



"""simple docstring"""
from __future__ import annotations

import random
from collections.abc import Iterable
class    a		:



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


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_:	dict[str, bool | None]            ={literal: None for literal in literals}



  def __str__(  self	:   List[str]						)       ->   str:


     '''simple docstring'''




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



  def __len__(  self	:   int						)       ->   int:


     '''simple docstring'''




     return len(self.literals						)



  def 		lowerCamelCase__    (  self	:   Tuple    ,						lowerCAmelCase	:   dict[str, bool | None]						)       ->   None:


     '''simple docstring'''




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





  def 		lowerCamelCase__    (  self	:   List[Any]    ,						lowerCAmelCase	:   dict[str, bool | None]						)       ->   bool | None:


     '''simple docstring'''




     for literal in self.literals:
        SCREAMING_SNAKE_CASE_:	List[Any]            =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    a		:



  def __init__(  self	:   Tuple    ,						lowerCAmelCase	:   Iterable[Clause]						)       ->   None:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_:	int            =list(lowerCAmelCase						)





  def __str__(  self	:   Any						)       ->   str:


     '''simple docstring'''




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







def        __magic_name__			(							):
   SCREAMING_SNAKE_CASE_:	Tuple            =[]
   SCREAMING_SNAKE_CASE_:	Optional[int]            =random.randint(1							,     5	)
   SCREAMING_SNAKE_CASE_:	Any            ="""A"""
   SCREAMING_SNAKE_CASE_:	Union[str, Any]            =0
   while i < no_of_literals:
      SCREAMING_SNAKE_CASE_:	Dict            =random.randint(1							,     5	)
      SCREAMING_SNAKE_CASE_:	int            =base_var + str(lowercase	)
      SCREAMING_SNAKE_CASE_:	int            =random.randint(0							,     1	)
      if var_complement == 1:
         var_name += "'"
      if var_name in literals:
         i -= 1
      else:
         literals.append(lowercase	)
      i += 1
   return Clause(lowercase	)





def        __magic_name__			(							):
   SCREAMING_SNAKE_CASE_:	set[Clause]            =set()
   SCREAMING_SNAKE_CASE_:	Optional[int]            =random.randint(1							,     10	)
   while len(lowercase	) < no_of_clauses:
      clauses.add(generate_clause()	)
   return Formula(lowercase	)





def        __magic_name__			(							lowercase	):
   SCREAMING_SNAKE_CASE_:	Optional[int]            =formula.clauses
   SCREAMING_SNAKE_CASE_:	Optional[int]            =[]
   for clause in formula.clauses:
      for literal in clause.literals:
         SCREAMING_SNAKE_CASE_:	List[str]            =literal[:2]
         if symbol not in symbols_set:
            symbols_set.append(lowercase	)
   return clauses, symbols_set





def        __magic_name__			(							lowercase							,     lowercase							,     lowercase	):
   SCREAMING_SNAKE_CASE_:	Union[str, Any]            =[]
   SCREAMING_SNAKE_CASE_:	dict[str, bool | None]            ={}
   SCREAMING_SNAKE_CASE_:	Optional[Any]            =[]

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

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





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

   return unit_symbols, assignment





def        __magic_name__			(							lowercase							,     lowercase							,     lowercase	):
   SCREAMING_SNAKE_CASE_:	Dict            =True
   for clause in clauses:
      SCREAMING_SNAKE_CASE_:	Dict            =clause.evaluate(lowercase	)
      if clause_check is False:
         return False, None
      elif clause_check is None:
         SCREAMING_SNAKE_CASE_:	Union[str, Any]            =False
         continue

   if check_clause_all_true:
      return True, model

   try:
      SCREAMING_SNAKE_CASE_     ,						SCREAMING_SNAKE_CASE_:	Optional[int]            =find_pure_symbols(lowercase							,     lowercase							,     lowercase	)
   except RecursionError:
      print("""raises a RecursionError and is"""	)
      return None, {}
   SCREAMING_SNAKE_CASE_:	Dict            =None
   if len(lowercase	) > 0:
      SCREAMING_SNAKE_CASE_     ,						SCREAMING_SNAKE_CASE_:	Any            =pure_symbols[0], assignment[pure_symbols[0]]

   if p:
      SCREAMING_SNAKE_CASE_:	Optional[Any]            =model
      SCREAMING_SNAKE_CASE_:	Optional[Any]            =value
      SCREAMING_SNAKE_CASE_:	int            =list(lowercase	)
      if p in tmp_symbols:
         tmp_symbols.remove(lowercase	)
      return dpll_algorithm(lowercase							,     lowercase							,     lowercase	)

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

   return dpll_algorithm(lowercase							,     lowercase							,     lowercase	) or dpll_algorithm(lowercase							,     lowercase							,     lowercase	)


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"""
from typing import List

from tokenizers import NormalizedString, PreTokenizedString, normalizers
class    a		:



  def __init__(  self	:   Optional[Any]    ,						lowerCAmelCase	:   List[str]						)       ->   None:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_:	int            =vocab
     SCREAMING_SNAKE_CASE_:	Union[str, Any]            =normalizers.BertNormalizer(
         clean_text=lowerCAmelCase    ,						handle_chinese_chars=lowerCAmelCase    ,						strip_accents=lowerCAmelCase    ,						lowercase=lowerCAmelCase    ,						)
     try:
        import rjieba
     except ImportError:
        raise ImportError(
            """You need to install rjieba to use RoFormerTokenizer. """
            """See https://pypi.org/project/rjieba/ for installation."""						)
     SCREAMING_SNAKE_CASE_:	Dict            =rjieba



  def 		lowerCamelCase__    (  self	:   Tuple    ,						lowerCAmelCase	:   int    ,						lowerCAmelCase	:   NormalizedString						)       ->   List[NormalizedString]:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_:	Optional[int]            =[]

     # this code slice normalized_string is too slow (6s) but test_alignement_methods can pass
     for token, start, end in self.jieba.tokenize(str(lowerCAmelCase						)    ,						hmm=lowerCAmelCase						):
        if token in self.vocab:
           splits.append(normalized_string[start:end]						)
        else:
           SCREAMING_SNAKE_CASE_:	List[Any]            =self.normalizers.normalize_str(lowerCAmelCase						).split()
           for token in token_list:
              if token:
                 SCREAMING_SNAKE_CASE_:	Dict            =start + len(lowerCAmelCase						)
                 splits.append(normalized_string[start:end]						)
                 SCREAMING_SNAKE_CASE_:	Optional[Any]            =end

        # this code test_alignement_methods can't pass but fast (300ms)
        # for token in self.jieba.cut(str(normalized_string), False):
        #     if token in self.vocab:
        #         splits.append(NormalizedString(token))
        #     else:
        #         token_list = self.normalizers.normalize_str(token).split()
        #         for token in token_list:
        #             if token:
        #                 splits.append(NormalizedString(token))

     return splits





  def 		lowerCamelCase__    (  self	:   Union[str, Any]    ,						lowerCAmelCase	:   PreTokenizedString						)       ->   Tuple:


     '''simple docstring'''




     pretok.split(self.jieba_split						)



