Why Height of Binary Tree in DSA Typescript?

The Big Idea

What if you could instantly know the deepest level of any family or company tree without counting each step?

The Scenario

Imagine you have a family tree drawn on paper. You want to know how many generations it has from the oldest ancestor to the youngest child. Counting each level by hand is tiring and easy to mess up.

The Problem

Manually counting levels in a tree can be slow and confusing, especially if the tree is big or uneven. You might skip a generation or count wrong, leading to mistakes.

The Solution

The height of a binary tree gives you the number of levels automatically. Using a simple method, you can find the longest path from the root to any leaf, so you know the tree's height without guessing.

Before vs After

✗ Before

let height = 0;
// Manually check each level and count
if (root.left) height++;
if (root.right) height++;

✓ After

function heightOfTree(node: TreeNode | null): number {
  if (!node) return 0;
  return 1 + Math.max(heightOfTree(node.left), heightOfTree(node.right));
}

What It Enables

This lets you quickly understand the depth of any tree structure, helping in tasks like balancing trees or searching efficiently.

Real Life Example

In a company's organizational chart, finding the height helps know how many management levels exist from the CEO down to the newest employee.

Key Takeaways

Manually counting tree height is slow and error-prone.

Using a recursive method finds height easily and correctly.

Knowing tree height helps in many computer and real-world tasks.

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