230. Kth Smallest Element in a BST

Posted on Edited on In

230. Kth Smallest Element in a BST

Description

Difficulty: Medium

Related Topics: Tree, Depth-First Search, Binary Search Tree, Binary Tree

Given the root of a binary search tree, and an integer k, return the kth smallest value (1-indexed) of all the values of the nodes in the tree.

Example 1:

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

Example 2:

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

Constraints:

  • The number of nodes in the tree is n.
  • 1 <= k <= n <= 104
  • 0 <= Node.val <= 104

Follow up: If the BST is modified often (i.e., we can do insert and delete operations) and you need to find the kth smallest frequently, how would you optimize?

Hints/Notes

Solution

Language: C++

Another recursive solution

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    int kthSmallest(TreeNode* root, int& k) {
        if (!root) {
            return -1;
        }
        int left = kthSmallest(root->left, k);
        if (left != -1) {
            return left;
        }
        if (--k == 0) {
            return root->val;
        }
        return kthSmallest(root->right, k);
    }
};
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    int index = 1, res = -1;
    int kthSmallest(TreeNode* root, int k) {
        traverse(root, k);
        return res;
    }

    void traverse(TreeNode* root, int k) {
        if (!root || res != -1) return;
        traverse(root->left, k);
        if (index++ == k) {
            res = root->val;
            return;
        }
        traverse(root->right, k);
    }
};