230 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.

Example 1:

Input: root = [3,1,4,null,2], k = 1
Output: 1
Example 2:

Input: root = [5,3,6,2,4,null,null,1], k = 3
Output: 3
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?

First Method, O(n) time complexity, use stack and inorder traversal

Notice: for inorder traversal while (!stack.isEmpty() || curt != null) for outer loop

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
/***
        3 
       / \
      1   4
       \
        2

***/
class Solution {
    public int kthSmallest(TreeNode root, int k) {
        if (root == null || k == 0) {
            return 0;
        }
        Stack<TreeNode> stack = new Stack<>();
        //inorder traversal
        TreeNode curt = root;
        while (curt != null || !stack.isEmpty()) {
         while (curt != null) {
            stack.push(curt);
            curt = curt.left;
        }
        curt = stack.pop();
        k--;  
        if (k == 0) {
            return curt.val;
        }
        curt = curt.right;
        }

        return -1;
    }
}