diff --git a/55/main.py b/55/main.py new file mode 100644 index 0000000..22b7229 --- /dev/null +++ b/55/main.py @@ -0,0 +1,83 @@ +''' +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() \ No newline at end of file