12. Kth Smallest Element in a BST

Given the root of a binary search tree, and an integer k, return the kth smallest value (1-indexed) of all the values of the nodes in the tree.

Example 1:

Input: root = [3,1,4,null,2], k = 1
Output: 1

Example 2:

Input: root = [5,3,6,2,4,null,null,1], k = 3
Output: 3

Constraints:

• The number of nodes in the tree is n.
• 1 <= k <= n <= 104
• 0 <= Node.val <= 104

Follow up: If the BST is modified often (i.e., we can do insert and delete operations) and you need to find the kth smallest frequently, how would you optimize?

Approach - Iterative

• Keep pushing left elements then start popping and then push starting from right
• Time: O(n) Space: O(n)

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode() {}
 *     TreeNode(int val) { this.val = val; }
 *     TreeNode(int val, TreeNode left, TreeNode right) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
class Solution {
    public int kthSmallest(TreeNode root, int k) {
        TreeNode c = root;
        Stack<TreeNode> s = new Stack<>();
        // In-order traversal using stack
        while (!s.isEmpty() || c != null) {
            // Go to the leftmost node
            while (c != null) {
                s.push(c);
                c = c.left;
            }
            // Pop the node from the stack and process it
            c = s.pop();
            k--;
            if (k == 0) return c.val;
            // Move to the right subtree
            c = c.right;
        }
        return -1;
    }
}