! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: byte-arrays fry hints kernel math math.primes sequences ;
IN: project-euler.049

! http://projecteuler.net/index.php?section=problems&id=49

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

! The arithmetic sequence, 1487, 4817, 8147, in which each of the terms
! increases by 3330, is unusual in two ways: (i) each of the three terms are
! prime, and, (ii) each of the 4-digit numbers are permutations of one another.

! There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes,
! exhibiting this property, but there is one other 4-digit increasing sequence.

! What 12-digit number do you form by concatenating the three terms in this
! sequence?


! SOLUTION
! --------

<PRIVATE

: count-digits ( n -- byte-array )
    10 <byte-array> [
        '[ 10 /mod _ [ 1+ ] change-nth dup 0 > ] loop drop
    ] keep ;

HINTS: count-digits fixnum ;

: permutations? ( n m -- ? )
    [ count-digits ] bi@ = ;

: collect-permutations ( seq -- seq )
    [ V{ } clone ] [ dup length ] bi* [
        unclip-slice 2dup '[ _ permutations? ] filter
        swap prefix pick push
    ] times drop ;

PRIVATE>

: euler049 ( -- answer )
    1000 9999 primes-between collect-permutations ;

! [ euler049 ] 20 ave-time
! 420 ms ave run time - 17.38 SD (20 trials)

MAIN: euler049