[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.

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?


  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).

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

Naive approach, convert BST to a sequence, find the Kth element.

O(n) in space, O(n) in time.

 * 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 {
    int kthSmallest(TreeNode* root, int k) {
        vector<TreeNode *> seq;
        convert2vector(root, seq);
        return seq[k - 1]->val;
    void convert2vector(TreeNode * root, vector<TreeNode *>& seq){
        if(root == nullptr){
            return ;
        convert2vector(root->left, seq);
        convert2vector(root->right, seq);

A better approach. Calculate the number of nodes in subtree of each node. Then use binary search.

O(h) in time for each search. h is the height of the tree. O(n) in generating the number of nodes information.


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