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).

Solution

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {

    int ans = 0;
    public int kthSmallest(TreeNode root, int k) {
        // how to do this recursively?
        search(root, k);
        return ans;
    }

    public int search(TreeNode root, int k) {
        if(root == null) return k;
        if(root.left != null) {
            k = search(root.left, k);
            if(k <= 0) return k;
        }

        if(--k == 0) {
            ans = root.val;
            return -1;
        }

        if(root.right != null) {
            k = search(root.right, k);
            if(k <= 0) return k;
        }

        return k;
    }

}