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?

 /**
  * 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:
     int kthSmallest(TreeNode* root, int k) {
         stack <TreeNode*> tmp_s;
         TreeNode* tmp=root;
         while(tmp!=NULL){
             tmp_s.push(tmp);
             tmp=tmp->left;
         }
         while(k>&&(tmp!=NULL||!tmp_s.empty())){
             if(tmp==NULL){
                 tmp=tmp_s.top();
                 tmp_s.pop();
                 if(--k==)
                     return tmp->val;
                 tmp=tmp->right;
             }
             else{
                 while(tmp!=NULL){
                     tmp_s.push(tmp);
                     tmp=tmp->left;
                 }
             }
         }
         return tmp->val;
     }
 };