data Tree x = Leaf x
            | Node x [Tree x]
 
data TraversalResult x = TraversalResult Int [x]
 
dfs tree limit
    | limit == 0 = TraversalResult 0 []
    | otherwise =
        case tree of
            Leaf x          -> TraversalResult 1 [x]
            Node x children ->
                let TraversalResult num_visited result = traverse children (limit - 1)
                in TraversalResult (num_visited + 1) result
 
traverse children limit
    | limit == 0 = TraversalResult 0 []
    | otherwise =
        case children of
            [] -> TraversalResult 0 []
            first : rest ->
                TraversalResult (visited_first + visited_rest) (result_first ++ result_rest)
                where TraversalResult visited_first result_first = dfs first limit
                      TraversalResult visited_rest result_rest   =
                          traverse rest (limit - visited_first)
 
example_tree =
    Node 0 [
        Node 1 [Leaf 2, Leaf 3],
        Node 4 [Node 5 [Leaf 6]],
        Leaf 7
    ]
 
main = do
    print $ map
        (\limit -> let TraversalResult _ result = dfs example_tree limit in result)
        [1..8]

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