Height of Binary Tree in DSA Typescript - 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 will be the output?

DSA Typescript

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

function height(root: Node | null): number {
  if (!root) return 0;
  return 1 + Math.max(height(root.left), height(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);

console.log(height(root));

A 4

B 3

C 5

D 2

💡 Hint

Height counts the number of nodes on the longest path from root to leaf.

The longest path is from root (1) to leaf (4 or 5) with 3 nodes, so height is 3.

❓ Predict Output

intermediate

Output of height function on a skewed tree

What is the output of the height function for this skewed binary tree?

DSA Typescript

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

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

const root = new Node(1);
root.right = new Node(2);
root.right.right = new Node(3);
root.right.right.right = new Node(4);

console.log(height(root));

A 1

B 3

C 2

D 4

💡 Hint

Height is the longest path from root to leaf. Here, the tree is skewed to the right.

The path is 1 -> 2 -> 3 -> 4, so height is 4.

🧠 Conceptual

advanced

What does the height of a binary tree represent?

Choose the best description of what the height of a binary tree means.

A The number of nodes on the longest path from root to a leaf node.

B The number of nodes in the tree.

C The number of leaf nodes in the tree.

D The number of edges on the longest path from root to a leaf node.

💡 Hint

Height counts nodes, not edges or total nodes.

Height is the count of nodes on the longest path from root to leaf, including both ends.

❓ Predict Output

advanced

Height of an empty tree

What will be the output of the height function when the tree is empty (root is null)?

DSA Typescript

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

console.log(height(null));

A 0

B 1

C null

D undefined

💡 Hint

Think about what the function returns when root is null.

The function returns 0 immediately if root is null, meaning empty tree has height 0.

🔧 Debug

expert

Why does this height function cause a runtime error?

Consider this height function. It causes a runtime error on some inputs. Why?

DSA Typescript

function height(root: any): number {
  if (root === null) return 0;
  return 1 + Math.max(height(root.left), height(root.right));
}

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

A Because the function does not handle leaf nodes correctly.

B Because root.left is null, causing infinite recursion.

C Because root.right is undefined, causing an error when accessed.

D Because the function is missing a return statement.

💡 Hint

Check if all child nodes exist before accessing their properties.

root.right is undefined, so accessing root.right causes an error when height tries to recurse on it.