Count Total Nodes in Binary Tree in DSA Javascript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Count nodes in a simple binary tree

What is the output of the following code that counts total nodes in a binary tree?

DSA Javascript

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

function countNodes(root) {
  if (!root) return 0;
  return 1 + countNodes(root.left) + countNodes(root.right);
}

const root = new Node(10);
root.left = new Node(5);
root.right = new Node(15);
root.left.left = new Node(3);

console.log(countNodes(root));

A 4

B 3

C 5

D 6

💡 Hint

Count each node including root, left child, right child, and left-left child.

The tree has 4 nodes: root (10), left (5), right (15), and left-left (3). The function counts all nodes recursively.

❓ Predict Output

intermediate

Count nodes in an empty tree

What is the output when counting nodes in an empty binary tree?

DSA Javascript

function countNodes(root) {
  if (!root) return 0;
  return 1 + countNodes(root.left) + countNodes(root.right);
}

const root = null;
console.log(countNodes(root));

A 0

B null

C 1

D undefined

💡 Hint

An empty tree has no nodes.

The function returns 0 immediately when root is null, meaning no nodes exist.

❓ Predict Output

advanced

Count nodes in a full binary tree

What is the output of counting nodes in this full binary tree?

DSA Javascript

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

function countNodes(root) {
  if (!root) return 0;
  return 1 + countNodes(root.left) + countNodes(root.right);
}

const root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.left.left = new Node(4);
root.left.right = new Node(5);
root.right.left = new Node(6);
root.right.right = new Node(7);

console.log(countNodes(root));

A 8

B 5

C 6

D 7

💡 Hint

Count all nodes including root, its two children, and their children.

The tree has 7 nodes: root (1), two children (2,3), and four grandchildren (4,5,6,7).

❓ Predict Output

advanced

Count nodes in an unbalanced binary tree

What is the output of counting nodes in this unbalanced binary tree?

DSA Javascript

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

function countNodes(root) {
  if (!root) return 0;
  return 1 + countNodes(root.left) + countNodes(root.right);
}

const root = new Node(10);
root.left = new Node(5);
root.left.left = new Node(3);
root.left.left.left = new Node(1);
root.right = new Node(15);

console.log(countNodes(root));

A 4

B 5

C 6

D 3

💡 Hint

Count all nodes including the deep left branch.

The tree has 5 nodes: 10, 5, 3, 1 on the left side and 15 on the right.

🧠 Conceptual

expert

Time complexity of counting nodes in binary tree

What is the time complexity of counting total nodes in a binary tree using a recursive function that visits each node once?

A O(n^2), where n is the number of nodes

B O(log n), where n is the number of nodes

C O(n), where n is the number of nodes

D O(1), constant time

💡 Hint

The function visits every node exactly once.

Since the function visits each node once, the time grows linearly with the number of nodes.