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.

Practice

1. What does the height of a binary tree represent?

easy

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

B. The total number of nodes in the tree

C. The number of leaf nodes in the tree

D. The number of nodes at the root level

Solution

1. Step 1: Understand the definition of height in a binary tree

   The height is the longest path from the root node down to the farthest leaf node, counted by edges.

2. Step 2: Differentiate height from other tree properties

   Number of nodes or leaf nodes are different concepts; height specifically counts edges on the longest path.

3. Final Answer:

   The number of edges on the longest path from root to a leaf -> Option A

4. Quick Check:

   Height = longest root-to-leaf edge count [OK]

Hint: Height counts edges, not nodes, on longest root-to-leaf path [OK]

Common Mistakes:

• Confusing height with total nodes count
• Counting nodes instead of edges for height
• Thinking height equals number of leaf nodes

2. Which TypeScript function signature correctly defines a recursive function to find the height of a binary tree node?

easy

A. function height(node: TreeNode | null): number

B. function height(node: number): number

C. function height(): void

D. function height(node: TreeNode): string

Solution

1. Step 1: Identify the correct parameter type for a tree node

   The function must accept a node or null (for empty subtree), so type is TreeNode | null.

2. Step 2: Confirm the return type is number

   The height is a numeric value, so the return type must be number.

3. Final Answer:

   function height(node: TreeNode | null): number -> Option A

4. Quick Check:

   Parameter: TreeNode|null, Return: number [OK]

Hint: Height function needs node or null input and returns number [OK]

Common Mistakes:

• Using wrong parameter type like number instead of node
• Returning void or string instead of number
• Missing null to handle empty subtree

3. What is the height of the following binary tree?

    1
   / \
  2   3
 / 
4  

Consider height as number of edges on longest path from root to leaf.

medium

A. 3

B. 4

C. 1

D. 2

Solution

1. Step 1: Identify all root-to-leaf paths and count edges

   Paths: 1->2->4 has 2 edges, 1->3 has 1 edge.

2. Step 2: Find the longest path edge count

   Longest path is 1->2->4 with 2 edges.

3. Final Answer:

   2 -> Option D

4. Quick Check:

   Longest path edges = 2 [OK]

Hint: Count edges, not nodes, on longest root-to-leaf path [OK]

Common Mistakes:

• Counting nodes instead of edges
• Choosing shorter path length
• Confusing height with tree depth

4. Identify the error in this TypeScript function to find binary tree height:

function height(node: TreeNode | null): number {
  if (!node) return 0;
  return Math.max(height(node.left), height(node.right));
}

medium

A. Returns 0 for null node instead of -1

B. Uses Math.min instead of Math.max

C. Missing +1 to count current node edge

D. Function should return void

Solution

1. Step 1: Analyze base case return value

   Returning 0 for null means empty subtree height is 0, which is acceptable if counting edges from nodes.

2. Step 2: Check recursive return statement

   Function returns max height of children but misses adding 1 for current edge from node to child.

3. Final Answer:

   Missing +1 to count current node edge -> Option C

4. Quick Check:

   Height = max child height + 1 edge [OK]

Hint: Add +1 after max to include current node edge [OK]

Common Mistakes:

• Forgetting to add 1 for current node edge
• Returning wrong base case value
• Using min instead of max for height

5. Given a binary tree where each node has a value, write a function to find the height of the tree but only counting nodes with even values. What is the height of this tree?

    2
   / \
  3   4
 /   / \
6   5   8

hard

A. 0

B. 2

C. 1

D. 3

Solution

1. Step 1: Identify nodes with even values and their connections

   Even nodes: 2 (root), 4 (right child), 6 (left-left child), 8 (right-right child). Paths counting only even nodes:
• 2 -> 4 -> 8 (edges = 2)
• 2 -> 3 (3 is odd, so path ends at 2)
• 2 -> 3 -> 6 (6 is even but 3 is odd, so path breaks at 3)

2. Step 2: Calculate height counting only edges between even nodes

   Longest path with even nodes is 2 -> 4 -> 8 with 2 edges.

3. Final Answer:

   2 -> Option B

4. Quick Check:

   Longest even-valued node path edges = 2 [OK]

Hint: Count edges only between even-valued nodes [OK]

Common Mistakes:

• Counting odd nodes in path
• Counting nodes instead of edges
• Ignoring breaks caused by odd nodes