! Copyright (c) 2008 Samuel Tardieu
! See http://factorcode.org/license.txt for BSD license.
-USING: kernel math math.functions math.parser sequences project-euler.common ;
+USING: kernel math math.parser project-euler.common sequences ;
IN: project-euler.057
! http://projecteuler.net/index.php?section=problems&id=57
! 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...
+! √ 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...
+! 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
>fraction [ number>string length ] bi@ > ; inline
: euler057 ( -- answer )
- 0 1000 [ drop 2 + recip dup 1+ longer-numerator? ] count nip ;
+ 0 1000 <iota> [ drop 2 + recip dup 1 + longer-numerator? ] count nip ;
-! [ euler057 ] time
-! 3.375118 seconds
+! [ euler057 ] 100 ave-time
+! 1728 ms ave run time - 80.81 SD (100 trials)
SOLUTION: euler057