53 lines
1.4 KiB
Factor
53 lines
1.4 KiB
Factor
! Copyright (c) 2008 Aaron Schaefer.
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel locals make math project-euler.common sequences ;
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IN: project-euler.073
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! http://projecteuler.net/index.php?section=problems&id=73
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! DESCRIPTION
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! -----------
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! Consider the fraction, n/d, where n and d are positive integers. If n<d and
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! HCF(n,d) = 1, it is called a reduced proper fraction.
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! If we list the set of reduced proper fractions for d <= 8 in ascending order of
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! size, we get:
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! 1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8,
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! 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8
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! It can be seen that there are 3 fractions between 1/3 and 1/2.
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! How many fractions lie between 1/3 and 1/2 in the sorted set of reduced
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! proper fractions for d <= 10,000?
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! SOLUTION
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! --------
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! Use the properties of a Farey sequence and mediants to recursively generate
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! the next fraction until the denominator is as close to 1000000 as possible
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! without going over.
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<PRIVATE
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:: (euler073) ( limit lo hi -- )
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[let | m [ lo hi mediant ] |
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m denominator limit <= [
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m ,
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limit lo m (euler073)
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limit m hi (euler073)
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] when
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] ;
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PRIVATE>
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: euler073 ( -- answer )
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[ 10000 1/3 1/2 (euler073) ] { } make length ;
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! [ euler073 ] 10 ave-time
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! 20506 ms ave run time - 937.07 SD (10 trials)
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MAIN: euler073
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