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?

 

/** * Definition for a binary tree node. * struct TreeNode { *     int val; *     TreeNode *left; *     TreeNode *right; *     TreeNode(int x) : val(x), left(NULL), right(NULL) {} * }; */class Solution {public:    void _get_in_order_list(TreeNode* root, vector
     
       &in_list) {        if (NULL == root) {            return;        }        _get_in_order_list(root->left, in_list);        in_list.push_back(root->val);        _get_in_order_list(root->right, in_list);    }        int kthSmallest(TreeNode* root, int k) {        vector
      
        in_list;        _get_in_order_list(root, in_list);        return in_list[k - 1];    }};