factor/extra/project-euler/203/203.factor

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Factor

! Copyright (c) 2008 Eric Mertens.
! See http://factorcode.org/license.txt for BSD license.
USING: fry kernel math math.primes.factors math.vectors sequences sets
project-euler.common ;
IN: project-euler.203
! http://projecteuler.net/index.php?section=problems&id=203
! DESCRIPTION
! -----------
! The binomial coefficients nCk can be arranged in triangular form, Pascal's
! triangle, like this:
! 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
! 1 7 21 35 35 21 7 1
! .........
! It can be seen that the first eight rows of Pascal's triangle contain twelve
! distinct numbers: 1, 2, 3, 4, 5, 6, 7, 10, 15, 20, 21 and 35.
! A positive integer n is called squarefree if no square of a prime divides n.
! Of the twelve distinct numbers in the first eight rows of Pascal's triangle,
! all except 4 and 20 are squarefree. The sum of the distinct squarefree numbers
! in the first eight rows is 105.
! Find the sum of the distinct squarefree numbers in the first 51 rows of
! Pascal's triangle.
! SOLUTION
! --------
<PRIVATE
: iterate ( n initial quot -- results )
swapd '[ @ dup ] replicate nip ; inline
: (generate) ( seq -- seq )
[ 0 prefix ] [ 0 suffix ] bi v+ ;
: generate ( n -- seq )
1 - { 1 } [ (generate) ] iterate combine ;
: squarefree ( n -- ? )
factors all-unique? ;
: solve ( n -- n )
generate [ squarefree ] filter sum ;
PRIVATE>
: euler203 ( -- n )
51 solve ;
! [ euler203 ] 100 ave-time
! 12 ms ave run time - 1.6 SD (100 trials)
SOLUTION: euler203