





'''simple docstring'''



from __future__ import annotations

import random
from collections.abc import Iterable






class 							__lowercase				:







	'''simple docstring'''

	def __init__(self   ,_lowerCamelCase       )							->							None:







				'''simple docstring'''





				__lowercase   =							{literal: None for literal in literals}


	def __str__(self       )							->							str:







				'''simple docstring'''





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


	def __len__(self       )							->							int:







				'''simple docstring'''





				return len(self.literals       )


	def   _UpperCAmelCase   (self   ,_lowerCamelCase       )							->							None:







				'''simple docstring'''





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


	def   _UpperCAmelCase   (self   ,_lowerCamelCase       )							->							bool | None:







				'''simple docstring'''





				for literal in self.literals:
							__lowercase   =							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 							__lowercase				:







	'''simple docstring'''

	def __init__(self   ,_lowerCamelCase       )							->							None:







				'''simple docstring'''





				__lowercase   =							list(_lowerCamelCase       )


	def __str__(self       )							->							str:







				'''simple docstring'''





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





def       _lowerCAmelCase  ( ):
			__lowercase   =							[]
			__lowercase   =							random.randint(1						,				5 )
			__lowercase   =							'''A'''
			__lowercase   =							0
			while i < no_of_literals:
						__lowercase   =							random.randint(1						,				5 )
						__lowercase   =							base_var + str(lowerCamelCase_ )
						__lowercase   =							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  ( ):
			__lowercase   =							set()
			__lowercase   =							random.randint(1						,				1_0 )
			while len(lowerCamelCase_ ) < no_of_clauses:
						clauses.add(generate_clause() )
			return Formula(lowerCamelCase_ )




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




def       _lowerCAmelCase  ( lowerCamelCase_	:     list[Clause]						,				lowerCamelCase_	:     list[str]						,				lowerCamelCase_	:     dict[str, bool | None] ):
			__lowercase   =							[]
			__lowercase   =							{}
			__lowercase   =							[]

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

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




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

			return unit_symbols, assignment




def       _lowerCAmelCase  ( lowerCamelCase_	:     list[Clause]						,				lowerCamelCase_	:     list[str]						,				lowerCamelCase_	:     dict[str, bool | None] ):
			__lowercase   =							True
			for clause in clauses:
						__lowercase   =							clause.evaluate(lowerCamelCase_ )
						if clause_check is False:
									return False, None
						elif clause_check is None:
									__lowercase   =							False
									continue

			if check_clause_all_true:
						return True, model

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

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

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

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


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	_SCREAMING_SNAKE_CASE    =			generate_formula()
	print(f'''The formula {formula} is''', end=''' ''')

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

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












'''simple docstring'''



import math




def       _lowerCAmelCase  ( lowerCamelCase_	:     int ):

			if 1 < number < 4:
						# 2 and 3 are primes
						return True
			elif number < 2 or number % 2 == 0 or number % 3 == 0:
						# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
						return False

			# All primes number are in format of 6k +/- 1
			for i in range(5						,				int(math.sqrt(lowerCamelCase_ ) + 1 )						,				6 ):
						if number % i == 0 or number % (i + 2) == 0:
									return False
			return True




def       _lowerCAmelCase  ( lowerCamelCase_	:     int = 6_0_0_8_5_1_4_7_5_1_4_3 ):

			try:
						__lowercase   =							int(lowerCamelCase_ )
			except (TypeError, ValueError):
						raise TypeError('''Parameter n must be int or castable to int.''' )
			if n <= 0:
						raise ValueError('''Parameter n must be greater than or equal to one.''' )
			__lowercase   =							0
			if is_prime(lowerCamelCase_ ):
						return n
			while n % 2 == 0:
						n //= 2
			if is_prime(lowerCamelCase_ ):
						return n
			for i in range(3						,				int(math.sqrt(lowerCamelCase_ ) ) + 1						,				2 ):
						if n % i == 0:
									if is_prime(n // i ):
												__lowercase   =							n // i
												break
									elif is_prime(lowerCamelCase_ ):
												__lowercase   =							i
			return max_number


if __name__ == "__main__":
	print(f'''{solution() = }''')





