Kth Smallest Element in a BST

Given a binary search tree, write a function kthSmallestto 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?

解题思路：

这道题求的是二分查找树种第k大的数。二分查找树有一个特点，每一个节点均大于左孩子树的全部节点，小于有孩子树的全部节点。

因此能够利用中序遍历的方法，扫描二分查找树，当扫描到第k个数时。停止继续扫描。

/** * 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) {        int count = 0;        int result = 0;        inOrder(root, k, count, result);        return result;    }        void inOrder(TreeNode* root, int k, int& count, int& result){        if(root==NULL || count>=k){            return;        }        inOrder(root->left, k, count, result);        count++;        if(count==k){            result=root->val;        }        inOrder(root->right, k, count, result);    }};