[LeetCode] Kth Smallest Element in a BST

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?

Hint:

1. Try to utilize the property of a BST.
2. What if you could modify the BST node's structure?

中序遍历，Morris，线索二叉树……。

 1 /**
 2  * Definition for a binary tree node.
 3  * struct TreeNode {
 4  *     int val;
 5  *     TreeNode *left;
 6  *     TreeNode *right;
 7  *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 8  * };
 9  */
10 class Solution {
11 public:
12     int kthSmallest(TreeNode* root, int k) {
13         int cnt = 0;
14         TreeNode *p = root;
15         stack<TreeNode *> st;
16         while (p != NULL || !st.empty()) {
17             if (p != NULL) {
18                 st.push(p);
19                 p = p->left;
20             } else {
21                 p = st.top();
22                 st.pop();
23                 if (++cnt == k) return p->val;
24                 p = p->right;
25             }
26         }
27     }
28 };