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