81 lines
1.8 KiB
Factor
81 lines
1.8 KiB
Factor
! Copyright (c) 2007, 2008 Aaron Schaefer, Alexander Solovyov, Vishal Talwar.
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel math sequences project-euler.common ;
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IN: project-euler.002
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! http://projecteuler.net/index.php?section=problems&id=2
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! DESCRIPTION
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! -----------
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! Each new term in the Fibonacci sequence is generated by adding the previous
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! two terms. By starting with 1 and 2, the first 10 terms will be:
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! 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
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! Find the sum of all the even-valued terms in the sequence which do not exceed
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! four million.
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! SOLUTION
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! --------
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<PRIVATE
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: (fib-upto) ( seq n limit -- seq )
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2dup <= [ [ over push dup 2 tail* sum ] dip (fib-upto) ] [ 2drop ] if ;
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PRIVATE>
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: fib-upto ( n -- seq )
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V{ 0 } clone 1 rot (fib-upto) ;
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: euler002 ( -- answer )
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4,000,000 fib-upto [ even? ] filter sum ;
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! [ euler002 ] 100 ave-time
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! 0 ms ave run time - 0.22 SD (100 trials)
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! ALTERNATE SOLUTIONS
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! -------------------
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: fib-upto* ( n -- seq )
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0 1 [ pick over >= ] [ [ nip ] 2keep + dup ] produce [ 3drop ] dip
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but-last-slice { 0 1 } prepend ;
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: euler002a ( -- answer )
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4,000,000 fib-upto* [ even? ] filter sum ;
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! [ euler002a ] 100 ave-time
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! 0 ms ave run time - 0.2 SD (100 trials)
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<PRIVATE
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: next-fibs ( x y -- y x+y )
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[ nip ] [ + ] 2bi ;
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: ?retotal ( total fib- fib+ -- retotal fib- fib+ )
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dup even? [ [ nip + ] 2keep ] when ;
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: (sum-even-fibs-below) ( partial fib- fib+ max -- total )
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2dup > [
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3drop
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] [
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[ ?retotal next-fibs ] dip (sum-even-fibs-below)
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] if ;
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PRIVATE>
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: sum-even-fibs-below ( max -- sum )
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[ 0 0 1 ] dip (sum-even-fibs-below) ;
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: euler002b ( -- answer )
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4000000 sum-even-fibs-below ;
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! [ euler002b ] 100 ave-time
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! 0 ms ave run time - 0.0 SD (100 trials)
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SOLUTION: euler002b
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