


from __future__ import annotations

import random
from collections.abc import Iterable

class 						snake_case			:
			'''simple docstring'''

			def __init__(	self     :     str							,							lowerCAmelCase_     :     list[str]					)					->					None:




								"""simple docstring"""






								SCREAMING_SNAKE_CASE_	      =       {literal: None for literal in literals}

			def __str__(	self     :     Dict					)					->					str:




								"""simple docstring"""






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

			def __len__(	self     :     List[str]					)					->					int:




								"""simple docstring"""






								return len(self.literals					)

			def _lowercase (	self     :     Optional[Any]							,							lowerCAmelCase_     :     dict[str, bool | None]					)					->					None:




								"""simple docstring"""






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




			def _lowercase (	self     :     Optional[Any]							,							lowerCAmelCase_     :     dict[str, bool | None]					)					->					bool | None:




								"""simple docstring"""






								for literal in self.literals:
													SCREAMING_SNAKE_CASE_	      =       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 						snake_case			:
			'''simple docstring'''

			def __init__(	self     :     Any							,							lowerCAmelCase_     :     Iterable[Clause]					)					->					None:




								"""simple docstring"""






								SCREAMING_SNAKE_CASE_	      =       list(lowerCAmelCase_					)




			def __str__(	self     :     Union[str, Any]					)					->					str:




								"""simple docstring"""






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







def 							UpperCAmelCase				(     )->		Clause:







					'''simple docstring'''



					SCREAMING_SNAKE_CASE_	      =       []
					SCREAMING_SNAKE_CASE_	      =       random.randint(1				,5      )
					SCREAMING_SNAKE_CASE_	      =       '''A'''
					SCREAMING_SNAKE_CASE_	      =       0
					while i < no_of_literals:
										SCREAMING_SNAKE_CASE_	      =       random.randint(1				,5      )
										SCREAMING_SNAKE_CASE_	      =       base_var + str(UpperCAmelCase      )
										SCREAMING_SNAKE_CASE_	      =       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 							UpperCAmelCase				(     )->		Formula:







					'''simple docstring'''



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







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







					'''simple docstring'''



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







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







					'''simple docstring'''



					SCREAMING_SNAKE_CASE_	      =       []
					SCREAMING_SNAKE_CASE_	      =       {}
					SCREAMING_SNAKE_CASE_	      =       []

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

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







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







					'''simple docstring'''



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

					return unit_symbols, assignment







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







					'''simple docstring'''



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

					if check_clause_all_true:
										return True, model

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

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

					SCREAMING_SNAKE_CASE_      ,SCREAMING_SNAKE_CASE_	      =       find_unit_clauses(UpperCAmelCase				,UpperCAmelCase      )
					SCREAMING_SNAKE_CASE_	      =       None
					if len(UpperCAmelCase      ) > 0:
										SCREAMING_SNAKE_CASE_      ,SCREAMING_SNAKE_CASE_	      =       unit_symbols[0], assignment[unit_symbols[0]]
					if p:
										SCREAMING_SNAKE_CASE_	      =       model
										SCREAMING_SNAKE_CASE_	      =       value
										SCREAMING_SNAKE_CASE_	      =       list(UpperCAmelCase      )
										if p in tmp_symbols:
															tmp_symbols.remove(UpperCAmelCase      )
										return dpll_algorithm(UpperCAmelCase				,UpperCAmelCase				,UpperCAmelCase      )
					SCREAMING_SNAKE_CASE_	      =       symbols[0]
					SCREAMING_SNAKE_CASE_	      =       symbols[1:]
					SCREAMING_SNAKE_CASE_      ,SCREAMING_SNAKE_CASE_	      =       model, model
					SCREAMING_SNAKE_CASE_      ,SCREAMING_SNAKE_CASE_	      =       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_							,A_														=      generate_parameters(formula)
		A_							,A_														=      dpll_algorithm(clauses, symbols, {})

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






def 							UpperCAmelCase				(     UpperCAmelCase      )->		bool:







					'''simple docstring'''



					if not isinstance(UpperCAmelCase				,UpperCAmelCase      ):
										SCREAMING_SNAKE_CASE_	      =       f'''Input value of [number={number}] must be an integer'''
										raise TypeError(UpperCAmelCase      )
					if number < 0 or number % 2 == 1:
										return False
					SCREAMING_SNAKE_CASE_	      =       int(number**0.5      )
					return number == number_sqrt * (number_sqrt + 1)


if __name__ == "__main__":
		import doctest

		doctest.testmod()


