/extra/project-euler/148/148.factor
http://github.com/abeaumont/factor · Factor · 54 lines · 15 code · 17 blank · 22 comment · 0 complexity · f31ca188e6325544bd1a120ca5ce1a43 MD5 · raw file
- ! 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