[LeetCode]Kth Smallest Element in a BST

最新推荐文章于 2025-09-07 20:32:33 发布

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原文链接：http://www.cnblogs.com/Sean-le/p/4812720.html

文章标签：

#数据结构与算法 #runtime

本文介绍了一种方法，通过中序遍历来查找给定二叉搜索树中的第K小元素，利用了二叉搜索树的性质来优化算法效率。

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:

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).

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。

 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     void traversal(TreeNode* root,vector<int>& result)
13     {
14         if(root)
15         {
16             traversal(root->left,result);
17             result.push_back(root->val);
18             traversal(root->right,result);
19         }
20     }
21     int kthSmallest(TreeNode* root, int k) {
22         vector<int> result;
23         traversal(root,result);
24         return result[k-1];
25     }
26 };