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);
}
}