#### /extra/project-euler/055/055.factor

Unknown | 69 lines | 49 code | 20 blank | 0 comment | 0 complexity | e7f2bf38942ca987fcace45ecac28517 MD5 | raw file

1! Copyright (c) 2008 Aaron Schaefer. 2! See http://factorcode.org/license.txt for BSD license. 3USING: kernel math math.parser math.ranges project-euler.common sequences ; 4IN: project-euler.055 5 6! http://projecteuler.net/index.php?section=problems&id=55 7 8! DESCRIPTION 9! ----------- 10 11! If we take 47, reverse and add, 47 + 74 = 121, which is palindromic. 12 13! Not all numbers produce palindromes so quickly. For example, 14 15! 349 + 943 = 1292, 16! 1292 + 2921 = 4213 17! 4213 + 3124 = 7337 18 19! That is, 349 took three iterations to arrive at a palindrome. 20 21! Although no one has proved it yet, it is thought that some numbers, like 196, 22! never produce a palindrome. A number that never forms a palindrome through 23! the reverse and add process is called a Lychrel number. Due to the 24! theoretical nature of these numbers, and for the purpose of this problem, we 25! shall assume that a number is Lychrel until proven otherwise. In addition you 26! are given that for every number below ten-thousand, it will either (i) become a 27! palindrome in less than fifty iterations, or, (ii) no one, with all the 28! computing power that exists, has managed so far to map it to a palindrome. In 29! fact, 10677 is the first number to be shown to require over fifty iterations 30! before producing a palindrome: 4668731596684224866951378664 (53 iterations, 31! 28-digits). 32 33! Surprisingly, there are palindromic numbers that are themselves Lychrel 34! numbers; the first example is 4994. 35 36! How many Lychrel numbers are there below ten-thousand? 37 38! NOTE: Wording was modified slightly on 24 April 2007 to emphasise the 39! theoretical nature of Lychrel numbers. 40 41 42! SOLUTION 43! -------- 44 45<PRIVATE 46 47: add-reverse ( n -- m ) 48 dup number>digits reverse 10 digits>integer + ; 49 50: (lychrel?) ( n iteration -- ? ) 51 dup 50 < [ 52 [ add-reverse ] dip over palindrome? 53 [ 2drop f ] [ 1 + (lychrel?) ] if 54 ] [ 55 2drop t 56 ] if ; 57 58: lychrel? ( n -- ? ) 59 1 (lychrel?) ; 60 61PRIVATE> 62 63: euler055 ( -- answer ) 64 10000 iota [ lychrel? ] count ; 65 66! [ euler055 ] 100 ave-time 67! 478 ms ave run time - 30.63 SD (100 trials) 68 69SOLUTION: euler055