[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?
3. The optimal runtime complexity is O(height of BST).

Credits:
Special thanks to @ts for adding this problem and creating all test cases.

利用BST的性质，中序遍历得到的就是从小到大的排列，返回第k-1个数字。

/**
 * 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:
    void traversal(TreeNode* root,vector<int>& result)
    {
        if(root)
        {
            traversal(root->left,result);
            result.push_back(root->val);
            traversal(root->right,result);
        }
    }
    int kthSmallest(TreeNode* root, int k) {
        vector<int> result;
        traversal(root,result);
        return result[k-1];
    }
};