43 lines
886 B
Factor
43 lines
886 B
Factor
! Copyright (c) 2007 Samuel Tardieu.
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! See http://factorcode.org/license.txt for BSD license.
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IN: project-euler.169
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USING: combinators kernel math math.functions memoize ;
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! http://projecteuler.net/index.php?section=problems&id=169
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! DESCRIPTION
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! -----------
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! Define f(0) = 1 and f(n) to be the number of different ways n can be
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! expressed as a sum of integer powers of 2 using each power no more than
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! twice.
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! For example, f(10) = 5 since there are five different ways to express 10:
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! 1 + 1 + 8
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! 1 + 1 + 4 + 4
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! 1 + 1 + 2 + 2 + 4
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! 2 + 4 + 4
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! 2 + 8
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! What is f(1025)?
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! SOLUTION
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! --------
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MEMO: fn ( n -- x )
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{
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{ [ dup 2 < ] [ drop 1 ] }
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{ [ dup odd? ] [ 2/ fn ] }
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[ 2/ [ fn ] [ 1- fn ] bi + ]
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} cond ;
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: euler169 ( -- result )
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10 25 ^ fn ;
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! [ euler169 ] 100 ave-time
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! 0 ms run / 0 ms GC ave time - 100 trials
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MAIN: euler169
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