Kth Smallest Element in a BST

LeetCode 230 | Difficulty: Medium

Medium

Problem Description

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

Example 1:

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

Example 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 <= 10^4`

- `0 <= Node.val <= 10^4`

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?

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

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Approach

Tree DFS

Traverse the tree recursively (or with a stack). At each node, decide: what information do I need from the left/right subtrees? Process: go left → go right → combine results. Consider preorder, inorder, or postorder traversal based on when you need to process the node.

When to use

Path problems, subtree properties, tree structure manipulation.

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Solutions

Solution 1: C# (Best: 108 ms)

Metric	Value
Runtime	108 ms
Memory	28.9 MB
Date	2021-09-23

Solution

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     public int val;
 *     public TreeNode left;
 *     public TreeNode right;
 *     public TreeNode(int val=0, TreeNode left=null, TreeNode right=null) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
public class Solution {
    public int KthSmallest(TreeNode root, int k) {
        int count = k;
    System.Collections.Generic.Stack<TreeNode> s = new Stack<TreeNode>();
    
    TreeNode current = root;
    s.Push(current);
    while(s.Count != 0)
    {
        while(current != null)
        {
            s.Push(current);
            current = current.left;
        }
        var popped = s.Pop();
        if(--count == 0)
        {
            return popped.val;
        }
        current = popped.right;
    }
        return -1;
}
}

📜 1 more C# submission(s)

Submission (2021-09-22) — 108 ms, 28.6 MB

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     public int val;
 *     public TreeNode left;
 *     public TreeNode right;
 *     public TreeNode(int val=0, TreeNode left=null, TreeNode right=null) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
public class Solution {
    public int KthSmallest(TreeNode root, int k) {
        int result = 0;
    int count = k;
    helper(root, ref result, ref count);
    return result;
    
}

public void helper(TreeNode n, ref int result, ref int count)
{
    if(n.left != null) 
    {
        helper(n.left, ref result, ref count);
    }
    count--;
    if(count==0)
    {
        result = n.val;
        return;
    }
    if(n.right != null) helper(n.right, ref result, ref count);
    
}
}

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Complexity Analysis

Approach	Time	Space
Tree Traversal	$O(n)$	$O(h)$

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Interview Tips

Key Points

• Discuss the brute force approach first, then optimize. Explain your thought process.
• Consider: "What information do I need from each subtree?" — this defines your recursive return value.
• LeetCode provides 4 hint(s) for this problem — try solving without them first.

💡 Hints

Hint 1: Try to utilize the property of a BST.

Hint 2: Try in-order traversal. (Credits to @chan13)

Hint 3: What if you could modify the BST node's structure?

Hint 4: The optimal runtime complexity is O(height of BST).