230 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.

Example 1:

Input: root = [3,1,4,null,2], k = 1
   3
  / \
 1   4
  \
   2
Output: 1

Example 2:

Input: root = [5,3,6,2,4,null,null,1], k = 3
       5
      / \
     3   6
    / \
   2   4
  /
 1
Output: 3

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?

Solution: Inorder traversal

Time complexity: O(n) Space compleixty: O(n)

class Solution {
public:
  int kthSmallest(TreeNode* root, int k) {
    return inorder(root, k);
  }
private:
  int inorder(TreeNode* root, int& k) {
    if (!root) return -1;
    int x = inorder(root->left, k);
    if (k == 0) return x;
    if (--k == 0) return root->val;
    return inorder(root->right, k);
  }
};