factor/extra/project-euler/044/044.factor

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2008-02-06 00:53:18 -05:00
! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel math math.functions math.ranges project-euler.common sequences ;
IN: project-euler.044
! http://projecteuler.net/index.php?section=problems&id=44
! DESCRIPTION
! -----------
! Pentagonal numbers are generated by the formula, Pn=n(3n1)/2. The first ten
! pentagonal numbers are:
! 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...
! It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference,
! 70 22 = 48, is not pentagonal.
! Find the pair of pentagonal numbers, Pj and Pk, for which their sum and
! difference is pentagonal and D = |Pk Pj| is minimised; what is the value of D?
! SOLUTION
! --------
! Brute force using a cartesian product and an arbitrarily chosen limit.
<PRIVATE
: nth-pentagonal ( n -- seq )
dup 3 * 1- * 2 / ;
: sum-and-diff? ( m n -- ? )
2dup + -rot - [ pentagonal? ] 2apply and ;
PRIVATE>
: euler044 ( -- answer )
2500 [1,b] [ nth-pentagonal ] map dup cartesian-product
[ first2 sum-and-diff? ] subset [ first2 - abs ] map infimum ;
! [ euler044 ] 10 ave-time
! 8924 ms run / 2872 ms GC ave time - 10 trials
! TODO: this solution is ugly and not very efficient...find a better algorithm
MAIN: euler044