[project @ 2005-10-26 22:52:58 by ross]

[haskell-directory.git] / Data / Tree.hs

diff --git a/Data/Tree.hs b/Data/Tree.hs
index c68e66e..5a30470 100644 (file)
--- a/Data/Tree.hs
+++ b/Data/Tree.hs
@@ -18,14 +18,28 @@ module Data.Tree(
        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.Sequence (Seq, empty, singleton, (<|), (|>), fromList, toList,
+                       ViewL(..), ViewR(..), viewl, viewr)
+import Data.Typeable
+
+#include "Typeable.h"
+
 -- | 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) */
@@ -35,6 +49,8 @@ instance Show a => Show (Tree a)
 #endif
 type Forest a = [Tree a]
 
+INSTANCE_TYPEABLE1(Tree,treeTc,"Tree")
+
 instance Functor Tree where
   fmap = mapTree
 
@@ -66,6 +82,60 @@ flatten t = squish t []
 
 -- | 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 getElement $ unfoldForestQ f (singleton b)
+  where getElement xs = case viewl xs of
+               x :< _ -> x
+               EmptyL -> error "unfoldTreeM_BF"
+
+-- | 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 toList . unfoldForestQ f . fromList
+
+-- takes a sequence (queue) of seeds
+-- produces a sequence (reversed queue) of trees of the same length
+unfoldForestQ :: Monad m => (b -> m (a, [b])) -> Seq b -> m (Seq (Tree a))
+unfoldForestQ f aQ = case viewl aQ of
+       EmptyL -> return empty
+       a :< aQ -> do
+               (b, as) <- f a
+               tQ <- unfoldForestQ f (foldl (|>) aQ as)
+               let (tQ', ts) = splitOnto [] as tQ
+               return (Node b ts <| tQ')
+  where splitOnto :: [a'] -> [b'] -> Seq a' -> (Seq a', [a'])
+       splitOnto as [] q = (q, as)
+       splitOnto as (_:bs) q = case viewr q of
+               q' :> a -> splitOnto (a:as) bs q'
+               EmptyR -> error "unfoldForestQ"