BST Search Operation in DSA Typescript - Build from Scratch

BST Search Operation

📖 Scenario: You are building a simple phone book app that stores contacts in a Binary Search Tree (BST). Each contact has a unique phone number. You want to find if a contact exists by searching the BST.

🎯 Goal: Build a TypeScript program that creates a BST with given phone numbers, then searches for a specific phone number in the BST.

📋 What You'll Learn

Create a BST node class with value, left, and right properties

Insert given phone numbers into the BST in the given order

Create a function to search for a phone number in the BST

Print true if the phone number is found, otherwise false

💡 Why This Matters

🌍 Real World

Binary Search Trees are used in phone books, contact lists, and databases to quickly find information by key.

💼 Career

Understanding BST search is important for software engineers working with data storage, search engines, and performance optimization.

1

Create BST Node Class and Insert Nodes

Create a class called BSTNode with a constructor that takes a value of type number. It should have public properties value, left, and right initialized to null. Then create a variable called root and insert these phone numbers in this order: 50, 30, 70, 20, 40, 60, 80 using a helper function insertNode.

DSA Typescript

// Define BSTNode class
// Create root node with value 50
// Insert other values using insertNode function
// Your code here

Hint

Think of each node as a contact with a phone number. Insert smaller numbers to the left, bigger to the right.

2

Set the Phone Number to Search

Create a variable called searchValue and set it to 40. This is the phone number you want to find in the BST.

DSA Typescript

class BSTNode {
    value: number;
    left: BSTNode | null;
    right: BSTNode | null;

    constructor(value: number) {
        this.value = value;
        this.left = null;
        this.right = null;
    }
}

function insertNode(root: BSTNode | null, value: number): BSTNode {
    if (root === null) {
        return new BSTNode(value);
    }
    if (value < root.value) {
        root.left = insertNode(root.left, value);
    } else {
        root.right = insertNode(root.right, value);
    }
    return root;
}

let root: BSTNode | null = new BSTNode(50);
root = insertNode(root, 30);
root = insertNode(root, 70);
root = insertNode(root, 20);
root = insertNode(root, 40);
root = insertNode(root, 60);
root = insertNode(root, 80);

// Create searchValue variable and set it to 40
// Your code here

Hint

This variable holds the phone number you want to find in the tree.

3

Implement BST Search Function

Create a function called searchBST that takes two parameters: root of type BSTNode | null and value of type number. It should return true if the value is found in the BST, otherwise false. Use the BST property to decide whether to search left or right subtree or return true if found.

DSA Typescript

function searchBST(root: BSTNode | null, value: number): boolean {
        return false;
    if (root.value === value) {
        return true;
        return searchBST(root.left, value);
        return searchBST(root.right, value);
// Print the search result below

Hint

Use recursion to go left if value is smaller, right if bigger, or return true if found.

4

Print Search Result

Use console.log to print the result of calling searchBST with root and searchValue. It should print true if the value is found, otherwise false.

DSA Typescript

Hint

Call searchBST(root, searchValue) and print the result using console.log.

Practice

1. What is the main purpose of the search operation in a Binary Search Tree (BST)?

easy

A. To delete a value from the BST

B. To insert a new value into the BST

C. To find whether a given value exists in the BST

D. To traverse all nodes in the BST

Solution

1. Step 1: Understand the purpose of search in BST

   The search operation is designed to check if a specific value is present in the BST.

2. Step 2: Differentiate from other operations

   Insertion adds new values, deletion removes values, and traversal visits all nodes. Search only checks existence.

3. Final Answer:

   To find whether a given value exists in the BST -> Option C

4. Quick Check:

   Search = Find value presence [OK]

Hint: Search checks presence, not insertion or deletion [OK]

Common Mistakes:

• Confusing search with insert or delete
• Thinking search returns all nodes
• Assuming search modifies the tree

2. Which of the following is the correct TypeScript function signature for a BST search method that returns a boolean?

easy

A. function search(root: TreeNode | null, value: number): boolean

B. function search(value: number): TreeNode

C. function search(root: TreeNode, value: string): boolean

D. function search(root: TreeNode | null, value: number): void

Solution

1. Step 1: Analyze parameter types

   The search needs the root node (which can be null) and the value to find (a number).

2. Step 2: Analyze return type

   Search returns true or false, so return type should be boolean.

3. Final Answer:

   function search(root: TreeNode | null, value: number): boolean -> Option A

4. Quick Check:

   Correct params and boolean return [OK]

Hint: Search returns boolean, root can be null [OK]

Common Mistakes:

• Using wrong parameter types
• Returning void instead of boolean
• Using string instead of number for value

3. Given the BST below and the search function call search(root, 7), what will be the output?

BST structure:
10
/ \
5 15
/ \ \
3 7 20

Code snippet:

function search(root: TreeNode | null, value: number): boolean {
  if (!root) return false;
  if (root.val === value) return true;
  if (value < root.val) return search(root.left, value);
  return search(root.right, value);
}

console.log(search(root, 7));

medium

A. false

B. Error

C. undefined

D. true

Solution

1. Step 1: Trace search for value 7

   Start at root 10: 7 < 10, go left to 5. Then 7 > 5, go right to 7.

2. Step 2: Check node value

   Node value is 7, matches search value, so return true.

3. Final Answer:

   true -> Option D

4. Quick Check:

   Found 7 in BST = true [OK]

Hint: Follow BST rules left/right to find value [OK]

Common Mistakes:

• Stopping search too early
• Confusing left and right child directions
• Returning false when node matches

4. The following TypeScript search function for a BST has a bug. What is the error?

function search(root: TreeNode | null, value: number): boolean {
  if (root === null) return false;
  if (root.val === value) return true;
  if (value > root.val) return search(root.left, value);
  else return search(root.right, value);
}

medium

A. The comparison operator should be >= instead of >

B. The recursive calls to left and right children are swapped

C. The function does not return a boolean

D. The base case is missing

Solution

1. Step 1: Check recursive calls logic

   For BST, if value > root.val, search should go right, but code goes left.

2. Step 2: Confirm swapped children calls

   Similarly, else goes right instead of left. So left and right calls are swapped.

3. Final Answer:

   The recursive calls to left and right children are swapped -> Option B

4. Quick Check:

   Left/right calls swapped = bug [OK]

Hint: Value > root goes right, not left [OK]

Common Mistakes:

• Mixing left and right child in recursion
• Ignoring base case (though present here)
• Wrong comparison operators

5. You want to search for a value in a BST that may contain duplicate values on the right subtree. Which modification to the standard BST search logic ensures you find the first occurrence of the value?

Choose the correct approach:

hard

A. Always search left subtree when value equals current node's value

B. Return true immediately when value equals current node's value

C. Search right subtree when value equals current node's value to find duplicates

D. Traverse entire tree inorder to find all occurrences

Solution

1. Step 1: Understand duplicate placement in BST

   Duplicates are stored in right subtree, so first occurrence is the leftmost matching node.

2. Step 2: Modify search to find first occurrence

   When value equals current node, continue searching left subtree to find earlier occurrence.

3. Final Answer:

   Always search left subtree when value equals current node's value -> Option A

4. Quick Check:

   Search left on equal to find first duplicate [OK]

Hint: On equal, go left to find first duplicate [OK]

Common Mistakes:

• Stopping search immediately on equal
• Searching right subtree on equal
• Doing full inorder traversal unnecessarily