1 ! Copyright (c) 2008 Aaron Schaefer.
2 ! See http://factorcode.org/license.txt for BSD license.
3 USING: combinators.short-circuit kernel math math.functions math.combinatorics
4 math.ranges project-euler.common sequences sets sorting ;
7 ! http://projecteuler.net/index.php?section=problems&id=43
12 ! The number, 1406357289, is a 0 to 9 pandigital number because it is made up
13 ! of each of the digits 0 to 9 in some order, but it also has a rather
14 ! interesting sub-string divisibility property.
16 ! Let d1 be the 1st digit, d2 be the 2nd digit, and so on. In this way, we note
19 ! * d2d3d4 = 406 is divisible by 2
20 ! * d3d4d5 = 063 is divisible by 3
21 ! * d4d5d6 = 635 is divisible by 5
22 ! * d5d6d7 = 357 is divisible by 7
23 ! * d6d7d8 = 572 is divisible by 11
24 ! * d7d8d9 = 728 is divisible by 13
25 ! * d8d9d10 = 289 is divisible by 17
27 ! Find the sum of all 0 to 9 pandigital numbers with this property.
33 ! Brute force generating all the pandigitals then checking 3-digit divisiblity
34 ! properties...this is very slow!
38 : subseq-divisible? ( n index seq -- ? )
39 [ 1 - dup 3 + ] dip subseq digits>number swap divisor? ;
41 : interesting? ( seq -- ? )
43 [ [ 17 8 ] dip subseq-divisible? ]
44 [ [ 13 7 ] dip subseq-divisible? ]
45 [ [ 11 6 ] dip subseq-divisible? ]
46 [ [ 7 5 ] dip subseq-divisible? ]
47 [ [ 5 4 ] dip subseq-divisible? ]
48 [ [ 3 3 ] dip subseq-divisible? ]
49 [ [ 2 2 ] dip subseq-divisible? ]
54 : euler043 ( -- answer )
55 1234567890 number>digits 0 [
59 ] reduce-permutations ;
62 ! 60280 ms run / 59 ms GC time
68 ! Build the number from right to left, generating the next 3-digits according
69 ! to the divisiblity rules and combining them with the previous digits if they
70 ! overlap and still have all unique digits. When done with that, add whatever
71 ! missing digit is needed to make the number pandigital.
75 : candidates ( n -- seq )
76 1000 over <range> [ number>digits 3 0 pad-head ] map [ all-unique? ] filter ;
78 : overlap? ( seq -- ? )
79 [ first 2 tail* ] [ second 2 head ] bi = ;
81 : clean ( seq -- seq )
82 [ unclip 1 head prefix concat ] map [ all-unique? ] filter ;
84 : add-missing-digit ( seq -- seq )
85 dup natural-sort 10 iota swap diff prepend ;
87 : interesting-pandigitals ( -- seq )
88 17 candidates { 13 11 7 5 3 2 } [
89 candidates swap cartesian-product concat
90 [ overlap? ] filter clean
91 ] each [ add-missing-digit ] map ;
95 : euler043a ( -- answer )
96 interesting-pandigitals [ digits>number ] map-sum ;
98 ! [ euler043a ] 100 ave-time
99 ! 10 ms ave run time - 1.37 SD (100 trials)