Leetcode: Kth Smallest Element in a BST

Given a binary search tree, write a function kthSmallest to find the kth smallest element in it.

Note: 
You may assume k is always valid, 1 ≤ k ≤ BST‘s total elements.

Follow up:
What if the BST is modified (insert/delete operations) often and you need to find the kth smallest frequently? How would you optimize the kthSmallest routine?

Hint:

Try to utilize the property of a BST.
What if you could modify the BST node‘s structure?
The optimal runtime complexity is O(height of BST).

 1 /**
 2  * Definition for a binary tree node.
 3  * public class TreeNode {
 4  *     int val;
 5  *     TreeNode left;
 6  *     TreeNode right;
 7  *     TreeNode(int x) { val = x; }
 8  * }
 9  */
10 public class Solution {
11     public int kthSmallest(TreeNode root, int k) {
12         TreeNode node = root;
13         Stack<TreeNode> st = new Stack<TreeNode>();
14         int counter = 0;
15         while (!st.isEmpty() || node != null) {
16             if (node != null) {
17                 st.push(node);
18                 node = node.left;
19             } 
20             else {
21                 node = st.pop();
22                 counter++;
23                 if (counter == k) return node.val;
24                 node = node.right;
25             }
26         }
27         return -1;
28     }
29 }