70 lines
2.1 KiB
Factor
70 lines
2.1 KiB
Factor
! Copyright (c) 2008 Aaron Schaefer.
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel math math.parser project-euler.common sequences ;
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IN: project-euler.055
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! http://projecteuler.net/index.php?section=problems&id=55
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! DESCRIPTION
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! -----------
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! If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.
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! Not all numbers produce palindromes so quickly. For example,
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! 349 + 943 = 1292,
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! 1292 + 2921 = 4213
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! 4213 + 3124 = 7337
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! That is, 349 took three iterations to arrive at a palindrome.
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! Although no one has proved it yet, it is thought that some numbers, like 196,
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! never produce a palindrome. A number that never forms a palindrome through
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! the reverse and add process is called a Lychrel number. Due to the
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! theoretical nature of these numbers, and for the purpose of this problem, we
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! shall assume that a number is Lychrel until proven otherwise. In addition you
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! are given that for every number below ten-thousand, it will either (i) become a
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! palindrome in less than fifty iterations, or, (ii) no one, with all the
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! computing power that exists, has managed so far to map it to a palindrome. In
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! fact, 10677 is the first number to be shown to require over fifty iterations
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! before producing a palindrome: 4668731596684224866951378664 (53 iterations,
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! 28-digits).
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! Surprisingly, there are palindromic numbers that are themselves Lychrel
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! numbers; the first example is 4994.
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! How many Lychrel numbers are there below ten-thousand?
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! NOTE: Wording was modified slightly on 24 April 2007 to emphasise the
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! theoretical nature of Lychrel numbers.
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! SOLUTION
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! --------
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<PRIVATE
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: add-reverse ( n -- m )
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dup number>digits reverse 10 digits>integer + ;
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: (lychrel?) ( n iteration -- ? )
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dup 50 < [
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[ add-reverse ] dip over palindrome?
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[ 2drop f ] [ 1+ (lychrel?) ] if
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] [
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2drop t
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] if ;
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: lychrel? ( n -- ? )
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1 (lychrel?) ;
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PRIVATE>
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: euler055 ( -- answer )
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10000 [ lychrel? ] count ;
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! [ euler055 ] 100 ave-time
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! 478 ms ave run time - 30.63 SD (100 trials)
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MAIN: euler055
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