Kth Smallest Element in a BST

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

Example 1:

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

Example 2:

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

Constraints:

• The number of elements of the BST is between 1 to 10^4.

• You may assume k is always valid, 1 ≤ k ≤ BST's total elements.

class Solution {
    int count = 0, result = Integer.MIN_VALUE;

    public int kthSmallest(TreeNode root, int k) {
        traverse(root, k);
        return result;
    }

    public void traverse(TreeNode root, int k) {
        if (root == null)
            return;
        traverse(root.left, k);
        count++;
        if (count == k)
            result = root.val;
        if (count < k)
            traverse(root.right, k);
    }
}