/extra/project-euler/043/043.factor
http://github.com/abeaumont/factor · Factor · 101 lines · 41 code · 28 blank · 32 comment · 6 complexity · 47529c9f07e6b03aa5a4bd62ccf80e1a MD5 · raw file
- ! 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.parser 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 10 digits>integer 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? [
- 10 digits>integer +
- ] [ 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 [ 10 digits>integer ] map-sum ;
- ! [ euler043a ] 100 ave-time
- ! 10 ms ave run time - 1.37 SD (100 trials)
- SOLUTION: euler043a