104 lines
2.5 KiB
Haskell
104 lines
2.5 KiB
Haskell
module HW2 where
|
|
|
|
-- | Binary trees with nodes labeled by values of an arbitrary type.
|
|
data Tree a
|
|
= Node a (Tree a) (Tree a)
|
|
| End
|
|
deriving (Eq,Show)
|
|
|
|
-- | One step in a path, indicating whether to follow the left subtree (L)
|
|
-- or the right subtree (R).
|
|
data Step = L | R
|
|
deriving (Eq,Show)
|
|
|
|
-- | A path is a sequence of steps. Each node in a binary tree can be
|
|
-- identified by a path, indicating how to move down the tree starting
|
|
-- from the root.
|
|
type Path = [Step]
|
|
|
|
-- | Create a leaf node.
|
|
leaf :: a -> Tree a
|
|
leaf x = Node x End End
|
|
|
|
-- | An example tree.
|
|
ex :: Tree Int
|
|
ex = Node 4 (Node 3 (leaf 2) End)
|
|
(Node 7 (Node 5 End (leaf 6))
|
|
(leaf 8))
|
|
|
|
instance Functor Tree where
|
|
fmap f End = End
|
|
fmap f (Node v l r) = Node (f v) (fmap f l) (fmap f r)
|
|
|
|
-- | Map a function over a tree. Applies the given function to every label
|
|
-- in the tree, preserving the tree's structure.
|
|
--
|
|
-- >>> mapTree odd End
|
|
-- End
|
|
--
|
|
-- >>> mapTree even (Node 5 (leaf 2) End)
|
|
-- Node False (Node True End End) End
|
|
--
|
|
-- >>> (mapTree not . mapTree even) (Node 5 End (leaf 2))
|
|
-- Node True End (Node False End End)
|
|
--
|
|
-- >>> mapTree (+10) ex
|
|
-- Node 14 (Node 13 (Node 12 End End) End) (Node 17 (Node 15 End (Node 16 End End)) (Node 18 End End))
|
|
--
|
|
-- >>> ex == (mapTree (subtract 27) . mapTree (+27)) ex
|
|
-- True
|
|
--
|
|
mapTree :: (a -> b) -> Tree a -> Tree b
|
|
mapTree = fmap
|
|
|
|
|
|
-- | Get the value at the node specified by a path. Returns 'Nothing' if
|
|
-- the given path is invalid.
|
|
--
|
|
-- >>> valueAt [] ex
|
|
-- Just 4
|
|
--
|
|
-- >>> valueAt [L,L] ex
|
|
-- Just 2
|
|
--
|
|
-- >>> valueAt [L,R] ex
|
|
-- Nothing
|
|
--
|
|
-- >>> valueAt [R,L,R] ex
|
|
-- Just 6
|
|
--
|
|
-- >>> valueAt [L,L,L] ex
|
|
-- Nothing
|
|
--
|
|
valueAt :: Path -> Tree a -> Maybe a
|
|
valueAt _ End = Nothing
|
|
valueAt [] (Node a _ _) = Just a
|
|
valueAt (x:xs) (Node _ l r) = valueAt xs $ if x == L then l else r
|
|
|
|
-- | Find a path to a node that contains the given value.
|
|
--
|
|
-- >>> pathTo 3 (leaf 5)
|
|
-- Nothing
|
|
--
|
|
-- >>> pathTo 5 ex
|
|
-- Just [R,L]
|
|
--
|
|
-- >>> pathTo 6 ex
|
|
-- Just [R,L,R]
|
|
--
|
|
-- >>> pathTo 4 ex
|
|
-- Just []
|
|
--
|
|
-- >>> pathTo 10 ex
|
|
-- Nothing
|
|
--
|
|
|
|
pathTo :: Eq a => a -> Tree a -> Maybe Path
|
|
pathTo _ End = Nothing
|
|
pathTo v (Node a l r) = orElse currentNode $ orElse (pathHelper v l L) $ pathHelper v r R
|
|
where
|
|
currentNode = if a == v then Just [] else Nothing
|
|
pathHelper _ tree dir = fmap (dir:) (pathTo v tree)
|
|
orElse m1 m2 = if isJust m1 then m1 else m2
|
|
isJust mx = mx /= Nothing
|