56 lines
1.5 KiB
Factor
56 lines
1.5 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 math.ranges project-euler.common sequences ;
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IN: project-euler.038
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! http://projecteuler.net/index.php?section=problems&id=38
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! DESCRIPTION
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! -----------
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! Take the number 192 and multiply it by each of 1, 2, and 3:
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! 192 × 1 = 192
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! 192 × 2 = 384
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! 192 × 3 = 576
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! By concatenating each product we get the 1 to 9 pandigital, 192384576. We
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! will call 192384576 the concatenated product of 192 and (1,2,3)
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! The same can be achieved by starting with 9 and multiplying by 1, 2, 3, 4,
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! and 5, giving the pandigital, 918273645, which is the concatenated product of
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! 9 and (1,2,3,4,5).
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! What is the largest 1 to 9 pandigital 9-digit number that can be formed as
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! the concatenated product of an integer with (1,2, ... , n) where n > 1?
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! SOLUTION
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! --------
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! Only need to search 4-digit numbers starting with 9 since a 2-digit number
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! starting with 9 would produce 8 or 11 digits, and a 3-digit number starting
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! with 9 would produce 7 or 11 digits.
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<PRIVATE
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: (concat-product) ( accum n multiplier -- m )
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pick length 8 > [
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2drop 10 swap digits>integer
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] [
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[ * number>digits over push-all ] 2keep 1+ (concat-product)
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] if ;
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: concat-product ( n -- m )
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V{ } clone swap 1 (concat-product) ;
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PRIVATE>
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: euler038 ( -- answer )
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9123 9876 [a,b] [ concat-product ] map [ pandigital? ] subset supremum ;
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! [ euler038 ] 100 ave-time
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! 37 ms run / 1 ms GC ave time - 100 trials
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MAIN: euler038
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