Kth Smallest Element in a BST

Question

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?

My Solution

/** * 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) {        /*中序遍历，取最小的k个*/        int rst, num;        rst = middleIterate(root, k, num);        return rst;            }        int middleIterate(TreeNode* root, int k, int& num){        /* 中序遍历树        0. 边界条件：if root == Null then num = 0, return 0;        1. rst = middleIterate(root->left, k, lnum)遍历左子树        2. if lnum >= k then num = lnum, return rst;        3. else if lnum == k - 1 then num = k, return root->val;        4. else k = k - lnum - 1, rst = middleIterate(root->left, k, rnum)遍历右子树        5. num = lnum + rnum + 1, return rst;        */        if(NULL == root){            num = 0;            return 0;        }                int r, lnum, rnum;        r = middleIterate(root->left, k, lnum);        if(lnum >= k){            num = lnum;            return r;        }else if(k - 1 == lnum)        {            num = k;            return root->val;        }else{            k = k - lnum - 1;            r = middleIterate(root->right, k, rnum);            num = lnum + rnum + 1;            return r;        }            }    };