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Use math.algebra to solve project Euler problem 134

db4
Samuel Tardieu 2007-12-26 23:08:43 +01:00
parent c4529fb557
commit 4eb7aad50b
1 changed files with 6 additions and 27 deletions
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extra/project-euler/134/134.factor
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! Copyright (c) 2007 Samuel Tardieu. ! Copyright (c) 2007 Samuel Tardieu.
! See http://factorcode.org/license.txt for BSD license. ! See http://factorcode.org/license.txt for BSD license.
USING: arrays kernel math math.functions math.ranges math.primes.list namespaces USING: arrays kernel math.algebra math math.functions math.primes.list
sequences vars ; math.ranges sequences ;
IN: project-euler.134 IN: project-euler.134
! http://projecteuler.net/index.php?section=problems&id=134 ! http://projecteuler.net/index.php?section=problems&id=134
@ -23,36 +23,15 @@ IN: project-euler.134
! SOLUTION ! SOLUTION
! -------- ! --------
<PRIVATE
! Compute the smallest power of 10 greater than m ! Compute the smallest power of 10 greater than m
: next-power-of-10 ( m -- n ) : next-power-of-10 ( m -- n )
10 swap log 10 log / >integer [ 10 * ] times ; foldable 10 swap log 10 log / >integer [ 10 * ] times ; foldable
! Helper variables and words for the extended Euclidian algorithm ! Compute S for a given pair (p1, p2) -- that is the smallest positive
! See http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm ! number such that X = p1 [npt] and X = 0 [p2] (npt being the smallest
! power of 10 above p1)
VARS: r-1 u-1 v-1 r u v ;
: init ( a b -- )
>r >r-1 0 >u 1 >u-1 1 >v 0 >v-1 ;
: advance ( r u v -- )
v> >v-1 >v u> >u-1 >u r> >r-1 >r ;
: step ( -- )
r-1> r> 2dup / >integer [ * - ] keep u-1> over u> * - v-1> rot v> * -
advance ;
! Compute the inverse of a in field Z/bZ where b is prime
: inverse ( a b -- a-1 )
[ init [ r> 0 > ] [ step ] [ ] while u-1> ] with-scope ;
! Compute S for a given pair (p1, p2)
: s ( p1 p2 -- s ) : s ( p1 p2 -- s )
over next-power-of-10 [ over inverse pick * neg swap rem ] keep * + ; over 0 2array rot next-power-of-10 rot 2array chinese-remainder ;
PRIVATE>
: euler134 ( -- answer ) : euler134 ( -- answer )
primes-under-million 2 tail dup 1 tail 1000003 add [ s ] 2map sum ; primes-under-million 2 tail dup 1 tail 1000003 add [ s ] 2map sum ;