1 ! Copyright (c) 2008 Eric Mertens.
2 ! See http://factorcode.org/license.txt for BSD license.
3 USING: circular disjoint-sets kernel math ranges sequences project-euler.common ;
6 ! http://projecteuler.net/index.php?section=problems&id=186
11 ! Here are the records from a busy telephone system with one million users:
19 ! The telephone number of the caller and the called number in record n are
20 ! Caller(n) = S2n-1 and Called(n) = S2n where S1,2,3,... come from the "Lagged
21 ! Fibonacci Generator":
23 ! For 1 <= k <= 55, Sk = [100003 - 200003k + 300007k^3] (modulo 1000000)
24 ! For 56 <= k, Sk = [Sk-24 + Sk-55] (modulo 1000000)
26 ! If Caller(n) = Called(n) then the user is assumed to have misdialled and the
27 ! call fails; otherwise the call is successful.
29 ! From the start of the records, we say that any pair of users X and Y are
30 ! friends if X calls Y or vice-versa. Similarly, X is a friend of a friend of Z
31 ! if X is a friend of Y and Y is a friend of Z; and so on for longer chains.
33 ! The Prime Minister's phone number is 524287. After how many successful calls,
34 ! not counting misdials, will 99% of the users (including the PM) be a friend,
35 ! or a friend of a friend etc., of the Prime Minister?
41 : (generator) ( k -- n )
42 dup sq 300007 * 200003 - * 100003 + 1000000 rem ;
44 : <generator> ( -- lag )
45 55 [1..b] [ (generator) ] map <circular> ;
48 [ [ first dup ] [ 31 swap nth ] bi + 1000000 rem ] keep circular-push ;
50 : (euler186) ( generator counter unionfind -- counter )
51 524287 over equiv-set-size 990000 < [
52 pick [ next ] [ next ] bi
56 pick equate [ 1 + ] dip
62 : <relation> ( n -- unionfind )
63 <iota> <disjoint-set> [ [ add-atom ] curry each ] keep ;
66 <generator> 0 1000000 <relation> (euler186) ;
68 ! [ euler186 ] 10 ave-time
69 ! 18572 ms ave run time - 796.87 SD (10 trials)