






"""simple docstring"""





from __future__ import annotations

import random
from collections.abc import Iterable







class 		_a       :





   '''simple docstring'''






   def __init__(   self			,				UpperCAmelCase_)	-> None:




          '''simple docstring'''




          lowercase__:    dict[str, bool | None]        =      {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 __lowercase    (   self			,				UpperCAmelCase_)	-> None:




          '''simple docstring'''




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





   def __lowercase    (   self			,				UpperCAmelCase_)	-> bool | None:




          '''simple docstring'''




          for literal in self.literals:
                 lowercase__:    Union[str, Any]        =      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 		_a       :





   '''simple docstring'''






   def __init__(   self			,				UpperCAmelCase_)	-> None:




          '''simple docstring'''




          lowercase__:    Tuple        =      list(UpperCAmelCase_)





   def __str__(   self)	-> str:




          '''simple docstring'''




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







def     A(  ):
       """simple docstring"""





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






def     A(  ):
       """simple docstring"""





       lowercase__:    set[Clause]        =      set()
       lowercase__:    str        =      random.randint(1						,       10		)
       while len(snake_case_		) < no_of_clauses:
              clauses.add(generate_clause()		)
       return Formula(snake_case_		)






def     A(  snake_case_		):
       """simple docstring"""





       lowercase__:    Optional[int]        =      formula.clauses
       lowercase__:    Dict        =      []
       for clause in formula.clauses:
              for literal in clause.literals:
                     lowercase__:    Optional[int]        =      literal[:2]
                     if symbol not in symbols_set:
                            symbols_set.append(snake_case_		)
       return clauses, symbols_set






def     A(  snake_case_						,       snake_case_						,       snake_case_		):
       """simple docstring"""





       lowercase__:    str        =      []
       lowercase__:    dict[str, bool | None]        =      {}
       lowercase__:    List[str]        =      []

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

       for s in symbols:
              lowercase__:    Union[str, Any]        =      s + "'"
              if (s in literals and sym not in literals) or (
                  s not in literals and sym in literals
              ):
                     pure_symbols.append(snake_case_		)
       for p in pure_symbols:
              lowercase__:    List[Any]        =      None
       for s in pure_symbols:
              lowercase__:    int        =      s + "'"
              if s in literals:
                     lowercase__:    str        =      True
              elif sym in literals:
                     lowercase__:    Dict        =      False
       return pure_symbols, assignment






def     A(  snake_case_						,       snake_case_		):
       """simple docstring"""





       lowercase__:    Any        =      []
       for clause in clauses:
              if len(snake_case_		) == 1:
                     unit_symbols.append(list(clause.literals.keys()		)[0]		)
              else:
                     lowercase__:    Union[str, Any]        =      0, 0
                     for literal, value in clause.literals.items():
                            if value is False:
                                   f_count += 1
                            elif value is None:
                                   lowercase__:    List[str]        =      literal
                                   n_count += 1
                     if f_count == len(snake_case_		) - 1 and n_count == 1:
                            unit_symbols.append(snake_case_		)
       lowercase__:    dict[str, bool | None]        =      {}
       for i in unit_symbols:
              lowercase__:    Any        =      i[:2]
              lowercase__:    List[Any]        =      len(snake_case_		) == 2
       lowercase__:    int        =      [i[:2] for i in unit_symbols]

       return unit_symbols, assignment






def     A(  snake_case_						,       snake_case_						,       snake_case_		):
       """simple docstring"""





       lowercase__:    Any        =      True
       for clause in clauses:
              lowercase__:    int        =      clause.evaluate(snake_case_		)
              if clause_check is False:
                     return False, None
              elif clause_check is None:
                     lowercase__:    Dict        =      False
                     continue

       if check_clause_all_true:
              return True, model

       try:
              lowercase__:    Any        =      find_pure_symbols(snake_case_						,       snake_case_						,       snake_case_		)
       except RecursionError:
              print("raises a RecursionError and is"		)
              return None, {}
       lowercase__:    List[str]        =      None
       if len(snake_case_		) > 0:
              lowercase__:    str        =      pure_symbols[0], assignment[pure_symbols[0]]

       if p:
              lowercase__:    Union[str, Any]        =      model
              lowercase__:    List[str]        =      value
              lowercase__:    Optional[int]        =      list(snake_case_		)
              if p in tmp_symbols:
                     tmp_symbols.remove(snake_case_		)
              return dpll_algorithm(snake_case_						,       snake_case_						,       snake_case_		)

       lowercase__:    Tuple        =      find_unit_clauses(snake_case_						,       snake_case_		)
       lowercase__:    Dict        =      None
       if len(snake_case_		) > 0:
              lowercase__:    List[Any]        =      unit_symbols[0], assignment[unit_symbols[0]]
       if p:
              lowercase__:    Optional[Any]        =      model
              lowercase__:    Any        =      value
              lowercase__:    Tuple        =      list(snake_case_		)
              if p in tmp_symbols:
                     tmp_symbols.remove(snake_case_		)
              return dpll_algorithm(snake_case_						,       snake_case_						,       snake_case_		)
       lowercase__:    str        =      symbols[0]
       lowercase__:    Dict        =      symbols[1:]
       lowercase__:    str        =      model, model
       lowercase__:    Tuple        =      True, False

       return dpll_algorithm(snake_case_						,       snake_case_						,       snake_case_		) or dpll_algorithm(snake_case_						,       snake_case_						,       snake_case_		)


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  UpperCamelCase			=      generate_formula()
  print(F"The formula {formula} is", end=""" """)

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

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














"""simple docstring"""





class 		_a       :





   '''simple docstring'''






   def __init__(   self			,				UpperCAmelCase_=None)	-> List[Any]:




          '''simple docstring'''




          lowercase__:    str        =      data
          lowercase__:    Any        =      None





   def __repr__(   self)	-> Optional[Any]:




          '''simple docstring'''




          lowercase__:    Any        =      ""
          lowercase__:    Dict        =      self
          while temp:
                 string_rep += F"""<{temp.data}> ---> """
                 lowercase__:    Tuple        =      temp.next
          string_rep += "<END>"
          return string_rep







def     A(  snake_case_		):
       """simple docstring"""





       if not elements_list:
              raise Exception("The Elements List is empty"		)

       # Set first element as Head
       lowercase__:    Any        =      Node(elements_list[0]		)
       lowercase__:    Optional[int]        =      head
       # Loop through elements from position 1
       for data in elements_list[1:]:
              lowercase__:    Dict        =      Node(snake_case_		)
              lowercase__:    Dict        =      current.next
       return head


UpperCamelCase			=      [1, 3, 5, 32, 44, 12, 43]
print(F"List: {list_data}")
print("""Creating Linked List from List.""")
UpperCamelCase			=      make_linked_list(list_data)
print("""Linked List:""")







print(linked_list)






