factor/extra/project-euler/148/148.factor

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Factor

! Copyright (c) 2008 Eric Mertens.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel math math.functions sequences project-euler.common ;
IN: project-euler.148
! http://projecteuler.net/index.php?section=problems&id=148
! DESCRIPTION
! -----------
! We can easily verify that none of the entries in the first seven rows of
! Pascal's triangle are divisible by 7:
! 1
! 1 1
! 1 2 1
! 1 3 3 1
! 1 4 6 4 1
! 1 5 10 10 5 1
! 1 6 15 20 15 6 1
! However, if we check the first one hundred rows, we will find that only 2361
! of the 5050 entries are not divisible by 7.
! Find the number of entries which are not divisible by 7 in the first one
! billion (10^9) rows of Pascal's triangle.
! SOLUTION
! --------
<PRIVATE
: sum-1toN ( n -- sum )
dup 1 + * 2/ ; inline
: >base7 ( x -- y )
[ dup 0 > ] [ 7 /mod ] produce nip ;
: (use-digit) ( prev x index -- next )
[ [ 1 + * ] [ sum-1toN 7 sum-1toN ] bi ] dip ^ * + ;
: (euler148) ( x -- y )
>base7 0 [ (use-digit) ] reduce-index ;
PRIVATE>
: euler148 ( -- answer )
10 9 ^ (euler148) ;
! [ euler148 ] 100 ave-time
! 0 ms ave run time - 0.17 SD (100 trials)
SOLUTION: euler148