59 lines
1.7 KiB
Factor
59 lines
1.7 KiB
Factor
! Copyright (c) 2007 Samuel Tardieu.
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! See http://factorcode.org/license.txt for BSD license.
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USING: combinators kernel math math.parser math.ranges sequences vectors ;
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IN: project-euler.175
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! http://projecteuler.net/index.php?section=problems&id=175
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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 ways to write n as a sum of
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! powers of 2 where no power occurs more than twice.
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! For example, f(10) = 5 since there are five different ways to express
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! 10: 10 = 8+2 = 8+1+1 = 4+4+2 = 4+2+2+1+1 = 4+4+1+1
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! It can be shown that for every fraction p/q (p0, q0) there exists at least
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! one integer n such that f(n) / f(n-1) = p/q.
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! For instance, the smallest n for which f(n) / f(n-1) = 13/17 is 241. The
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! binary expansion of 241 is 11110001. Reading this binary number from the most
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! significant bit to the least significant bit there are 4 one's, 3 zeroes and
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! 1 one. We shall call the string 4,3,1 the Shortened Binary Expansion of 241.
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! Find the Shortened Binary Expansion of the smallest n for which
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! f(n) / f(n-1) = 123456789/987654321.
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! Give your answer as comma separated integers, without any whitespaces.
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! SOLUTION
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! --------
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<PRIVATE
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: add-bits ( vec n b -- )
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over zero? [
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3drop
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] [
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pick length 1 bitand = [ over pop + ] when swap push
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] if ;
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: compute ( vec ratio -- )
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{
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{ [ dup integer? ] [ 1- 0 add-bits ] }
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{ [ dup 1 < ] [ 1 over - / dupd compute 1 1 add-bits ] }
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{ [ t ] [ [ 1 mod compute ] 2keep >integer 0 add-bits ] }
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} cond ;
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PRIVATE>
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: euler175 ( -- result )
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V{ 1 } clone dup 123456789/987654321 compute [ number>string ] map "," join ;
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! [ euler175 ] 100 ave-time
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! 0 ms run / 0 ms GC ave time - 100 trials
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MAIN: euler175
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