steve
/
factor
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Project Euler - problem 57

db4
Samuel Tardieu 2008-12-27 21:46:01 +01:00
parent 0182a3430d
commit 3fbb9f7081
2 changed files with 50 additions and 7 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

43
extra/project-euler/057/057.factor Normal file
View File

@ -0,0 +1,43 @@
! Copyright (c) 2008 Samuel Tardieu
! See http://factorcode.org/license.txt for BSD license.
USING: kernel math math.functions math.parser 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 [ drop 2 + recip dup 1+ longer-numerator? ] count nip ;
! [ euler057 ] time
! 3.375118 seconds
MAIN: euler057

14
extra/project-euler/project-euler.factor
View File

@ -15,13 +15,13 @@ USING: definitions io io.files io.pathnames kernel math math.parser
project-euler.041 project-euler.042 project-euler.043 project-euler.044 project-euler.041 project-euler.042 project-euler.043 project-euler.044
project-euler.045 project-euler.046 project-euler.047 project-euler.048 project-euler.045 project-euler.046 project-euler.047 project-euler.048
project-euler.052 project-euler.053 project-euler.055 project-euler.056 project-euler.052 project-euler.053 project-euler.055 project-euler.056
project-euler.059 project-euler.067 project-euler.071 project-euler.073 project-euler.057 project-euler.059 project-euler.067 project-euler.071
project-euler.075 project-euler.076 project-euler.079 project-euler.092 project-euler.073 project-euler.075 project-euler.076 project-euler.079
project-euler.097 project-euler.099 project-euler.100 project-euler.116 project-euler.092 project-euler.097 project-euler.099 project-euler.100
project-euler.117 project-euler.134 project-euler.148 project-euler.150 project-euler.116 project-euler.117 project-euler.134 project-euler.148
project-euler.151 project-euler.164 project-euler.169 project-euler.173 project-euler.150 project-euler.151 project-euler.164 project-euler.169
project-euler.175 project-euler.186 project-euler.190 project-euler.203 project-euler.173 project-euler.175 project-euler.186 project-euler.190
project-euler.215 ; project-euler.203 project-euler.215 ;
IN: project-euler IN: project-euler
<PRIVATE <PRIVATE