Height of Binary Tree in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the height of a binary tree?

The height of a binary tree is the number of edges on the longest path from the root node to a leaf node. If the tree has only one node, its height is 0.

beginner

How do you calculate the height of a binary tree recursively?

Calculate the height of the left subtree and the right subtree recursively, then the height of the tree is 1 plus the maximum of these two heights.

beginner

What is the height of an empty binary tree?

The height of an empty binary tree is defined as -1 because there are no nodes.

beginner

Why is the height of a single-node binary tree 0?

Because the height counts edges on the longest path from root to leaf, and a single node has no edges, so height is 0.

intermediate

What is the time complexity of computing the height of a binary tree?

The time complexity is O(n), where n is the number of nodes, because each node is visited once during the height calculation.

What is the height of a binary tree with only one node?

A 0

B 1

C -1

D 2

A single node has no edges, so height is 0.

What is the height of an empty binary tree?

A 0

B Undefined

C 1

D -1

By definition, an empty tree has height -1.

Which method is commonly used to find the height of a binary tree?

A Iterative level order traversal only

B Recursive depth calculation

C Sorting nodes

D Counting leaf nodes

Height is usually found by recursively calculating the depth of subtrees.

If left subtree height is 3 and right subtree height is 5, what is the height of the tree?

A 6

B 4

C 5

D 3

Height = 1 + max(left height, right height) = 1 + 5 = 6.

What is the time complexity to compute the height of a binary tree with n nodes?

A O(n log n)

B O(log n)

C O(n)

D O(1)

Each node is visited once, so time complexity is O(n).

Explain how to find the height of a binary tree using recursion.

Think about how you break down the problem into smaller parts.

Describe the difference between the height of an empty tree and a single-node tree.

Consider what height means in terms of edges.

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