factor/extra/project-euler/043/043.factor

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2.8 KiB
Factor

! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: combinators.short-circuit kernel math math.functions math.combinatorics
math.ranges project-euler.common sequences sets sorting ;
IN: project-euler.043
! http://projecteuler.net/index.php?section=problems&id=43
! DESCRIPTION
! -----------
! The number, 1406357289, is a 0 to 9 pandigital number because it is made up
! of each of the digits 0 to 9 in some order, but it also has a rather
! interesting sub-string divisibility property.
! Let d1 be the 1st digit, d2 be the 2nd digit, and so on. In this way, we note
! the following:
! * d2d3d4 = 406 is divisible by 2
! * d3d4d5 = 063 is divisible by 3
! * d4d5d6 = 635 is divisible by 5
! * d5d6d7 = 357 is divisible by 7
! * d6d7d8 = 572 is divisible by 11
! * d7d8d9 = 728 is divisible by 13
! * d8d9d10 = 289 is divisible by 17
! Find the sum of all 0 to 9 pandigital numbers with this property.
! SOLUTION
! --------
! Brute force generating all the pandigitals then checking 3-digit divisiblity
! properties...this is very slow!
<PRIVATE
: subseq-divisible? ( n index seq -- ? )
[ 1 - dup 3 + ] dip subseq digits>number swap divisor? ;
: interesting? ( seq -- ? )
{
[ [ 17 8 ] dip subseq-divisible? ]
[ [ 13 7 ] dip subseq-divisible? ]
[ [ 11 6 ] dip subseq-divisible? ]
[ [ 7 5 ] dip subseq-divisible? ]
[ [ 5 4 ] dip subseq-divisible? ]
[ [ 3 3 ] dip subseq-divisible? ]
[ [ 2 2 ] dip subseq-divisible? ]
} 1&& ;
PRIVATE>
: euler043 ( -- answer )
1234567890 number>digits 0 [
dup interesting? [
digits>number +
] [ drop ] if
] reduce-permutations ;
! [ euler043 ] time
! 60280 ms run / 59 ms GC time
! ALTERNATE SOLUTIONS
! -------------------
! Build the number from right to left, generating the next 3-digits according
! to the divisiblity rules and combining them with the previous digits if they
! overlap and still have all unique digits. When done with that, add whatever
! missing digit is needed to make the number pandigital.
<PRIVATE
: candidates ( n -- seq )
1000 over <range> [ number>digits 3 0 pad-head ] map [ all-unique? ] filter ;
: overlap? ( seq -- ? )
[ first 2 tail* ] [ second 2 head ] bi = ;
: clean ( seq -- seq )
[ unclip 1 head prefix concat ] map [ all-unique? ] filter ;
: add-missing-digit ( seq -- seq )
dup natural-sort 10 <iota> swap diff prepend ;
: interesting-pandigitals ( -- seq )
17 candidates { 13 11 7 5 3 2 } [
candidates swap cartesian-product concat
[ overlap? ] filter clean
] each [ add-missing-digit ] map ;
PRIVATE>
: euler043a ( -- answer )
interesting-pandigitals [ digits>number ] map-sum ;
! [ euler043a ] 100 ave-time
! 10 ms ave run time - 1.37 SD (100 trials)
SOLUTION: euler043a