LeetCode (Trees&Graphs) Kth Smallest Element in a BST

Kth Smallest Element in a BST

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.

Example 1:

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

Example 2:

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

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?

思路：最简单的思路就是利用二叉排序树的规律，二叉排序树的中序遍历的序列是递增的，所以我们只要做一个中序遍历，然后找到第k个最小值即可。

代码如下：

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public int kthSmallest(TreeNode root, int k) {
        inOrderTraversal(root);
        if(k<1){
            return 0;
        }
        return inlist.get(k-1);
    }
    
    List<Integer> inlist=new ArrayList<Integer>();
    public void inOrderTraversal(TreeNode root){
        if(root==null){
            return ;
        }
        inOrderTraversal(root.left);
        inlist.add(root.val);
        inOrderTraversal(root.right);
    } 
}