44 lines
1.2 KiB
Factor
44 lines
1.2 KiB
Factor
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! Copyright (c) 2008 Samuel Tardieu
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel math math.functions math.parser sequences ;
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IN: project-euler.057
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! http://projecteuler.net/index.php?section=problems&id=57
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! DESCRIPTION
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! -----------
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! It is possible to show that the square root of two can be expressed
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! as an infinite continued fraction.
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! √ 2 = 1 + 1/(2 + 1/(2 + 1/(2 + ... ))) = 1.414213...
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! By expanding this for the first four iterations, we get:
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! 1 + 1/2 = 3/2 = 1.5
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! 1 + 1/(2 + 1/2) = 7/5 = 1.4
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! 1 + 1/(2 + 1/(2 + 1/2)) = 17/12 = 1.41666...
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! 1 + 1/(2 + 1/(2 + 1/(2 + 1/2))) = 41/29 = 1.41379...
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! The next three expansions are 99/70, 239/169, and 577/408, but the
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! eighth expansion, 1393/985, is the first example where the number of
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! digits in the numerator exceeds the number of digits in the
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! denominator.
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! In the first one-thousand expansions, how many fractions contain a
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! numerator with more digits than denominator?
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! SOLUTION
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! --------
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: longer-numerator? ( seq -- ? )
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>fraction [ number>string length ] bi@ > ; inline
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: euler057 ( -- answer )
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0 1000 [ drop 2 + recip dup 1+ longer-numerator? ] count nip ;
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! [ euler057 ] time
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! 3.375118 seconds
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MAIN: euler057
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