Given a binary search tree, write a functionkthSmallestto find thekth 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?

Credits:
Special thanks to@tsfor adding this problem and creating all test cases.

tag: DFS, Binary Tree, In Order Traversal

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    int count = 0;
    int ans = -1;
    public int kthSmallest(TreeNode root, int k) {
        dfs(root, k);

        return ans;
    }

    private void dfs(TreeNode root, int k){
        if (root == null) return;

        dfs(root.left, k);
        count++;
        if (count == k) ans = root.val;
        dfs(root.right, k);
    }
}