LeetCode OJ 230. Kth Smallest Element in a BST

Total Accepted: 46445 Total Submissions: 122594 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.

二叉搜索树特点是对于任意一个节点，它的左子树的节点值都比它小，它的右子树的值都比它大。因此可以从树的最左边向上递归，同时计数，直到计数达到当前指定数字。

 /**
  * Definition for a binary tree node.
  * public class TreeNode {
  *     int val;
  *     TreeNode left;
  *     TreeNode right;
  *     TreeNode(int x) { val = x; }
  * }
  */
 public class Solution {
     private int cnt = 0;
     public int kthSmallest(TreeNode root, int k) {
         int result = 0;
         if(root != null){
             result = kthSmallest(root.left,k);
             cnt++;
             if(cnt == k){
                 return root.val;
             }
             result += kthSmallest(root.right,k);
         }
         return result;
     }
 }