




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

import random
from collections.abc import Iterable






class 			SCREAMING_SNAKE_CASE:

       def __init__(       self   ,						lowerCamelCase__	)       ->   None:

           """simple docstring"""



           __lowercase     							=		{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        snake_case__     (       self   ,						lowerCamelCase__	)       ->   None:

           """simple docstring"""



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




       def        snake_case__     (       self   ,						lowerCamelCase__	)       ->   bool | None:

           """simple docstring"""



           for literal in self.literals:
               __lowercase     							=		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 			SCREAMING_SNAKE_CASE:

       def __init__(       self   ,						lowerCamelCase__	)       ->   None:

           """simple docstring"""



           __lowercase     							=		list(lowerCamelCase__	)




       def __str__(       self	)       ->   str:

           """simple docstring"""



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

def 							snake_case_    (  ):



    """simple docstring"""




    __lowercase     							=		[]
    __lowercase     							=		random.randint(1       ,5     )
    __lowercase     							=		"""A"""
    __lowercase     							=		0
    while i < no_of_literals:
        __lowercase     							=		random.randint(1       ,5     )
        __lowercase     							=		base_var + str(a__     )
        __lowercase     							=		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 							snake_case_    (  ):



    """simple docstring"""




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



    """simple docstring"""




    __lowercase     							=		formula.clauses
    __lowercase     							=		[]
    for clause in formula.clauses:
        for literal in clause.literals:
            __lowercase     							=		literal[:2]
            if symbol not in symbols_set:
                symbols_set.append(a__     )
    return clauses, symbols_set
def 							snake_case_    (  a__						:      list[Clause]       ,a__						:      list[str]       ,a__						:      dict[str, bool | None]     ):



    """simple docstring"""




    __lowercase     							=		[]
    __lowercase     							=		{}
    __lowercase     							=		[]

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

    for s in symbols:
        __lowercase     							=		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:
        __lowercase     							=		None
    for s in pure_symbols:
        __lowercase     							=		s + """'"""
        if s in literals:
            __lowercase     							=		True
        elif sym in literals:
            __lowercase     							=		False
    return pure_symbols, assignment
def 							snake_case_    (  a__						:      list[Clause]       ,a__						:      dict[str, bool | None]     ):



    """simple docstring"""




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

    return unit_symbols, assignment
def 							snake_case_    (  a__						:      list[Clause]       ,a__						:      list[str]       ,a__						:      dict[str, bool | None]     ):



    """simple docstring"""




    __lowercase     							=		True
    for clause in clauses:
        __lowercase     							=		clause.evaluate(a__     )
        if clause_check is False:
            return False, None
        elif clause_check is None:
            __lowercase     							=		False
            continue

    if check_clause_all_true:
        return True, model

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

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

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

    return dpll_algorithm(a__       ,a__       ,a__     ) or dpll_algorithm(a__       ,a__       ,a__     )


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  A				: Tuple					      =			generate_formula()
  print(F"""The formula {formula} is""", end=""" """)

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

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










'''simple docstring'''
def 							snake_case_    (  a__						:      int     ):



    """simple docstring"""




    __lowercase     							=		1
    __lowercase     							=		0
    __lowercase     							=		1
    __lowercase     							=		1
    __lowercase     							=		3
    __lowercase     							=		3
    __lowercase     							=		limit
    __lowercase     							=		0

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

            if decimal == counter:
                break

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



    """simple docstring"""




    print(f'{calculate_pi(50     ) = }'     )
    import doctest

    doctest.testmod()


if __name__ == "__main__":
  main()




