The code below is, I think, n log n, a few seconds on a million + element list. I wonder if it's possible to get this down to O(N) by using a hashtable implemementation, or other better data structure. Further, is there a hashtable implementation for haskell that doesn't live in IO? Maybe in ST or something? import Data.HashTable import qualified Data.Set as S import Data.List (foldl') testdata = [1,4,8,9,20,11,20,14,2,15] ++ [1..(10^6)] wantedsum = 29 -- set data structure -- findsums locates pairs of integers in a list that add up to a wanted sum. findsums :: [Int] -> Int -> S.Set (Int,Int) findsums xs wanted = snd . foldl' f (S.empty,S.empty) $ xs where f (candidates,successes) next = if S.member (wanted-next) candidates then (candidates, S.insert (next,wanted-next) successes) else (S.insert next candidates,successes) -- hashtable data structure -- result: t -- fromList [(15,14),(16,13),(17,12),(18,11),(19,10),(20,9),(21,8),(22,7),(23,6),(24,5),(25,4),(26,3),(27,2),(28,1)] -- probably O(n log n) complexity since using tree based Data.Set (a few seconds on million+ element list) t = findsums testdata wantedsum