Height of Binary Tree in DSA Javascript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the height of this binary tree?

Consider the following binary tree structure and code to calculate its height. What is the output printed by the code?

DSA Javascript

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

function height(root) {
  if (!root) return 0;
  const leftHeight = height(root.left);
  const rightHeight = height(root.right);
  return Math.max(leftHeight, rightHeight) + 1;
}

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);

console.log(height(root));

A 3

B 4

C 2

D 5

💡 Hint

Think about the longest path from the root to a leaf node.

The height is the number of nodes on the longest path from the root to a leaf. Here, the longest path is 1 -> 2 -> 4, which has 3 nodes, so height is 3.

❓ Predict Output

intermediate

Output of height function on a skewed tree

What will be the output of the height function when called on this skewed binary tree?

DSA Javascript

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

function height(root) {
  if (!root) return 0;
  return Math.max(height(root.left), height(root.right)) + 1;
}

const root = new Node(10);
root.right = new Node(20);
root.right.right = new Node(30);
root.right.right.right = new Node(40);

console.log(height(root));

A 0

B 3

C 1

D 4

💡 Hint

Count the nodes along the right side.

The tree is skewed to the right with 4 nodes in a line, so height is 4.

🔧 Debug

advanced

Identify the error in height calculation

The following code is intended to calculate the height of a binary tree. What error will it produce when run?

DSA Javascript

function height(root) {
  if (root == null) {
    return -1;
  }
  const leftHeight = height(root.left);
  const rightHeight = height(root.right);
  return Math.max(leftHeight, rightHeight);
}

const root = { value: 1, left: null, right: null };
console.log(height(root));

A 0

B TypeError

C -1

D Infinity

💡 Hint

Check the base case and the return statement.

The base case returns -1 for null nodes, but the function does not add 1 after max, so height of a single node returns -1 instead of 0.

🧠 Conceptual

advanced

Height of an empty tree

What is the height of an empty binary tree (null root)?

A 0

B -1

C 1

D undefined

💡 Hint

Think about how height is defined for no nodes.

An empty tree has height 0 because there are no nodes.

🚀 Application

expert

Calculate height after inserting nodes

Given an initially empty binary tree, nodes are inserted in this order: 5, 3, 8, 1, 4, 7, 9. What is the height of the tree after all insertions?

A 4

B 3

C 2

D 5

💡 Hint

Visualize the tree structure after inserting nodes in given order.

The tree is balanced with height 3 after inserting nodes in given order.