! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: combinators.lib kernel math project-euler.common sequences sorting ;
IN: project-euler.052

! http://projecteuler.net/index.php?section=problems&id=52

! DESCRIPTION
! -----------

! It can be seen that the number, 125874, and its double, 251748, contain
! exactly the same digits, but in a different order.

! Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x,
! contain the same digits.


! SOLUTION
! --------

! Analysis shows the number must be odd, divisible by 3, and larger than 123456

<PRIVATE

: map-nx ( n x -- seq )
    [ 1+ * ] with map ; inline

: all-same-digits? ( seq -- ? )
    [ number>digits natural-sort ] map all-equal? ;

: candidate? ( n -- ? )
    { [ dup odd? ] [ dup 3 mod zero? ] } 0&& nip ;

: next-all-same ( x n -- n )
    dup candidate? [
        2dup swap map-nx all-same-digits?
        [ nip ] [ 1+ next-all-same ] if
    ] [
        1+ next-all-same
    ] if ;

PRIVATE>

: euler052 ( -- answer )
    6 123456 next-all-same ;

! [ euler052 ] 100 ave-time
! 403 ms run / 7 ms GC ave time - 100 trials

MAIN: euler052