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data Tree a = Empty | Branch a (Tree a) (Tree a) deriving (Show, Eq)
treeToString :: Tree Char -> [Char]
treeToString Empty = ""
treeToString (Branch x Empty Empty) = [x]
treeToString (Branch x l r) = x:'(':(treeToString l) ++ "," ++ (treeToString r) ++ ")"
stringToTree :: Monad m => [Char] -> m (Tree Char)
stringToTree "" = return (Empty)
stringToTree [x] = return (Branch x Empty Empty)
stringToTree x = fmap fst $ parse x
where parse (x:xs)
| x == ',' || x == ')' = return (Empty, x:xs)
parse (x:y:xs)
| y == ',' || y == ')' = return (Branch x Empty Empty, y:xs)
| y == '(' = do (lt, ',':xs') <- parse xs
(rt, ')':xs'') <- parse xs'
return (Branch x lt rt, xs'')
parse _ = fail "parse error"
cbtFromList :: [a] -> Tree a
cbtFromList xs = let (t, xss) = cbt (xs:xss) in t
where cbt ((x:xs):xss) = (Branch x lt rt, xs:xss'')
where (lt, xss') = cbt xss
(rt, xss'') = cbt xss'
cbt _ = (Empty, [])
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