Create a Binary Tree Manually in DSA Typescript - Time & Space Complexity

Time Complexity: Create a Binary Tree Manually

O(n)

Understanding Time Complexity

When we create a binary tree manually by adding nodes one by one, it is important to understand how the time needed grows as the tree gets bigger.

We want to know how long it takes to build the tree as we add more nodes.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

const root = new TreeNode(1);
root.left = new TreeNode(2);
root.right = new TreeNode(3);
root.left.left = new TreeNode(4);
root.left.right = new TreeNode(5);
    

This code creates a binary tree by manually assigning child nodes to the root and its children.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Creating and linking each node manually.
• How many times: Once per node added, no loops or recursion here.

How Execution Grows With Input

Each new node requires one step to create and link it.

Input Size (n)	Approx. Operations
10	10 steps
100	100 steps
1000	1000 steps

Pattern observation: The time grows directly with the number of nodes added.

Final Time Complexity

Time Complexity: O(n)

This means the time to create the tree grows linearly with the number of nodes you add.

Common Mistake

[X] Wrong: "Creating a binary tree manually is always very slow because it involves complex operations."

[OK] Correct: Actually, each node is created and linked in a simple step, so the time grows only as you add more nodes, not more complex than that.

Interview Connect

Understanding how manual tree creation scales helps you explain basic data structure building blocks clearly and confidently in interviews.

Self-Check

"What if we added a loop to create nodes instead of manual assignments? How would the time complexity change?"

Practice

1. What is the main purpose of manually creating a binary tree in TypeScript?

easy

A. To avoid using classes or objects

B. To automatically sort data without coding

C. To understand how nodes connect and form the tree structure

D. To create a linked list instead of a tree

Solution

1. Step 1: Understand binary tree structure

   A binary tree consists of nodes where each node has at most two children, left and right.

2. Step 2: Purpose of manual creation

   Manually creating a binary tree helps visualize and understand how nodes connect to form the tree.

3. Final Answer:

   To understand how nodes connect and form the tree structure -> Option C

4. Quick Check:

   Manual creation = Understand tree structure [OK]

Hint: Manual creation helps visualize node connections [OK]

Common Mistakes:

• Thinking it automatically sorts data
• Confusing binary tree with linked list
• Assuming no objects or classes are needed

2. Which of the following is the correct way to define a binary tree node class in TypeScript?

easy

A. class Node { value: number; left: Node | null; right: Node | null; constructor(value: number) { this.value = value; this.left = null; this.right = null; } }

B. class Node { value: number; left: number; right: number; constructor(value: number) { this.value = value; this.left = 0; this.right = 0; } }

C. class Node { value: number; left: Node; right: Node; constructor(value: number) { this.value = value; } }

D. class Node { value: number; left: any; right: any; constructor() { this.value = 0; } }

Solution

1. Step 1: Check node properties and types

   A binary tree node should have a value and left/right children which can be nodes or null.

2. Step 2: Verify constructor initialization

   Constructor must initialize value and set left and right to null initially.

3. Final Answer:

   class Node { value: number; left: Node | null; right: Node | null; constructor(value: number) { this.value = value; this.left = null; this.right = null; } } -> Option A

4. Quick Check:

   Node class with nullable children = class Node { value: number; left: Node | null; right: Node | null; constructor(value: number) { this.value = value; this.left = null; this.right = null; } } [OK]

Hint: Children must be Node or null, initialized in constructor [OK]

Common Mistakes:

• Using number type for left/right instead of Node or null
• Not initializing left and right to null
• Omitting constructor parameters

3. Given the following TypeScript code to create a binary tree manually, what will be the output of console.log(root.left?.value)?

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

const root = new Node(10);
root.left = new Node(5);
root.right = new Node(15);

medium

A. 5

B. 10

C. 15

D. undefined

Solution

1. Step 1: Understand tree structure from code

   Root node has value 10, left child is node with value 5, right child is node with value 15.

2. Step 2: Access left child's value

   root.left?.value accesses left node's value safely, which is 5.

3. Final Answer:

   5 -> Option A

4. Quick Check:

   root.left.value = 5 [OK]

Hint: Access left child value directly with root.left?.value [OK]

Common Mistakes:

• Confusing root value with left child value
• Expecting right child value instead
• Not using optional chaining and getting error

4. Identify the error in the following TypeScript code that tries to create a binary tree node manually:

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

const root = new Node(10);
root.left = 5;
root.right = new Node(15);

medium

A. Missing constructor parameters in Node class

B. Using wrong class name for Node

C. Not initializing root.right

D. Assigning number 5 to root.left instead of a Node or null

Solution

1. Step 1: Check type of root.left assignment

   root.left is declared as Node or null, but assigned number 5 which is invalid.

2. Step 2: Confirm correct assignment type

   root.left should be assigned a Node instance or null, not a number.

3. Final Answer:

   Assigning number 5 to root.left instead of a Node or null -> Option D

4. Quick Check:

   Type mismatch in root.left assignment = Assigning number 5 to root.left instead of a Node or null [OK]

Hint: Children must be Node or null, not a number [OK]

Common Mistakes:

• Assigning primitive values to node children
• Ignoring type errors in assignments
• Assuming number can be assigned directly

5. You want to manually create a binary tree with root value 20, left child 10, and right child 30. Which code snippet correctly creates this tree and prints the root, left, and right values in order?

hard

A. const root = new Node(20);
root.left = 10;
root.right = 30;
console.log(root.value, root.left, root.right);

B. const root = new Node(20);
root.left = new Node(10);
root.right = new Node(30);
console.log(root.value, root.left?.value, root.right?.value);

C. const root = new Node(20);
root.left = new Node(30);
root.right = new Node(10);
console.log(root.value, root.left?.value, root.right?.value);

D. const root = new Node(20);
root.left = null;
root.right = null;
console.log(root.left?.value, root.value, root.right?.value);

Solution

1. Step 1: Create root and children nodes correctly

   Root node with value 20, left child 10, right child 30 must be Node instances.

2. Step 2: Print values in order root, left, right

   console.log prints root.value, root.left?.value, root.right?.value which outputs 20 10 30.

3. Final Answer:

   const root = new Node(20); root.left = new Node(10); root.right = new Node(30); console.log(root.value, root.left?.value, root.right?.value); -> Option B

4. Quick Check:

   Correct node creation and print order = const root = new Node(20); root.left = new Node(10); root.right = new Node(30); console.log(root.value, root.left?.value, root.right?.value); [OK]

Hint: Create nodes with new, assign children as nodes, print values [OK]

Common Mistakes:

• Assigning numbers directly to children
• Swapping left and right child values
• Printing children before root or using null children