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.

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 { public: 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); seq.push_back(root); 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.