factor/extra/project-euler/112/112.factor

53 lines
1.5 KiB
Factor

! Copyright (c) 2009 Guillaume Nargeot.
! See http://factorcode.org/license.txt for BSD license.
USING: arrays kernel math project-euler.common sequences sorting ;
IN: project-euler.112
! http://projecteuler.net/index.php?section=problems&id=112
! DESCRIPTION
! -----------
! Working from left-to-right if no digit is exceeded by the digit to its left
! it is called an increasing number; for example, 134468.
! Similarly if no digit is exceeded by the digit to its right it is called a
! decreasing number; for example, 66420.
! We shall call a positive integer that is neither increasing nor decreasing a
! "bouncy" number; for example, 155349.
! Clearly there cannot be any bouncy numbers below one-hundred, but just over
! half of the numbers below one-thousand (525) are bouncy. In fact, the least
! number for which the proportion of bouncy numbers first reaches 50% is 538.
! Surprisingly, bouncy numbers become more and more common and by the time we
! reach 21780 the proportion of bouncy numbers is equal to 90%.
! Find the least number for which the proportion of bouncy numbers is exactly
! 99%.
! SOLUTION
! --------
<PRIVATE
: bouncy? ( n -- ? )
number>digits dup natural-sort
[ = not ] [ reverse = not ] 2bi and ;
PRIVATE>
: euler112 ( -- answer )
0 0 0 [
2dup swap 99 * = not
] [
[ 1 + ] 2dip pick bouncy? [ 1 + ] [ [ 1 + ] dip ] if
] do while 2drop ;
! [ euler112 ] 100 ave-time
! 2749 ms ave run time - 33.76 SD (100 trials)
SOLUTION: euler112