import Tree
import Control.Applicative

completeBinaryTree n = makeTree 1
    where makeTree x
            | x > n = Empty
            | otherwise = Branch 'x' (makeTree (2*x)) (makeTree (2*x+1))

isCompleteBinaryTree t = b>a where
    [a, b] = getZipList $ maxmin t 1
    maxmin Empty m = ZipList [0, m]
    maxmin (Branch _ l r) m = ZipList [max.(max m),min] <*> (maxmin l (2*m)) <*> (maxmin r (2*m + 1))