
from __future__ import annotations

import random
from collections.abc import Iterable

class 		lowercase_       :

 def __init__(      self     ,	__UpperCamelCase     ):




        """simple docstring"""


        UpperCamelCase_							       =       {literal: None for literal in literals}

 def __str__(      self     ):




        """simple docstring"""


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

 def __len__(      self     ):




        """simple docstring"""


        return len(self.literals     )

 def lowerCamelCase_				(      self     ,	__UpperCamelCase     ):




        """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     ,	__UpperCamelCase     ):




        """simple docstring"""


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

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



class 		lowercase_       :

 def __init__(      self     ,	__UpperCamelCase     ):




        """simple docstring"""


        UpperCamelCase_							       =       list(__UpperCamelCase     )

 def __str__(      self     ):




        """simple docstring"""


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




def 				lowerCamelCase__				(						)		->	Clause:
       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 				lowerCamelCase__				(						)		->	Formula:
       UpperCamelCase_							       =       set()
       UpperCamelCase_							       =       random.randint(1	,      10     )
       while len(a__     ) < no_of_clauses:
              clauses.add(generate_clause()     )
       return Formula(a__     )




def 				lowerCamelCase__				(						a__  :  Formula     )		->	tuple[list[Clause], list[str]]:
       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 				lowerCamelCase__				(						a__  :  list[Clause]	,      a__  :  list[str]	,      a__  :  dict[str, bool | None]     )		->	tuple[list[str], dict[str, bool | None]]:
       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 				lowerCamelCase__				(						a__  :  list[Clause]	,      a__  :  dict[str, bool | None]     )		->	tuple[list[str], dict[str, bool | None]]:
       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 				lowerCamelCase__				(						a__  :  list[Clause]	,      a__  :  list[str]	,      a__  :  dict[str, bool | None]     )		->	tuple[bool | None, dict[str, bool | None] | None]:
       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()

      _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 				lowerCamelCase__				(						a__  :  int     )		->	str:
       UpperCamelCase_							       =       1
       UpperCamelCase_							       =       0
       UpperCamelCase_							       =       1
       UpperCamelCase_							       =       1
       UpperCamelCase_							       =       3
       UpperCamelCase_							       =       3
       UpperCamelCase_							       =       limit
       UpperCamelCase_							       =       0

       UpperCamelCase_							       =       """"""
       while counter != decimal + 1:
              if 4 * q + r - t < n * t:
                     result += str(a__     )
                     if counter == 0:
                            result += "."

                     if decimal == counter:
                            break

                     counter += 1
                     UpperCamelCase_							       =       10 * (r - n * t)
                     UpperCamelCase_							       =       ((10 * (3 * q + r)) // t) - 10 * n
                     q *= 10
                     UpperCamelCase_							       =       nr
              else:
                     UpperCamelCase_							       =       (2 * q + r) * l
                     UpperCamelCase_							       =       (q * (7 * k) + 2 + (r * l)) // (t * l)
                     q *= k
                     t *= l
                     l += 2
                     k += 1
                     UpperCamelCase_							       =       nn
                     UpperCamelCase_							       =       nr
       return result




def 				lowerCamelCase__				(						)		->	None:
       print(f'''{calculate_pi(50     ) = }'''     )
       import doctest

       doctest.testmod()


if __name__ == "__main__":
      main()



