[LeetCode]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?

这里一开始我有两个思路，一个是用数组求出BST的前序遍历，然后得到第k个叶子节点，这样需要开辟新的空间，而且时间复杂度是O(N)
第二个就是求一个节点左边有多少个节点，那么他是第几个。这样的时间复杂度也达不到要求
顺着第二个思路想下去，如果我直接先到最左边的节点，然后倒着过来，就可以得到我想要的解了

/**
 * 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 st;
        TreeNode* temp = root;
        while (temp || !st.empty()) {
            while (temp) {
                st.push(temp);
                temp = temp->left;
            }
            temp = st.top();
            if(--k == 0) {
                return temp->val;
            }
            st.pop();
            temp = temp->right;
        }
    }
};