LeetCode:Kth Smallest Element in a BST

Kth Smallest Element in a BST

Total Accepted: 49142  Total Submissions: 128501  Difficulty: Medium

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:

1. Try to utilize the property of a BST.
2. What if you could modify the BST node's structure?
3. The optimal runtime complexity is O(height of BST).

Credits:
Special thanks to @ts for adding this problem and creating all test cases.

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  (M) Binary Tree Inorder Traversal

java code:

/**
 * 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) {
        
        int count = countNode(root.left);
        
        if(k == count + 1)
            return root.val;
        else if(k < count + 1)
            return kthSmallest(root.left, k);
        else // k > count + 1
            return kthSmallest(root.right, k - count - 1);
            
    }
    
    // 自定义函数:计算树中结点个数
    int countNode(TreeNode root) {
        if(root == null) return 0;
        
        return countNode(root.left) + countNode(root.right) + 1;
    }
    
}