Solution2.java

/**
 * 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) {
        BST bst = new BST(root);
        return bst.kthSmallest(k);
    }
}

class BST {
    private TreeNode root;
    private Map<TreeNode, Integer> cnt = new HashMap<>();

    public BST(TreeNode root) {
        this.root = root;
        count(root);
    }

    public int kthSmallest(int k) {
        TreeNode node = root;
        while (node != null) {
            int v = node.left == null ? 0 : cnt.get(node.left);
            if (v == k - 1) {
                return node.val;
            }
            if (v < k - 1) {
                node = node.right;
                k -= (v + 1);
            } else {
                node = node.left;
            }
        }
        return 0;
    }

    private int count(TreeNode root) {
        if (root == null) {
            return 0;
        }
        int n = 1 + count(root.left) + count(root.right);
        cnt.put(root, n);
        return n;
    }
}