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

Solution to Project Euler problem 73

db4
Aaron Schaefer 2008-11-10 22:56:37 -05:00
parent db7cbed3a5
commit 3b204ff971
3 changed files with 62 additions and 6 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

4
extra/project-euler/073/073-tests.factor Normal file
View File

@ -0,0 +1,4 @@
USING: project-euler.073 tools.test ;
IN: project-euler.073.tests
[ 5066251 ] [ euler073 ] unit-test

52
extra/project-euler/073/073.factor Normal file
View File

@ -0,0 +1,52 @@
! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel locals make math project-euler.common sequences ;
IN: project-euler.073
! http://projecteuler.net/index.php?section=problems&id=73
! DESCRIPTION
! -----------
! Consider the fraction, n/d, where n and d are positive integers. If n<d and
! HCF(n,d) = 1, it is called a reduced proper fraction.
! If we list the set of reduced proper fractions for d <= 8 in ascending order of
! size, we get:
! 1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8,
! 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8
! It can be seen that there are 3 fractions between 1/3 and 1/2.
! How many fractions lie between 1/3 and 1/2 in the sorted set of reduced
! proper fractions for d <= 10,000?
! SOLUTION
! --------
! Use the properties of a Farey sequence and mediants to recursively generate
! the next fraction until the denominator is as close to 1000000 as possible
! without going over.
<PRIVATE
:: (euler073) ( limit lo hi -- )
[let | m [ lo hi mediant ] |
m denominator limit <= [
m ,
limit lo m (euler073)
limit m hi (euler073)
] when
] ;
PRIVATE>
: euler073 ( -- answer )
[ 10000 1/3 1/2 (euler073) ] { } make length ;
! [ euler073 ] 10 ave-time
! 20506 ms ave run time - 937.07 SD (10 trials)
MAIN: euler073

12
extra/project-euler/project-euler.factor
View File

@ -15,12 +15,12 @@ USING: definitions io io.files 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.075 project-euler.059 project-euler.067 project-euler.071 project-euler.073
project-euler.076 project-euler.079 project-euler.092 project-euler.097 project-euler.075 project-euler.076 project-euler.079 project-euler.092
project-euler.100 project-euler.116 project-euler.117 project-euler.134 project-euler.097 project-euler.100 project-euler.116 project-euler.117
project-euler.148 project-euler.150 project-euler.151 project-euler.164 project-euler.134 project-euler.148 project-euler.150 project-euler.151
project-euler.169 project-euler.173 project-euler.175 project-euler.186 project-euler.164 project-euler.169 project-euler.173 project-euler.175
project-euler.190 ; project-euler.186 project-euler.190 ;
IN: project-euler IN: project-euler
<PRIVATE <PRIVATE