'''
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 time
import math

def reverseInt(n):
    res = 0
    while n > 0:
        res *= 10
        res += n % 10
        n = n // 10
    
    return res

def palint(n):
    if n == 0:
        return True
    if int(math.log10(n)) + 1 <= 1:
        return True
    s = str(n)
    if s[0] != s[-1]:
        return False
    if len(s) == 2:
        return True
    return palint(int(s[1:-1]))

def lychrel(n, iterations):
    res = n
    visited = set()

    for _ in range(iterations):
        visited.add(res)
        res += reverseInt(res)
        if palint(res):
            return res, visited
    
    return False, visited


def main():
    print("Hello, this is Patrick")
    t0 = time.time()

    counter = 0
    lychrels = set()
    nonLychrels = set()

    for i in range(1, 10000):
        if i in lychrels:
            counter += 1
        elif i in nonLychrels:
            continue
        else:
            ans, visited = lychrel(i, 50)
            if ans:
                nonLychrels = nonLychrels.union(visited)
            else:
                lychrels = lychrels.union(visited)
                counter += 1

    print(counter, time.time() - t0)


if __name__ == "__main__":
    main()