55_lychrel_numbers.py

# https://projecteuler.net/problem=55
#
# 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.

import utils


def reverse_and_add(x):
    """
    >>> reverse_and_add(47)
    121
    """
    return x + utils.reverse_int(x)


def main():
    # examine 1-> 10,000
    lychrels = range(1, 10001)
    for i in xrange(1, 10001):
        # Fifty iterations per number to try and prove it is non-lychrel
        r = reverse_and_add(i)
        for j in xrange(0, 50):
            if utils.is_palindrome(r):
                # print "%s is a palindrome of %s on iteration %d" % (r, i, j)
                lychrels.remove(i)
                break
            r = reverse_and_add(r)
    return len(lychrels)

if __name__ == "__main__":
    import doctest
    doctest.testmod()
    print main()