Lowest Common Ancestor in a Binary Tree, Haskell

Lowest Common Ancestor in a Binary Tree

--ghc 8.0.1 /opt/ghc/8.0.1/lib/ghc-8.0.0.20160127/

import Text.Printf

data Tree a = Empty | Node a (Tree a) (Tree a) deriving Show

myTree :: Tree Int
myTree = Node 1 
    (Node 2 
        (Node 4 Empty Empty)
        (Node 5 Empty Empty))
    (Node 3 
        (Node 6 Empty Empty)
        (Node 7 Empty Empty))

lca :: Eq a => Tree a -> a -> a -> Either Bool a
lca Empty _ _ = Left False
lca (Node v tl tr) n1 n2 = 
    let l = lca tl n1 n2
        r = lca tr n1 n2
        onroot = v == n1 || v == n2
    in case (l, r, onroot) of
        (Right a  , _         , _    ) -> Right a
        (_        , Right a   , _    ) -> Right a
        (Left True, Left True , _    ) -> Right v
        (Left True, _         , True ) -> Right v
        (_        , Left True , True ) -> Right v
        (Left True, _         , False) -> Left True
        (_         , Left True, False) -> Left True
        (_         , _        , True ) -> Left True
        _ -> Left False

lca_show :: (Eq a, Show a, PrintfArg a) => Tree a -> a -> a -> String
lca_show t n1 n2 = printf "LCA(%d,%d)=%s" n1 n2 result
    where result = case lca t n1 n2 of
                        Right a -> show a
                        _ -> "not found"

main = mapM print [
            lca_show myTree 0 9,
            lca_show myTree 0 5,
            lca_show myTree 4 5,
            lca_show myTree 4 6,
            lca_show myTree 3 4,
            lca_show myTree 2 4]


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