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) {        if (root == null) return 0;        int cnt = cntNode(root.left);        if (k > cnt+1) return kthSmallest(root.right, k-cnt-1);        else if (k <= cnt) return kthSmallest(root.left, k);        return root.val;    }    public int cntNode(TreeNode root) {        if (root == null) return 0;        return 1 + cntNode(root.left) + cntNode(root.right);    }}