LeetCode #230 - Kth Smallest Element in a BST - Medium

Problem

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:

• Try to utilize the property of a BST.
• What if you could modify the BST node’s structure?
• The optimal runtime complexity is O(height of BST).

Example

Input: [1]Output: 1

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Algorithm

整理一下题意：给定一棵二叉搜索树和整数k，要求返回树中第k个最小的元素。假设k总是有效输入。

解题的关键在于利用好二叉搜索树的性质。二叉搜索树的特征是：左子<父<右子。于是中序遍历得到的序列必然是升序序列。于是根据k可以直接返回升序序列的第k-1项了。

代码如下。

//版本，时间复杂度O(n)class Solution {public:    int kthSmallest(TreeNode* root, int k) {        vector<int> path;        inorder(path,root);        return path[k-1];    }    void inorder(vector<int>& path,TreeNode* root){        if(root==NULL) return;        inorder(path,root->left);        path.push_back(root->val);        inorder(path,root->right);    }};