Kth Smallest Element in BST in DSA Typescript - Build from Scratch

Kth Smallest Element in BST

📖 Scenario: You are working with a binary search tree (BST) that stores numbers in a way that smaller numbers go to the left and larger numbers go to the right. You want to find the kth smallest number in this tree, which means the number that would appear in position k if you listed all numbers in order.

🎯 Goal: Build a TypeScript program that creates a BST, sets a value for k, finds the kth smallest element in the BST using an in-order traversal, and prints the result.

📋 What You'll Learn

Create a BST with the exact nodes given

Set a variable k to the given value

Write a function kthSmallest that finds the kth smallest element using in-order traversal

Print the kth smallest element

💡 Why This Matters

🌍 Real World

Finding the kth smallest element is useful in databases, search engines, and ranking systems where you want to quickly find a specific order statistic.

💼 Career

Understanding BSTs and order statistics is important for software engineers working on efficient data retrieval, algorithm design, and coding interviews.

1

Create the BST nodes

Create a class called TreeNode with properties val, left, and right. Then create the BST with these exact nodes and connections:
root with value 5,
root.left with value 3,
root.right with value 7,
root.left.left with value 2,
root.left.right with value 4,
root.right.left with value 6,
root.right.right with value 8.

DSA Typescript

// Define TreeNode class and create the BST nodes
// Your code here

Hint

Start by defining the TreeNode class with a constructor. Then create the root node and connect its left and right children as described.

2

Set the value of k

Create a variable called k and set it to 3.

DSA Typescript

class TreeNode {
    val: number;
    left: TreeNode | null;
    right: TreeNode | null;
    constructor(val: number) {
        this.val = val;
        this.left = null;
        this.right = null;
    }
}

const 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.left = new TreeNode(6);
root.right.right = new TreeNode(8);

// Set k to 3
// Your code here

Hint

Simply create a constant k and assign it the value 3.

3

Write the function to find kth smallest element

Write a function called kthSmallest that takes root of type TreeNode | null and k of type number. Use an in-order traversal to find and return the kth smallest element's value in the BST.

DSA Typescript

class TreeNode {
    val: number;
    left: TreeNode | null;
    right: TreeNode | null;
    constructor(val: number) {
        this.val = val;
        this.left = null;
        this.right = null;
    }
}

const 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.left = new TreeNode(6);
root.right.right = new TreeNode(8);

const k = 3;

// Write kthSmallest function below
// Your code here

Hint

Use a helper function inorder to visit nodes in order. Keep a count of visited nodes. When count equals k, save the node's value and stop.

4

Print the kth smallest element

Write a console.log statement to print the result of calling kthSmallest(root, k).

DSA Typescript

class TreeNode {
    val: number;
    left: TreeNode | null;
    right: TreeNode | null;
    constructor(val: number) {
        this.val = val;
        this.left = null;
        this.right = null;
    }
}

const 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.left = new TreeNode(6);
root.right.right = new TreeNode(8);

const k = 3;

function kthSmallest(root: TreeNode | null, k: number): number {
    let count = 0;
    let result = -1;

    function inorder(node: TreeNode | null) {
        if (!node || result !== -1) return;
        inorder(node.left);
        count++;
        if (count === k) {
            result = node.val;
            return;
        }
        inorder(node.right);
    }

    inorder(root);
    return result;
}

// Print the kth smallest element
// Your code here

Hint

Call kthSmallest(root, k) and print the result using console.log.

Practice

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

easy

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

B. The largest element in the Binary Search Tree

C. The height of the Binary Search Tree

D. The number of nodes in the Binary Search Tree

Solution

1. Step 1: Understand the BST property

   A Binary Search Tree (BST) stores values so that left child nodes are smaller and right child nodes are larger than the parent.

2. Step 2: Define the Kth smallest element

   The Kth smallest element is the element that would appear in position K if all elements were sorted in ascending order.

3. Final Answer:

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

4. Quick Check:

   Kth smallest means sorted order position K [OK]

Hint: Remember BST in-order traversal gives sorted order [OK]

Common Mistakes:

• Confusing Kth smallest with largest element
• Thinking it means tree height
• Counting nodes instead of values

2. Which TypeScript function signature correctly represents a function to find the Kth smallest element in a BST node structure?

easy

A. function kthSmallest(k: number, root: TreeNode): void

B. function kthSmallest(root: TreeNode | null, k: number): number

C. function kthSmallest(root: TreeNode, k: string): string

D. function kthSmallest(root: TreeNode, k: number): TreeNode

Solution

1. Step 1: Check parameter types and order

   The function should take the root node (which can be null) and a number k representing the position.

2. Step 2: Check return type

   The function returns the value (number) of the Kth smallest element, not a node or void.

3. Final Answer:

   function kthSmallest(root: TreeNode | null, k: number): number -> Option B

4. Quick Check:

   Correct parameter types and return number [OK]

Hint: Root node first, k as number, return value number [OK]

Common Mistakes:

• Swapping parameter order
• Using wrong return type
• Using string instead of number for k

3. Given the BST below and k = 3, what is the output of the function kthSmallest(root, 3)?

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

medium

A. 3

B. 5

C. 4

D. 7

Solution

1. Step 1: Perform in-order traversal

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

2. Step 2: Identify the 3rd element

   The 3rd element in this order is 4.

3. Final Answer:

   4 -> Option C

4. Quick Check:

   In-order 3rd element = 4 [OK]

Hint: In-order traversal gives sorted nodes; pick Kth [OK]

Common Mistakes:

• Counting root as first without traversal
• Confusing left and right subtree order
• Picking value by node depth

4. Consider this TypeScript code snippet to find the Kth smallest element in a BST:

function kthSmallest(root: TreeNode | null, k: number): number {
  let count = 0;
  let result = -1;
  function inorder(node: TreeNode | null) {
    if (!node) return;
    inorder(node.left);
    count++;
    if (count === k) {
      result = node.val;
      return;
    }
    inorder(node.right);
  }
  inorder(root);
  return result;
}

What is the main problem with this code?

medium

A. The function does not stop traversal after finding the Kth element

B. The count variable is not incremented correctly

C. The result variable is initialized incorrectly

D. The function does not handle null root

Solution

1. Step 1: Analyze traversal stopping condition

   The code sets result when count equals k but does not stop further recursion, so it continues traversing unnecessarily.

2. Step 2: Understand impact of not stopping traversal

   Without stopping, the function wastes time and may overwrite result if not careful.

3. Final Answer:

   The function does not stop traversal after finding the Kth element -> Option A

4. Quick Check:

   Traversal must stop after Kth element found [OK]

Hint: Stop recursion immediately after finding Kth element [OK]

Common Mistakes:

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

5. You want to find the Kth smallest element in a BST but the tree is very large and you need to optimize for multiple queries with different K values. Which approach is best?

hard

A. Perform in-order traversal each time for every K query

B. Use breadth-first search to find the Kth smallest element

C. Randomly pick nodes until Kth smallest is found

D. Store the in-order traversal result in an array once, then answer queries by indexing

Solution

1. Step 1: Consider repeated queries

   Performing in-order traversal each time is costly for large trees and many queries.

2. Step 2: Use pre-processing for efficiency

   Storing the sorted elements from one in-order traversal allows O(1) access for each Kth smallest query.

3. Step 3: Evaluate other options

   Breadth-first search does not give sorted order; random picking is inefficient and unreliable.

4. Final Answer:

   Store the in-order traversal result in an array once, then answer queries by indexing -> Option D

5. Quick Check:

   Precompute once, query fast [OK]

Hint: Precompute sorted list once for fast multiple queries [OK]

Common Mistakes:

• Recomputing traversal for each query
• Using BFS which is unsorted
• Random selection guessing