leetcode-Kth Smallest Element in a BST

Given a binary search tree, write a function kthSmallest to find thekth 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?

注意：sum在中序遍历过程中负责记录着遍历过节点总个数，当左边的树遍历完毕(相对于当前节点而言)的时候sum表示前sum-1个数(根据BST特点，左边的树的值小于当前节点的值)，当前节点的值相当于第sum个数(当前节点的值总小于右边的树的值)，当sum==k时，即找到了第k个数。之后的遍历也不需要了。

class Solution {
    bool kthSmallest(TreeNode *root,int k,int &sum,int &res){
        
        if(root->left&&kthSmallest(root->left,k,sum,res))
            return true;
        if(++sum==k){
            res=root->val;
            return true;
        }
        if(root->right&&kthSmallest(root->right,k,sum,res))
            return true;
    
        return false;
    }
public:
    int kthSmallest(TreeNode* root, int k) {
        if(!root)
            return -1;
        int res;    
        int sum=0;
        kthSmallest(root,k,sum,res);  
        return res;
    }
};