Java 深度优先搜索找到二叉树的最大深度

我要解leetcode problem来求二叉树的最大深度.递归解决方案相当简单，所以我try 实现迭代DFS方法.以下是我的 idea :

public class TreeNode {
    int val;
    TreeNode left;
    TreeNode right;
    public TreeNode() {}
    public TreeNode(int val) { this.val = val; }
    public TreeNode(int val, TreeNode left, TreeNode right) {
        this.val = val;
        this.left = left;
        this.right = right;
    }
}

public static int maxDepthDfs(TreeNode root){
    Deque<TreeNode> stack = new LinkedList<>();
    Deque<Integer> depths = new LinkedList<>();
    TreeNode current = root;
    int maxDepth = 0;
    int currentDepth = 0;
    while(!stack.isEmpty() || current != null){
        if(current == null){
            if(currentDepth > maxDepth){
                maxDepth = currentDepth;
            }
            current = stack.pop().right;
            currentDepth = depths.pop() + 1;
        } else {
            stack.push(current);
            current = current.left;
            depths.push(currentDepth);
            currentDepth++;
        }
    }
    return maxDepth;
}

这个解决方案的问题是有太多额外的空间.有没有办法优化它？也许莫里斯·特拉弗斯的 idea 在这里会有所帮助？