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);
}
}