Group the elements of a set into disjoint subsets.
a) In how many ways can a group of 9 people work in 3 disjoint subgroups of 2, 3 and 4 persons? Write a function that generates all the possibilities and returns them in a list.
b) Generalize the above predicate in a way that we can specify a list of group sizes and the predicate will return a list of groups.
combination :: Int -> [a] -> [([a],[a])] combination 0 xs = [(,xs)] combination n  =  combination n (x:xs) = ts ++ ds where ts = [ (x:ys,zs) | (ys,zs) <- combination (n-1) xs ] ds = [ (ys,x:zs) | (ys,zs) <- combination n xs ] group :: [Int] -> [a] -> [[[a]]] group  _ = [] group (n:ns) xs = [ g:gs | (g,rs) <- combination n xs , gs <- group ns rs ]
And a way for those who like it shorter (but less comprehensive):
group :: [Int] -> [a] -> [[[a]]] group  = const [] group (n:ns) = concatMap (uncurry $ (. group ns) . map . (:)) . combination n
And for an intermediate length solution
group :: [Int] -> [a] -> [[[a]]] group  xs = [] group (g:gs) xs = concatMap helper $ combination g xs where helper (as, bs) = map (as:) (group gs bs)