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