drawTree, drawForest,
-- * Extraction
flatten, levels,
+ -- * Building trees
+ unfoldTree, unfoldForest,
+ unfoldTreeM, unfoldForestM,
+ unfoldTreeM_BF, unfoldForestM_BF,
) where
#ifdef __HADDOCK__
import Prelude
#endif
+import Control.Monad
+import Data.Maybe
+import Data.Queue
+
-- | Multi-way trees, also known as /rose trees/.
-data Tree a = Node a (Forest a) -- ^ a value and zero or more child trees.
+data Tree a = Node {
+ rootLabel :: a, -- ^ label value
+ subForest :: Forest a -- ^ zero or more child trees
+ }
#ifndef __HADDOCK__
deriving (Eq, Read, Show)
#else /* __HADDOCK__ (which can't figure these out by itself) */
-- | Lists of nodes at each level of the tree.
levels :: Tree a -> [[a]]
-levels t = map (map root) $ takeWhile (not . null) $ iterate subforest [t]
- where root (Node x _) = x
- subforest f = [t | Node _ ts <- f, t <- ts]
+levels t = map (map rootLabel) $
+ takeWhile (not . null) $
+ iterate (concatMap subForest) [t]
+
+-- | Build a tree from a seed value
+unfoldTree :: (b -> (a, [b])) -> b -> Tree a
+unfoldTree f b = let (a, bs) = f b in Node a (unfoldForest f bs)
+
+-- | Build a forest from a list of seed values
+unfoldForest :: (b -> (a, [b])) -> [b] -> Forest a
+unfoldForest f = map (unfoldTree f)
+
+-- | Monadic tree builder, in depth-first order
+unfoldTreeM :: Monad m => (b -> m (a, [b])) -> b -> m (Tree a)
+unfoldTreeM f b = do
+ (a, bs) <- f b
+ ts <- unfoldForestM f bs
+ return (Node a ts)
+
+-- | Monadic forest builder, in depth-first order
+#ifndef __NHC__
+unfoldForestM :: Monad m => (b -> m (a, [b])) -> [b] -> m (Forest a)
+#endif
+unfoldForestM f = mapM (unfoldTreeM f)
+
+-- | Monadic tree builder, in breadth-first order,
+-- using an algorithm adapted from
+-- /Breadth-First Numbering: Lessons from a Small Exercise in Algorithm Design/,
+-- by Chris Okasaki, /ICFP'00/.
+unfoldTreeM_BF :: Monad m => (b -> m (a, [b])) -> b -> m (Tree a)
+unfoldTreeM_BF f b = liftM (fst . fromJust . deQueue) $
+ unfoldForestQ f (listToQueue [b])
+
+-- | Monadic forest builder, in breadth-first order,
+-- using an algorithm adapted from
+-- /Breadth-First Numbering: Lessons from a Small Exercise in Algorithm Design/,
+-- by Chris Okasaki, /ICFP'00/.
+unfoldForestM_BF :: Monad m => (b -> m (a, [b])) -> [b] -> m (Forest a)
+unfoldForestM_BF f = liftM (reverseOnto []) . unfoldForestQ f . listToQueue
+ where reverseOnto :: [a'] -> Queue a' -> [a']
+ reverseOnto as q = case deQueue q of
+ Nothing -> as
+ Just (a, q') -> reverseOnto (a:as) q'
+
+-- takes a queue of seeds
+-- produces a queue of trees of the same length, but in the reverse order
+unfoldForestQ :: Monad m => (b -> m (a, [b])) -> Queue b -> m (Queue (Tree a))
+unfoldForestQ f aQ = case deQueue aQ of
+ Nothing -> return emptyQueue
+ Just (a, aQ) -> do
+ (b, as) <- f a
+ tQ <- unfoldForestQ f (foldl addToQueue aQ as)
+ let (ts, tQ') = splitOnto [] as tQ
+ return (addToQueue tQ' (Node b ts))
+ where splitOnto :: [a'] -> [b'] -> Queue a' -> ([a'], Queue a')
+ splitOnto as [] q = (as, q)
+ splitOnto as (_:bs) q = case fromJust (deQueue q) of
+ (a, q') -> splitOnto (a:as) bs q'