From: Richard O'Keefe [mailto:ok@cs.otago.ac.nz]
These lines of Haskell code find the Zumkeller numbers up to 5000 in 5 seconds on a 2.2GHz intel Mac. The equivalent in SML took 1.1 seconds. Note that this just finds whether a suitable partition exists; it does not report the partition.
factors :: Int -> [Int]
factors n = [m | m <- [1..n], mod n m == 0]
can_part :: [Int] -> Int -> Bool
can_part _ 0 = True can_part xs t = loop xs [] where loop [] _ = False loop (x:xs) ys = x <= t && can_part (xs++ys) (t-x) || loop xs ys
is_Zumkeller :: Int -> Bool is_Zumkeller n = let facs = factors n fsum = sum facs in mod fsum 2 == 0 && can_part facs (div fsum 2)
main = print (filter is_Zumkeller [1..5000])
Thanks, I like this solution! Pure functional, easy to understand, no monads and fast :-) -- Frank Buss, fb@frank-buss.de http://www.frank-buss.de, http://www.it4-systems.de