56 lines
1.3 KiB
Factor
56 lines
1.3 KiB
Factor
! Copyright (c) 2007 Aaron Schaefer.
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel math math.functions namespaces sequences sorting ;
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IN: project-euler.009
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! http://projecteuler.net/index.php?section=problems&id=9
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! DESCRIPTION
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! -----------
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! A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
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! a² + b² = c²
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! For example, 3² + 4² = 9 + 16 = 25 = 5².
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! There exists exactly one Pythagorean triplet for which a + b + c = 1000.
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! Find the product abc.
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! SOLUTION
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! --------
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! Algorithm adapted from http://www.friesian.com/pythag.com
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<PRIVATE
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: next-pq ( p1 q1 -- p2 q2 )
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! p > q and both are odd integers
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dup 1 = [ swap 2 + nip dup 2 - ] [ 2 - ] if ;
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: abc ( p q -- triplet )
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[
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2dup * , ! a = p * q
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2dup sq swap sq swap - 2 / , ! b = (p² - q²) / 2
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sq swap sq swap + 2 / , ! c = (p² + q²) / 2
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] { } make natural-sort ;
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: (ptriplet) ( target p q triplet -- target p q )
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roll dup >r swap sum = r> -roll
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[
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next-pq 2dup abc (ptriplet)
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] unless ;
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: ptriplet ( target -- triplet )
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3 1 { 3 4 5 } (ptriplet) abc nip ;
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PRIVATE>
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: euler009 ( -- answer )
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1000 ptriplet product ;
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! [ euler009 ] 100 ave-time
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! 1 ms run / 0 ms GC ave time - 100 trials
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MAIN: euler009
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