREAMING_SNAKE_CASE							(   ):
					a__ 							=	set()
					a__ 							=	random.randint(1			,  10)
					while len(lowerCamelCase_) < no_of_clauses:
										clauses.add(generate_clause())
					return Formula(lowerCamelCase_)





def 							SCREAMING_SNAKE_CASE							(   lowerCamelCase_):
					a__ 							=	formula.clauses
					a__ 							=	[]
					for clause in formula.clauses:
										for literal in clause.literals:
															a__ 							=	literal[:2]
															if symbol not in symbols_set:
																				symbols_set.append(lowerCamelCase_)
					return clauses, symbols_set





def 							SCREAMING_SNAKE_CASE							(   lowerCamelCase_			,  lowerCamelCase_			,  lowerCamelCase_):
					a__ 							=	[]
					a__ 							=	{}
					a__ 							=	[]

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

					for s in symbols:
										a__ 							=	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:
										a__ 							=	None
					for s in pure_symbols:
										a__ 							=	s + '''\''''
										if s in literals:
															a__ 							=	True
										elif sym in literals:
															a__ 							=	False
					return pure_symbols, assignment





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

					return unit_symbols, assignment





def 							SCREAMING_SNAKE_CASE							(   lowerCamelCase_			,  lowerCamelCase_			,  lowerCamelCase_):
					a__ 							=	True
					for clause in clauses:
										a__ 							=	clause.evaluate(lowerCamelCase_)
										if clause_check is False:
															return False, None
										elif clause_check is None:
															a__ 							=	False
															continue

					if check_clause_all_true:
										return True, model

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

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

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

					return dpll_algorithm(lowerCamelCase_			,  lowerCamelCase_			,  lowerCamelCase_) or dpll_algorithm(lowerCamelCase_			,  lowerCamelCase_			,  lowerCamelCase_)


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	__a							:						Dict   							=			generate_formula()
	print(F'''The formula {formula} is''', end=' ')

	__a							,			__a							:						List[Any]   							=			generate_parameters(formula)
	__a							,			__a							:						int   							=			dpll_algorithm(clauses, symbols, {})

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










"""simple docstring"""







from __future__ import annotations

from collections.abc import Iterator
from typing import Any







class 							_SCREAMING_SNAKE_CASE    :





							"""simple docstring"""





							def __init__( self:  Optional[int]					,		__A:  Any     ):

												'''simple docstring'''

												a__ 							=	data
												a__ 							=	None





							def __str__( self:  str     ):

												'''simple docstring'''

												return F'{self.data}'







class 							_SCREAMING_SNAKE_CASE    :





							"""simple docstring"""





							def __init__( self:  int     ):

												'''simple docstring'''

												a__ 							=	None
												a__ 							=	None




							def __iter__( self:  Tuple     ):

												'''simple docstring'''

												a__ 							=	self.front
												while node:
																	yield node.data
																	a__ 							=	node.next




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

												'''simple docstring'''

												return len(tuple(iter(self     )     )     )




							def __str__( self:  Any     ):

												'''simple docstring'''

												return " <- ".join(str(__A     ) for item in self     )




							def 			lowercase		( self:  Any     ):

												'''simple docstring'''

												return len(self     ) == 0




							def 			lowercase		( self:  Tuple					,		__A:  Any     ):

												'''simple docstring'''

												a__ 							=	Node(__A     )
												if self.is_empty():
																	a__ 							=	a__ 							=	node
												else:
																	assert isinstance(self.rear					,		__A     )
																	a__ 							=	node
																	a__ 							=	node




							def 			lowercase		( self:  List[Any]     ):

												'''simple docstring'''

												if self.is_empty():
																	raise IndexError('''dequeue from empty queue'''     )
												assert isinstance(self.front					,		__A     )
												a__ 							=	self.front
												a__ 							=	self.front.next
												if self.front is None:
																	a__ 							=	None
												return node.data





							def 			lowercase		( self:  Dict     ):

												'''simple docstring'''

												a__ 							=	a__ 							=	None


if __name__ == "__main__":
	from doctest import testmod

	testmod()


