






from __future__ import annotations

import random
from collections.abc import Iterable


class 		lowerCAmelCase_				:





     def __init__(	self							, _UpperCAmelCase  )		->				None:
        lowerCamelCase									={literal: None for literal in literals}





     def __str__(	self  )		->				str:
        return "{" + " , ".join(self.literals  ) + "}"





     def __len__(	self  )		->				int:
        return len(self.literals  )





     def 						lowerCamelCase							(	self							, _UpperCAmelCase  )		->				None:






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





     def 						lowerCamelCase							(	self							, _UpperCAmelCase  )		->				bool | None:






        for literal in self.literals:
           lowerCamelCase									=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 		lowerCAmelCase_				:





     def __init__(	self							, _UpperCAmelCase  )		->				None:
        lowerCamelCase									=list(_UpperCAmelCase  )





     def __str__(	self  )		->				str:
        return "{" + " , ".join(str(_UpperCAmelCase  ) for clause in self.clauses  ) + "}"






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






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






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






def  UpperCAmelCase__						(    lowerCamelCase	:			Any			,lowerCamelCase	:			List[str]			,lowerCamelCase	:			int    ):
   lowerCamelCase									=[]
   lowerCamelCase									={}
   lowerCamelCase									=[]

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

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






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

   return unit_symbols, assignment






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

   if check_clause_all_true:
      return True, model

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

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

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

   return dpll_algorithm(lowerCamelCase			,lowerCamelCase			,lowerCamelCase    ) or dpll_algorithm(lowerCamelCase			,lowerCamelCase			,lowerCamelCase    )


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   _UpperCAmelCase					:						str         =     generate_formula()
   print(f"The formula {formula} is", end=' ')

   _UpperCAmelCase					:						Optional[Any]         =     generate_parameters(formula)
   _UpperCAmelCase					:						List[str]         =     dpll_algorithm(clauses, symbols, {})

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

"""simple docstring"""




def __snake_case (      UpperCamelCase    )       ->    float:


		"""simple docstring"""





		return -num if num < 0 else num

def __snake_case (      UpperCamelCase    )       ->    int:


		"""simple docstring"""





		if len(UpperCamelCase    ) == 0:
				raise ValueError('''abs_min() arg is an empty sequence'''    )
		a__   		=     x[0]
		for i in x:
				if abs_val(UpperCamelCase    ) < abs_val(UpperCamelCase    ):
						a__   		=     i
		return j

def __snake_case (      UpperCamelCase    )       ->    int:


		"""simple docstring"""





		if len(UpperCamelCase    ) == 0:
				raise ValueError('''abs_max() arg is an empty sequence'''    )
		a__   		=     x[0]
		for i in x:
				if abs(UpperCamelCase    ) > abs(UpperCamelCase    ):
						a__   		=     i
		return j

def __snake_case (      UpperCamelCase    )       ->    int:


		"""simple docstring"""





		if len(UpperCamelCase    ) == 0:
				raise ValueError('''abs_max_sort() arg is an empty sequence'''    )
		return sorted(UpperCamelCase						,					key=UpperCamelCase    )[-1]

def __snake_case (      )       ->    Optional[int]:


		"""simple docstring"""





		assert abs_val(0    ) == 0
		assert abs_val(34    ) == 34
		assert abs_val(-100_000_000_000    ) == 100_000_000_000

		a__   		=     [-3, -1, 2, -11]
		assert abs_max(UpperCamelCase    ) == -11
		assert abs_max_sort(UpperCamelCase    ) == -11
		assert abs_min(UpperCamelCase    ) == -1


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					test_abs_val()
					print(abs_val(-34))  # --> 34




