Kth Smallest Element in BST in DSA C# - Build from Scratch

Kth Smallest Element in BST

📖 Scenario: You are working with a simple phone book application that stores contacts in a Binary Search Tree (BST). Each contact has a unique phone number. You want to find the contact with the kth smallest phone number to quickly access contacts in order.

🎯 Goal: Build a program that creates a BST with given phone numbers, sets a value for k, and finds the kth smallest phone number in the BST.

📋 What You'll Learn

Create a BST by inserting nodes with exact phone numbers

Create a variable k to specify which smallest element to find

Implement an in-order traversal to find the kth smallest element

Print the kth smallest phone number

💡 Why This Matters

🌍 Real World

Finding the kth smallest element in a BST is useful in applications like phone books, databases, and search engines where ordered data retrieval is needed.

💼 Career

Understanding BSTs and traversal algorithms is important for software developers working with data structures, optimizing search operations, and building efficient applications.

1

Create the BST with given phone numbers

Create a class Node with an integer Value, and two Node references Left and Right. Then create a class BST with a Node variable Root and a method Insert(int value) to insert nodes in the BST. Insert these exact phone numbers in order: 40, 20, 60, 10, 30, 50, 70.

DSA C#

// Define Node class
// Define BST class with Insert method
// Insert nodes with values 40, 20, 60, 10, 30, 50, 70

Hint

Start by defining the Node class with value and child nodes. Then create the BST class with an insert method that places values correctly. Insert the given numbers in order.

2

Set the value of k

Create an integer variable k and set it to 3 to find the 3rd smallest phone number in the BST.

DSA C#

using System;

// Previous code...

public class Program
{
    public static void Main()
    {
        BST bst = new BST();
        bst.Insert(40);
        bst.Insert(20);
        bst.Insert(60);
        bst.Insert(10);
        bst.Insert(30);
        bst.Insert(50);
        bst.Insert(70);
        // Create variable k and set it to 3
        // Your code here
    }
}

Hint

Simply create an integer variable named k and assign it the value 3.

3

Implement method to find kth smallest element

In the BST class, add a method FindKthSmallest(int k) that returns the kth smallest value in the BST. Use an in-order traversal to visit nodes in ascending order. Use a helper method InOrder(Node node, int k, ref int count, ref int result) to traverse and count nodes. Return the result when count reaches k.

DSA C#

using System;

// Previous code...

public class BST
{
    public Node Root;

    // Previous methods...

    // Add FindKthSmallest method here
    // Your code here
}

Hint

Use in-order traversal to visit nodes in ascending order. Keep a count of visited nodes. When count equals k, save the node's value as the result.

4

Print the kth smallest phone number

In the Main method, call FindKthSmallest(k) on the BST instance and print the returned value using Console.WriteLine.

DSA C#

using System;

// Previous code...

public class Program
{
    public static void Main()
    {
        BST bst = new BST();
        bst.Insert(40);
        bst.Insert(20);
        bst.Insert(60);
        bst.Insert(10);
        bst.Insert(30);
        bst.Insert(50);
        bst.Insert(70);
        int k = 3;
        // Call FindKthSmallest and print the result
        // Your code here
    }
}

Hint

Call FindKthSmallest(k) on the BST instance and print the returned value with Console.WriteLine.

Practice

1. What does the Kth Smallest Element in BST problem ask you to find?

easy

A. The largest element in the Binary Search Tree

B. The height of the Binary Search Tree

C. The element that is the Kth smallest value in the Binary Search Tree

D. The number of nodes in the Binary Search Tree

Solution

1. Step 1: Understand the problem statement

   The problem asks to find the Kth smallest element, meaning the element that would appear in position K if the BST elements were sorted.

2. Step 2: Recognize BST property

   In a BST, an inorder traversal visits nodes in ascending order, so the Kth visited node is the Kth smallest.

3. Final Answer:

   The element that is the Kth smallest value in the Binary Search Tree -> Option C

4. Quick Check:

   Kth smallest = Kth visited in inorder traversal [OK]

Hint: Inorder traversal gives sorted order; pick Kth node [OK]

Common Mistakes:

• Confusing Kth smallest with Kth largest
• Ignoring BST property and sorting separately
• Using preorder or postorder traversal instead of inorder

2. Which of the following C# method signatures correctly represents a function to find the Kth smallest element in a BST node class named TreeNode?

easy

A. public int KthSmallest(TreeNode root, int k)

B. public void KthSmallest(int root, int k)

C. public int KthSmallest(TreeNode root)

D. public int KthSmallest(int k)

Solution

1. Step 1: Identify correct parameter types

   The method needs the root node of type TreeNode and an integer k to find the Kth smallest element.

2. Step 2: Check return type and parameters

   The method returns an int (the value of the Kth smallest node) and takes TreeNode root and int k as parameters.

3. Final Answer:

   public int KthSmallest(TreeNode root, int k) -> Option A

4. Quick Check:

   Correct signature includes root node and k as parameters [OK]

Hint: Method needs root node and k as inputs, returns int [OK]

Common Mistakes:

• Using void return type instead of int
• Missing root node parameter
• Using wrong parameter types

3. Given the BST below and k = 3, what will the following C# code print?

class TreeNode {
  public int val;
  public TreeNode left, right;
  public TreeNode(int v) { val = v; }
}

// BST structure:
//       5
//      / \
//     3   7
//    / \   \
//   2   4   8

int KthSmallest(TreeNode root, int k) {
  List<int> vals = new List<int>();
  void Inorder(TreeNode node) {
    if (node == null) return;
    Inorder(node.left);
    vals.Add(node.val);
    Inorder(node.right);
  }
  Inorder(root);
  return vals[k - 1];
}

TreeNode root = new TreeNode(5);
root.left = new TreeNode(3);
root.right = new TreeNode(7);
root.left.left = new TreeNode(2);
root.left.right = new TreeNode(4);
root.right.right = new TreeNode(8);

Console.WriteLine(KthSmallest(root, 3));

medium

A. 4

B. 3

C. 5

D. 7

Solution

1. Step 1: Perform inorder traversal of BST

   Inorder traversal visits nodes in ascending order: 2, 3, 4, 5, 7, 8.

2. Step 2: Find the 3rd element in the sorted list

   The 3rd element (index 2) is 4.

3. Final Answer:

   4 -> Option A

4. Quick Check:

   Inorder sorted list = [2,3,4,5,7,8], 3rd element = 4 [OK]

Hint: Inorder traversal sorts BST; pick element at index k-1 [OK]

Common Mistakes:

• Using preorder or postorder traversal order
• Off-by-one error in indexing k-1
• Confusing left and right subtree values

4. The following code attempts to find the Kth smallest element in a BST but fails to stop the traversal early after finding the Kth element. What is the main issue?

int KthSmallest(TreeNode root, int k) {
  int count = 0;
  int result = -1;
  void Inorder(TreeNode node) {
    if (node == null) return;
    Inorder(node.left);
    count++;
    if (count == k) {
      result = node.val;
      return;
    }
    Inorder(node.right);
  }
  Inorder(root);
  return result;
}

medium

A. The function does not handle empty trees

B. The variable count is not incremented correctly

C. The result variable is not initialized

D. The return inside Inorder does not stop the entire traversal

Solution

1. Step 1: Analyze the recursive Inorder function

   The return statement inside Inorder only exits the current call, not the entire traversal, so traversal continues after finding the Kth element.

2. Step 2: Understand why this is problematic

   Continuing traversal after setting result wastes time and space; no mechanism to stop recursion early.

3. Final Answer:

   The return inside Inorder does not stop the entire traversal -> Option D

4. Quick Check:

   Return in recursion stops only current call, not whole traversal [OK]

Hint: Return in recursion stops only one call, not full traversal [OK]

Common Mistakes:

• Assuming return stops all recursion
• Not using a flag to stop traversal after finding element
• Ignoring null root case

5. You want to find the Kth smallest element in a BST but the tree is very large and you want to optimize for time and space. Which approach is best?

Options:
A) Use an iterative inorder traversal with a stack and stop when the Kth element is found.
B) Perform a full inorder traversal and store all elements in a list, then return the Kth element.
C) Convert the BST to a sorted array by any method, then binary search for the Kth element.
D) Use preorder traversal and count nodes until K is reached.

hard

A. Perform full inorder traversal and store all elements

B. Use iterative inorder traversal with stack, stop at Kth element

C. Convert BST to sorted array then binary search for Kth element

D. Use preorder traversal and count nodes until K is reached

Solution

1. Step 1: Evaluate full inorder traversal approach

   Storing all elements uses extra space and time, not efficient for large trees.

2. Step 2: Consider iterative inorder traversal with early stop

   This approach uses a stack to traverse nodes in order and stops immediately after finding the Kth smallest, saving time and space.

3. Step 3: Analyze other options

   Binary search requires sorted array, which needs full traversal first; preorder traversal does not guarantee sorted order.

4. Final Answer:

   Use iterative inorder traversal with stack, stop at Kth element -> Option B

5. Quick Check:

   Iterative inorder + early stop = efficient Kth smallest search [OK]

Hint: Iterative inorder with stack stops early, saves time and space [OK]

Common Mistakes:

• Using full traversal wasting memory
• Using preorder which is unsorted
• Trying binary search without sorted array