[Haskell-cafe] Extracting all pruned sub trees
markl at glyphic.com
Thu Jan 21 10:07:46 EST 2010
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:
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