






'''simple docstring'''
from __future__ import annotations

import random
from collections.abc import Iterable


class     _UpperCAmelCase  :




    def __init__(     self					:    int					,       a					:    list[str]     ):






       '''simple docstring'''






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




    def __str__(     self					:    Optional[Any]     ):






       '''simple docstring'''






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




    def __len__(     self					:    Optional[int]     ):






       '''simple docstring'''






       return len(self.literals     )




    def 			lowerCAmelCase__			(     self					:    Dict					,       a					:    dict[str, bool | None]     ):






       '''simple docstring'''






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





    def 			lowerCAmelCase__			(     self					:    List[str]					,       a					:    dict[str, bool | None]     ):






       '''simple docstring'''






       for literal in self.literals:
          lowercase_		:      List[Any]          =       literal.rstrip("'"     ) if literal.endswith("'"     ) else literal + "'"
          if symbol in self.literals:
             return True

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


class     _UpperCAmelCase  :




    def __init__(     self					:    Union[str, Any]					,       a					:    Iterable[Clause]     ):






       '''simple docstring'''






       lowercase_		:      str          =       list(a     )





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






       '''simple docstring'''






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




def 						__SCREAMING_SNAKE_CASE   (					):


   """simple docstring"""




   lowercase_		:      Any          =       []
   lowercase_		:      List[Any]          =       random.randint(1  ,						5							)
   lowercase_		:      Tuple          =       "A"
   lowercase_		:      Optional[Any]          =       0
   while i < no_of_literals:
      lowercase_		:      Tuple          =       random.randint(1  ,						5							)
      lowercase_		:      Any          =       base_var + str(_UpperCamelCase							)
      lowercase_		:      Any          =       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 						__SCREAMING_SNAKE_CASE   (					):


   """simple docstring"""




   lowercase_		:      set[Clause]          =       set()
   lowercase_		:      int          =       random.randint(1  ,						10							)
   while len(_UpperCamelCase							) < no_of_clauses:
      clauses.add(generate_clause()							)
   return Formula(_UpperCamelCase							)




def 						__SCREAMING_SNAKE_CASE   (					_UpperCamelCase							):


   """simple docstring"""




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




def 						__SCREAMING_SNAKE_CASE   (					_UpperCamelCase  ,						_UpperCamelCase  ,						_UpperCamelCase							):


   """simple docstring"""




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

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

   for s in symbols:
      lowercase_		:      List[str]          =       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:
      lowercase_		:      Optional[Any]          =       None
   for s in pure_symbols:
      lowercase_		:      Optional[Any]          =       s + "'"
      if s in literals:
         lowercase_		:      Tuple          =       True
      elif sym in literals:
         lowercase_		:      str          =       False
   return pure_symbols, assignment




def 						__SCREAMING_SNAKE_CASE   (					_UpperCamelCase  ,						_UpperCamelCase							):


   """simple docstring"""




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

   return unit_symbols, assignment




def 						__SCREAMING_SNAKE_CASE   (					_UpperCamelCase  ,						_UpperCamelCase  ,						_UpperCamelCase							):


   """simple docstring"""




   lowercase_		:      Optional[int]          =       True
   for clause in clauses:
      lowercase_		:      Tuple          =       clause.evaluate(_UpperCamelCase							)
      if clause_check is False:
         return False, None
      elif clause_check is None:
         lowercase_		:      List[Any]          =       False
         continue

   if check_clause_all_true:
      return True, model

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

   if p:
      lowercase_		:      Union[str, Any]          =       model
      lowercase_		:      int          =       value
      lowercase_		:      Dict          =       list(_UpperCamelCase							)
      if p in tmp_symbols:
         tmp_symbols.remove(_UpperCamelCase							)
      return dpll_algorithm(_UpperCamelCase  ,						_UpperCamelCase  ,						_UpperCamelCase							)

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

   return dpll_algorithm(_UpperCamelCase  ,						_UpperCamelCase  ,						_UpperCamelCase							) or dpll_algorithm(_UpperCamelCase  ,						_UpperCamelCase  ,						_UpperCamelCase							)


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'''
def 						__SCREAMING_SNAKE_CASE   (					_UpperCamelCase  ,						_UpperCamelCase							):


   """simple docstring"""




   sequence.append(_UpperCamelCase							)

   lowercase_		:      Union[str, Any]          =       0
   while sequence[index] != target:
      index += 1

   sequence.pop()

   if index == len(_UpperCamelCase							):
      return None

   return index


if __name__ == "__main__":
 UpperCamelCase__	=     input('Enter numbers separated by comma:\n').strip()
 UpperCamelCase__	=     [int(item) for item in user_input.split(',')]

 UpperCamelCase__	=     input('Enter a single number to be found in the list:\n')
 UpperCamelCase__	=     int(target_input)
 UpperCamelCase__	=     sentinel_linear_search(sequence, target)
 if result is not None:
  print(f"""{target} found at positions: {result}""")
 else:
  print('Not found')




