45 lines
1.3 KiB
Factor
45 lines
1.3 KiB
Factor
! Copyright (c) 2008 Samuel Tardieu
|
|
! See http://factorcode.org/license.txt for BSD license.
|
|
USING: kernel math math.functions math.parser math.ranges project-euler.common
|
|
sequences ;
|
|
IN: project-euler.057
|
|
|
|
! http://projecteuler.net/index.php?section=problems&id=57
|
|
|
|
! DESCRIPTION
|
|
! -----------
|
|
|
|
! It is possible to show that the square root of two can be expressed
|
|
! as an infinite continued fraction.
|
|
|
|
! √ 2 = 1 + 1/(2 + 1/(2 + 1/(2 + ... ))) = 1.414213...
|
|
|
|
! By expanding this for the first four iterations, we get:
|
|
|
|
! 1 + 1/2 = 3/2 = 1.5
|
|
! 1 + 1/(2 + 1/2) = 7/5 = 1.4
|
|
! 1 + 1/(2 + 1/(2 + 1/2)) = 17/12 = 1.41666...
|
|
! 1 + 1/(2 + 1/(2 + 1/(2 + 1/2))) = 41/29 = 1.41379...
|
|
|
|
! The next three expansions are 99/70, 239/169, and 577/408, but the
|
|
! eighth expansion, 1393/985, is the first example where the number of
|
|
! digits in the numerator exceeds the number of digits in the
|
|
! denominator.
|
|
|
|
! In the first one-thousand expansions, how many fractions contain a
|
|
! numerator with more digits than denominator?
|
|
|
|
! SOLUTION
|
|
! --------
|
|
|
|
: longer-numerator? ( seq -- ? )
|
|
>fraction [ number>string length ] bi@ > ; inline
|
|
|
|
: euler057 ( -- answer )
|
|
0 1000 iota [ drop 2 + recip dup 1 + longer-numerator? ] count nip ;
|
|
|
|
! [ euler057 ] 100 ave-time
|
|
! 1728 ms ave run time - 80.81 SD (100 trials)
|
|
|
|
SOLUTION: euler057
|