/extra/project-euler/169/169.factor

 1! Copyright (c) 2007 Samuel Tardieu.
 2! See http://factorcode.org/license.txt for BSD license.
 3IN: project-euler.169
 4USING: combinators kernel math math.functions memoize project-euler.common ;
 5
 6! http://projecteuler.net/index.php?section=problems&id=169
 7
 8! DESCRIPTION
 9! -----------
10
11! Define f(0) = 1 and f(n) to be the number of different ways n can be
12! expressed as a sum of integer powers of 2 using each power no more than
13! twice.
14
15! For example, f(10) = 5 since there are five different ways to express 10:
16
17! 1 + 1 + 8
18! 1 + 1 + 4 + 4
19! 1 + 1 + 2 + 2 + 4
20! 2 + 4 + 4
21! 2 + 8
22
23! What is f(10^25)?
24
25
26! SOLUTION
27! --------
28
29MEMO: fn ( n -- x )
30    {
31        { [ dup 2 < ]  [ drop 1 ] }
32        { [ dup odd? ] [ 2/ fn ] }
33        [ 2/ [ fn ] [ 1 - fn ] bi + ]
34    } cond ;
35
36: euler169 ( -- result )
37    10 25 ^ fn ;
38
39! [ euler169 ] 100 ave-time
40! 0 ms ave run time - 0.2 SD (100 trials)
41
42SOLUTION: euler169