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