from util import *


def p1():
	# Language rule 1, n is less than or equal to 2
	n = 2
	# Language rule 2, m is less than or equal to n
	m = n
	strings = []
	# Language rule 3, n and m are both non-negative integers
	for i in range(0, n + 1):
		for j in range(0, m + 1):
			if j > i:
				continue
			strings.append('0' * j + '1' * i)

	return strings


def p2():
	possible_n = [2, 3, 4, 5, 6]

	strings = []
	for i in possible_n:
		integer_divisors = []
		for j in range(1, i + 1):
			if i % j == 0:
				integer_divisors.append(j)
		for j in integer_divisors:
			strings.append('a' * j + 'b' * i)
	return strings


def p3():
	possible_n = [1, 2, 3]

	strings = []
	for i in possible_n:
		an = i
		bn = 2 * i - 1
		cn = 3 * i - 2
		strings.append('a' * an + 'b' * bn + 'c' * cn)

	return strings


def p4():
	alphabet = ['a', 'b']

	# include empty string
	strings = get_all_strings_with_a_given_alphabet_and_length(alphabet, 3)

	def is_palindrome(s):
		return s == s[::-1]

	strings = list(filter(is_palindrome, strings))

	return strings


def main():
	print_strings(p1())
	print_strings(p2())
	print_strings(p3())
	print_strings(p4())


if __name__ == '__main__':
	main()