(java) 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.

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).

思路1：中序遍历，然后输出第k的树就是结果

思路2：一个节点计算它的左子树节点数left

if left+1=k 则这个数就是要找的那个数

if left+1<k 则 k=k-left-1在右字数中找

if(left+1)>k 则在左子树中找

给出了思路1的代码，思路2的代码也不难写

代码如下(已通过leetcode)

public class Solution {
   public int kthSmallest(TreeNode root, int k) {
    List<Integer> list=new ArrayList<Integer>();
    InOrderTravel(list,root);
    return list.get(k-1);
   }


private void InOrderTravel(List<Integer> list, TreeNode root) {
// TODO Auto-generated method stub
if(root==null) return;
if(root.left!=null) InOrderTravel(list, root.left);
list.add(root.val);
if(root.right!=null) InOrderTravel(list, root.right);
}
}