stringBuilder :: Tree -> [Char] -> [Char]
stringBuilder t s =
    let c  = fst (decode t s)
        xs = snd (decode t s)
    in c ++ (stringBuilder t xs)

-- Recursively builds the output string by traversing
-- the tree built in parse.
decode :: Tree -> [Char] -> ([Char], [Char])
decode (Leaf c)     (x:xs) = ([c], xs)
decode (Leaf c)       []   = ([c], [])
decode (Branch a b) (x:xs) =
    if x == '0'
        then decode a (x:xs)
    else if x == '1'
        then decode b (x:xs)
    else undefined
decode (Branch a b)   []   = ([], [])