
'''simple docstring'''

def 					UpperCAmelCase__      (							_lowerCAmelCase						: list,			_lowerCAmelCase						: list)						->		list:



						"""simple docstring"""

						snake_case   :					int							=						len(_lowerCAmelCase)
						snake_case   :					int							=						len(_lowerCAmelCase)
						snake_case   :					int							=						(
						    first_input_list_length
						    if first_input_list_length > second_input_list_length
						    else second_input_list_length
						)
						snake_case   :					list							=						[]
						for char_count in range(_lowerCAmelCase):
												if char_count < first_input_list_length:
																		output_result_list.append(first_input_list[char_count])
												if char_count < second_input_list_length:
																		output_result_list.append(second_input_list[char_count])

						return output_result_list


if __name__ == "__main__":
						print(alternative_list_arrange(["A", "B", "C"], [1, 2, 3, 4, 5]), end=" ")






'''simple docstring'''

from __future__ import annotations

import random
from collections.abc import Iterable




class 		SCREAMING_SNAKE_CASE_				:



			"""simple docstring"""






			def __init__(       self							, snake_case_				):
									snake_case   :					dict[str, bool | None]							=						{literal: None for literal in literals}



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



			def __len__(       self				):
									return len(self.literals				)



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






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

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







class 		SCREAMING_SNAKE_CASE_				:



			"""simple docstring"""






			def __init__(       self							, snake_case_				):
									snake_case   :					Tuple							=						list(snake_case_				)






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







def 					UpperCAmelCase__      (							)						->		Clause:



						"""simple docstring"""

						snake_case   :					Optional[Any]							=						[]
						snake_case   :					Optional[Any]							=						random.randint(1,			5)
						snake_case   :					Tuple							=						"A"
						snake_case   :					Optional[Any]							=						0
						while i < no_of_literals:
												snake_case   :					Union[str, Any]							=						random.randint(1,			5)
												snake_case   :					List[Any]							=						base_var + str(_lowerCAmelCase)
												snake_case   :					Union[str, Any]							=						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__      (							)						->		Formula:



						"""simple docstring"""

						snake_case   :					set[Clause]							=						set()
						snake_case   :					Union[str, Any]							=						random.randint(1,			10)
						while len(_lowerCAmelCase) < no_of_clauses:
												clauses.add(generate_clause())
						return Formula(_lowerCAmelCase)


def 					UpperCAmelCase__      (							_lowerCAmelCase						: Formula)						->		tuple[list[Clause], list[str]]:



						"""simple docstring"""

						snake_case   :					Dict							=						formula.clauses
						snake_case   :					List[Any]							=						[]
						for clause in formula.clauses:
												for literal in clause.literals:
																		snake_case   :					Any							=						literal[:2]
																		if symbol not in symbols_set:
																								symbols_set.append(_lowerCAmelCase)
						return clauses, symbols_set


def 					UpperCAmelCase__      (							_lowerCAmelCase						: list[Clause],			_lowerCAmelCase						: list[str],			_lowerCAmelCase						: dict[str, bool | None])						->		tuple[list[str], dict[str, bool | None]]:



						"""simple docstring"""

						snake_case   :					Optional[int]							=						[]
						snake_case   :					dict[str, bool | None]							=						{}
						snake_case   :					Dict							=						[]

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

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


def 					UpperCAmelCase__      (							_lowerCAmelCase						: list[Clause],			_lowerCAmelCase						: dict[str, bool | None])						->		tuple[list[str], dict[str, bool | None]]:



						"""simple docstring"""

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

						return unit_symbols, assignment


def 					UpperCAmelCase__      (							_lowerCAmelCase						: list[Clause],			_lowerCAmelCase						: list[str],			_lowerCAmelCase						: dict[str, bool | None])						->		tuple[bool | None, dict[str, bool | None] | None]:



						"""simple docstring"""

						snake_case   :					Optional[int]							=						True
						for clause in clauses:
												snake_case   :					List[Any]							=						clause.evaluate(_lowerCAmelCase)
												if clause_check is False:
																		return False, None
												elif clause_check is None:
																		snake_case   :					Union[str, Any]							=						False
																		continue

						if check_clause_all_true:
												return True, model

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

						if p:
												snake_case   :					str							=						model
												snake_case   :					Union[str, Any]							=						value
												snake_case   :					Optional[Any]							=						list(_lowerCAmelCase)
												if p in tmp_symbols:
																		tmp_symbols.remove(_lowerCAmelCase)
												return dpll_algorithm(_lowerCAmelCase,			_lowerCAmelCase,			_lowerCAmelCase)

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

						return dpll_algorithm(_lowerCAmelCase,			_lowerCAmelCase,			_lowerCAmelCase) or dpll_algorithm(_lowerCAmelCase,			_lowerCAmelCase,			_lowerCAmelCase)


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						A_        =   generate_formula()
						print(f"The formula {formula} is", end=" ")

						A_      ,   A_        =   generate_parameters(formula)
						A_      ,   A_        =   dpll_algorithm(clauses, symbols, {})

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





