




import numpy as np

lowercase__    :					List[Any]					=						[
    ["a", "b", "c", "d", "e"],
    ["f", "g", "h", "i", "k"],
    ["l", "m", "n", "o", "p"],
    ["q", "r", "s", "t", "u"],
    ["v", "w", "x", "y", "z"],
]
class 		UpperCAmelCase       :







						'''simple docstring'''





						def __init__(						self							:					Tuple						):






							"""simple docstring"""






							snake_case_		   =					np.array(__lowercase						)






						def 	snake_case__						(						self							:					Union[str, Any]	,     __lowercase							:					str						):






							"""simple docstring"""






							snake_case_   ,				snake_case_		   =					np.where(letter == self.SQUARE						)
							snake_case_		   =					np.concatenate([indexa + 1, indexa + 1]						)
							return indexes






						def 	snake_case__						(						self							:					Dict	,     __lowercase							:					int	,     __lowercase							:					int						):






							"""simple docstring"""






							return self.SQUARE[indexa - 1, indexa - 1]






						def 	snake_case__						(						self							:					Dict	,     __lowercase							:					str						):






							"""simple docstring"""






							snake_case_		   =					message.lower()
							snake_case_		   =					message.replace("j"	,     "i"						)

							snake_case_		   =					""
							for letter_index in range(len(__lowercase						)						):
								if message[letter_index] != " ":
									snake_case_		   =					self.letter_to_numbers(message[letter_index]						)
									snake_case_		   =					encoded_message + str(numbers[0]						) + str(numbers[1]						)
								elif message[letter_index] == " ":
									snake_case_		   =					encoded_message + " "

							return encoded_message






						def 	snake_case__						(						self							:					Union[str, Any]	,     __lowercase							:					str						):






							"""simple docstring"""






							snake_case_		   =					message.replace(" "	,     "  "						)
							snake_case_		   =					""
							for numbers_index in range(int(len(__lowercase						) / 2						)						):
								if message[numbers_index * 2] != " ":
									snake_case_		   =					message[numbers_index * 2]
									snake_case_		   =					message[numbers_index * 2 + 1]

									snake_case_		   =					self.numbers_to_letter(int(__lowercase						)	,     int(__lowercase						)						)
									snake_case_		   =					decoded_message + letter
								elif message[numbers_index * 2] == " ":
									snake_case_		   =					decoded_message + " "

							return decoded_message






from __future__ import annotations

import random
from collections.abc import Iterable
class 		UpperCAmelCase       :







						'''simple docstring'''





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






							"""simple docstring"""






							snake_case_		   =					{literal: None for literal in literals}






						def __str__(						self							:					str						):






							"""simple docstring"""






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






						def __len__(						self							:					Optional[int]						):






							"""simple docstring"""






							return len(self.literals						)






						def 	snake_case__						(						self							:					Dict	,     __lowercase							:					dict[str, bool | None]						):






							"""simple docstring"""






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






						def 	snake_case__						(						self							:					List[Any]	,     __lowercase							:					dict[str, bool | None]						):






							"""simple docstring"""






							for literal in self.literals:
								snake_case_		   =					literal.rstrip("'"						) if literal.endswith("'"						) else literal + "'"
								if symbol in self.literals:
									return True

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







class 		UpperCAmelCase       :







						'''simple docstring'''





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






							"""simple docstring"""






							snake_case_		   =					list(__lowercase						)






						def __str__(						self							:					Dict						):






							"""simple docstring"""






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







def 						lowerCamelCase__   (		):







	'''simple docstring'''





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







	'''simple docstring'''





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


def 						lowerCamelCase__   (		_A							):







	'''simple docstring'''





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


def 						lowerCamelCase__   (		_A					,     _A					,     _A							):







	'''simple docstring'''





	snake_case_		   =					[]
	snake_case_		   =					{}
	snake_case_		   =					[]

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

	for s in symbols:
		snake_case_		   =					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:
		snake_case_		   =					None
	for s in pure_symbols:
		snake_case_		   =					s + "'"
		if s in literals:
			snake_case_		   =					True
		elif sym in literals:
			snake_case_		   =					False
	return pure_symbols, assignment


def 						lowerCamelCase__   (		_A					,     _A							):







	'''simple docstring'''





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

	return unit_symbols, assignment


def 						lowerCamelCase__   (		_A					,     _A					,     _A							):







	'''simple docstring'''





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

	if check_clause_all_true:
		return True, model

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

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

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

	return dpll_algorithm(_A					,     _A					,     _A							) or dpll_algorithm(_A					,     _A					,     _A							)


if __name__ == "__main__":
		import doctest

		doctest.testmod()

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

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

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