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

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Factor

! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel math math.ranges project-euler.common sequences ;
IN: project-euler.055
! http://projecteuler.net/index.php?section=problems&id=55
! DESCRIPTION
! -----------
! 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.
! SOLUTION
! --------
<PRIVATE
: add-reverse ( n -- m )
dup number>digits reverse digits>number + ;
: (lychrel?) ( n iteration -- ? )
dup 50 < [
[ add-reverse ] dip over palindrome?
[ 2drop f ] [ 1 + (lychrel?) ] if
] [
2drop t
] if ;
: lychrel? ( n -- ? )
1 (lychrel?) ;
PRIVATE>
: euler055 ( -- answer )
10000 <iota> [ lychrel? ] count ;
! [ euler055 ] 100 ave-time
! 478 ms ave run time - 30.63 SD (100 trials)
SOLUTION: euler055