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