On Thu, Jan 21, 2010 at 4:07 PM, Mark Lentczner
On Jan 20, 2010, at 10:09 AM, Tom Hawkins wrote:
I'm looking for an elegant way to generate a list of all pruned trees where each pruned tree has one of its leaves removed.
This turned out to be a thornier problem than I thought! (pun intended)
-- | A simple Tree type. data Tree a = Leaf a | Branches [Tree a] deriving Show
-- | Produce a list of all possible Trees that can result from pruning one Leaf allPrunings :: Tree a -> [Tree a] allPrunings (Leaf _) = [] allPrunings (Branches ts) = Branches `fmap` pruneInTurn ts where pruneInTurn (a:as) = pruneOneWith a as ++ map (a:) (pruneInTurn as) pruneInTurn _ = [] pruneOneWith (Leaf _) as = [ as ] pruneOneWith a as = map (:as) (allPrunings a)
The difficulty lies in the treatment of Branches vs Leaf: Pruning Branches laves a Tree who's head (well, "root") is of the same form, whereas pruning Leaf leaves nothing (no valid Tree). This gives rise for the need for the pruneOneWith function.
A more complete module with a small parser for a string tree language, and a nice, input and pring all prunings function can be found here:
http://bitbucket.org/mtnviewmark/haskell-playground/src/tip/cafe/TreePrune.h...
Enjoy!
Very nice. Thanks! -Tom