factor/extra/project-euler/009/009.factor

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1.3 KiB
Factor

! Copyright (c) 2007, 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel make math sequences sorting project-euler.common ;
IN: project-euler.009
! http://projecteuler.net/index.php?section=problems&id=9
! DESCRIPTION
! -----------
! A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
! a² + b² = c²
! For example, 3² + 4² = 9 + 16 = 25 = 5².
! There exists exactly one Pythagorean triplet for which a + b + c = 1000.
! Find the product abc.
! SOLUTION
! --------
! Algorithm adapted from http://www.friesian.com/pythag.com
<PRIVATE
: next-pq ( p1 q1 -- p2 q2 )
! p > q and both are odd integers
dup 1 = [ drop 2 + dup ] when 2 - ;
: abc ( p q -- triplet )
[
2dup * , ! a = p * q
[ sq ] bi@
[ - 2 / , ] ! b = (p² - q²) / 2
[ + 2 / , ] 2bi ! c = (p² + q²) / 2
] { } make natural-sort ;
: (ptriplet) ( target p q triplet -- target p q )
sum [ pick ] dip = [ next-pq 2dup abc (ptriplet) ] unless ;
: ptriplet ( target -- triplet )
3 1 { 3 4 5 } (ptriplet) abc nip ;
PRIVATE>
: euler009 ( -- answer )
1000 ptriplet product ;
! [ euler009 ] 100 ave-time
! 1 ms ave run time - 0.73 SD (100 trials)
SOLUTION: euler009