【LeetCode】 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.

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?

Hint:
Try to utilize the property of a BST.
What if you could modify the BST node's structure?
The optimal runtime complexity is O(height of BST).

/**
* 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 = countNode(root.left);
if (k <= count) {
return kthSmallest(root.left, k);
} else if (k > count + 1) {
return kthSmallest(root.right, k - count - 1);
}
return root.val;
}

private int countNode(TreeNode node) {
if (node == null) {
return 0;
}
return 1 + countNode(node.left) + countNode(node.right);
}
}