The following function finds all the partitions of an integer that are
made of unique parts.
It works, but I'm not happy with it--seems too complex. Is there a
more haskelly (clever)
way to implement this?
-- parts n finds all the partitions of n having unique parts
-- helper function parts' n r m finds partitions of n from a set
r of remaining possible parts,
-- with a minimum part of m.
parts n = parts' n [1..n] 1 where
parts' 0 _ _ = [[]] -- there's always one way ([])
to get a sum of 0
parts' n [] _ = [] -- if n /= 0, there are no
possible partitions of the empty list
parts' n remaining atleast = [(x:y) | x <- filter (>= atleast)
remaining, y <- (parts' (n-x) (remaining \\ [x])) x]
*Main> parts 11
[[1,2,3,5],[1,2,8],[1,3,7],[1,4,6],[1,10],[2,3,6],[2,4,5],[2,9],[3,8],[4,7],[5,6],[11]]
