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>0&&(tmp!=NULL||!tmp_s.empty())){
            if(tmp==NULL){
                tmp=tmp_s.top();
                tmp_s.pop();
                if(--k==0)
                    return tmp->val;
                tmp=tmp->right;
            }
            else{
                while(tmp!=NULL){
                    tmp_s.push(tmp);
                    tmp=tmp->left;
                }
            }
        }
        return tmp->val;
    }
};