problem_055.py

# coding: utf-8


'''
If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.

Not all numbers produce palindromes so quickly. For example,

349 + 943 = 1292,
1292 + 2921 = 4213
4213 + 3124 = 7337

That is, 349 took three iterations to arrive at a palindrome.

Although no one has proved it yet, it is thought that some numbers, like 196, never produce a palindrome. A number that never forms a palindrome through the reverse and add process is called a Lychrel number. Due to the theoretical nature of these numbers, and for the purpose of this problem, we shall assume that a number is Lychrel until proven otherwise. In addition you are given that for every number below ten-thousand, it will either (i) become a palindrome in less than fifty iterations, or, (ii) no one, with all the computing power that exists, has managed so far to map it to a palindrome. In fact, 10677 is the first number to be shown to require over fifty iterations before producing a palindrome: 4668731596684224866951378664 (53 iterations, 28-digits).

Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.

How many Lychrel numbers are there below ten-thousand?

NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers.
'''


from helpers import memoize


def reverse_and_add(number):
    return number + int(str(number)[::-1])


def is_palindrome(number):
    return int(str(number)[::-1]) == number


@memoize
def give_palindrome_or_not(number):
    for counter in range(50):
        number = reverse_and_add(number)
        if is_palindrome(number):
            return True
    return False


def main():
    return sum([1 for _ in range(10001) if not give_palindrome_or_not(_)])


if __name__ == '__main__':
    print(main())
    # 249 in 1.08ms