# "Unfriendly Number" challenge

I tried to solve the Unfriendly Number problem on InterviewStreet:

There is one friendly number, K, and N unfriendly numbers. We want to find how many numbers are there which exactly divide the friendly number, but does not divide any of the unfriendly numbers.

$1 \le N \le 10^6$

$1 \le K \le 10^13$

$1 \le$ unfriendly numbers $\le 10^{18}$

The algorithm is quite simple:

1. Find the set S. The set of gcd's of each unfriendly number with the friendly number.
2. Find the set of divisors of the friendly number.
3. Check if a divisor of the friendly number is a divisor of any element in S.

My code, where u is the list of unfriendly numbers, k is the friendly number. nubOrd is the O(n log n) time version of nub.

test u k = length $filter (not)$ map try divisors
where try t = or $map (t divides ) (nubOrd$ map (gcd k) u)
divisors = concat [ [i,div k i] | i<-[1..floor $sqrt$ fromIntegral k],
i divides k]
d divides n = n mod d == 0


This code exceeds the time limit. The Java version of this algorithm solves the problem fine. Are there any ways to improve this code or is Haskell too slow for solving this problem?

• It might be more efficient to replace the length . filter not . map try chain with a fold like foldl (\count t -> if try t then count + 1 else count) 0 (probably with more strictness). But it's unlikely to make that much difference, since GHC is pretty smart.
– huon
Aug 24, 2012 at 15:30
• can we see your nubOrd? You compile it with -O2 right? Aug 24, 2012 at 15:39
• the nubOrd is the one here: stackoverflow.com/a/3100764/303863 Aug 24, 2012 at 16:10

You may try using rem instead of mod.
Also try making (nubOrd \$ map (gcd k) u) a separate expression and name it to ensure sharing, giving your function a concrete type signature too.