230. Kth Smallest Element in a BST(Java)

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?

/** * Definition for a binary tree node. * public class TreeNode { *     int val; *     TreeNode left; *     TreeNode right; *     TreeNode(int x) { val = x; } * } */public class Solution {    public int kthSmallest(TreeNode root, int k) {        int count = countNodes(root.left);        if (k <= count) {            return kthSmallest(root.left, k);        } else if (k > count + 1) {            return kthSmallest(root.right, k - 1 - count);        }        return root.val;    }    private int countNodes(TreeNode node) {        if (node == null) return 0;        return 1 + countNodes(node.left) + countNodes(node.right);    } }