int tree_sum_helper(tree_t tree, int sum)
{
    tree_t left, right;

    if (tree_isEmpty(tree)) return sum;
    else {
        left = tree_left(tree);
        right = tree_right(tree);
    }
    if (!tree_isEmpty(left)) sum+= tree_sum_helper(left, sum);
    if (!tree_isEmpty(right)) sum += tree_sum_helper(right, sum);

    return tree_elt(tree) + sum;
}