55 lines
1.3 KiB
Factor
55 lines
1.3 KiB
Factor
! Copyright (c) 2008 Aaron Schaefer.
|
||
! See http://factorcode.org/license.txt for BSD license.
|
||
USING: kernel math math.functions math.ranges math.order
|
||
project-euler.common sequences layouts ;
|
||
IN: project-euler.044
|
||
|
||
! http://projecteuler.net/index.php?section=problems&id=44
|
||
|
||
! DESCRIPTION
|
||
! -----------
|
||
|
||
! Pentagonal numbers are generated by the formula, Pn=n(3n−1)/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 /i ; inline
|
||
|
||
: sum-and-diff? ( m n -- ? )
|
||
[ + ] [ - ] 2bi [ pentagonal? ] bi@ and ; inline
|
||
|
||
: euler044-step ( min m n -- min' )
|
||
[ nth-pentagonal ] bi@
|
||
2dup sum-and-diff? [ - abs min ] [ 2drop ] if ; inline
|
||
|
||
PRIVATE>
|
||
|
||
: euler044 ( -- answer )
|
||
most-positive-fixnum
|
||
2500 [1,b] [
|
||
dup [1,b] [
|
||
euler044-step
|
||
] with each
|
||
] each ;
|
||
|
||
! [ euler044 ] 10 ave-time
|
||
! 289 ms ave run time - 0.27 SD (10 trials)
|
||
|
||
SOLUTION: euler044
|