




from __future__ import annotations

import random
from collections.abc import Iterable







class __snake_case     :







   def __init__( self						:		List[str]   ,		_snake_case						:		list[str]):

        """simple docstring"""


        UpperCAmelCase_		=				{literal: None for literal in literals}







   def __str__( self						:		Dict):

        """simple docstring"""


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







   def __len__( self						:		Optional[int]):

        """simple docstring"""


        return len(self.literals)







   def lowerCamelCase		( self						:		int   ,		_snake_case						:		dict[str, bool | None]):

        """simple docstring"""


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







   def lowerCamelCase		( self						:		Union[str, Any]   ,		_snake_case						:		dict[str, bool | None]):

        """simple docstring"""


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

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







class __snake_case     :







   def __init__( self						:		List[str]   ,		_snake_case						:		Iterable[Clause]):

        """simple docstring"""


        UpperCAmelCase_		=				list(_snake_case)







   def __str__( self						:		str):

        """simple docstring"""


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







def   A		()  -> Clause:







     """simple docstring"""


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


def   A		()  -> Formula:







     """simple docstring"""


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


def   A		(__A  :       Formula			)  -> tuple[list[Clause], list[str]]:







     """simple docstring"""


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


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







     """simple docstring"""


     UpperCAmelCase_		=				[]
     UpperCAmelCase_		=				{}
     UpperCAmelCase_		=				[]

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

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


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







     """simple docstring"""


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

     return unit_symbols, assignment


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







     """simple docstring"""


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

     if check_clause_all_true:
          return True, model

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

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

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

     return dpll_algorithm(__A  ,							__A  ,							__A			) or dpll_algorithm(__A  ,							__A  ,							__A			)


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    snake_case_					:					Union[str, Any]       						=			generate_formula()
    print(f"The formula {formula} is", end=" ")

    snake_case_						,			snake_case_					:					Tuple       						=			generate_parameters(formula)
    snake_case_						,			snake_case_					:					Optional[Any]       						=			dpll_algorithm(clauses, symbols, {})

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












from .stack import Stack


def   A		(__A  :       str			)  -> bool:







     """simple docstring"""


     UpperCAmelCase_		=				Stack()
     UpperCAmelCase_		=				{'''(''': ''')''', '''[''': ''']''', '''{''': '''}'''}
     for bracket in parentheses:
          if bracket in bracket_pairs:
               stack.push(__A			)
          elif bracket in (")", "]", "}"):
               if stack.is_empty() or bracket_pairs[stack.pop()] != bracket:
                    return False
     return stack.is_empty()


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

    testmod()

    snake_case_					:					Dict       						=			["((()))", "((())", "(()))"]
    print("Balanced parentheses demonstration:\n")
    for example in examples:
        snake_case_					:					Optional[int]       						=			"" if balanced_parentheses(example) else "not "
        print(f"{example} is {not_str}balanced")






