Height of Binary Tree in DSA Javascript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to return the height of a binary tree recursively.

DSA Javascript

function height(node) {
  if (node === null) {
    return 0;
  }
  return 1 + Math.max(height(node.left), height(node[1]));
}

Drag options to blanks, or click blank then click option'

A.parent

B.right

C.left

D.child

Attempts:

3 left

💡 Hint

Common Mistakes

Using node.left twice instead of node.right

Using node.parent which is not part of height calculation

The height of a binary tree is 1 plus the maximum height of its left and right subtrees. We already have height(node.left), so the other subtree is node.right.

2fill in blank

medium

Complete the code to check if the node is null before calculating height.

DSA Javascript

function height(node) {
  if (node [1] null) {
    return 0;
  }
  return 1 + Math.max(height(node.left), height(node.right));
}

Drag options to blanks, or click blank then click option'

A===

B!==

C==

D!=

Attempts:

3 left

💡 Hint

Common Mistakes

Using !== which reverses the logic

Using loose equality == which can cause unexpected results

We check if node is exactly null to stop recursion and return 0 height for empty subtree.

3fill in blank

hard

Fix the error in the recursive call to height for the right subtree.

DSA Javascript

function height(node) {
  if (node === null) {
    return 0;
  }
  return 1 + Math.max(height(node.left), height(node[1]));
}

Drag options to blanks, or click blank then click option'

A.rigt

B.parent

C.right

D.leftt

Attempts:

3 left

💡 Hint

Common Mistakes

Typos like '.leftt' or '.rigt'

Using '.parent' which is not a child node

The correct property for the right child is node.right. Misspelled properties cause runtime errors.

4fill in blank

hard

Fill both blanks to create a function that returns the height of a binary tree using recursion.

DSA Javascript

function height(node) {
  if (node [1] null) {
    return 0;
  }
  return 1 + Math.max(height(node[2]), height(node.right));
}

Drag options to blanks, or click blank then click option'

A===

B!==

C.left

D.parent

Attempts:

3 left

💡 Hint

Common Mistakes

Using !== instead of === in null check

Using '.parent' instead of '.left' for child node

Check if node is exactly null, then recursively get height of left and right children.

5fill in blank

hard

Fill all three blanks to complete the height function with correct null check and recursive calls.

DSA Javascript

function height(node) {
  if (node [1] null) {
    return 0;
  }
  return 1 + Math.max(height(node[2]), height(node[3]));
}

Drag options to blanks, or click blank then click option'

A!==

B===

C.right

D.left

Attempts:

3 left

💡 Hint

Common Mistakes

Using !== instead of === for null check

Swapping left and right child properties

Use strict equality to check null, then recursively call height on left and right children.

Practice

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

easy

A. The number of children of the root node

B. The total 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

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 D

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 of the following is the correct base case to find the height of a binary tree recursively in JavaScript?

easy

A. if (node === null) return -1;

B. if (node === null) return 0;

C. if (node === undefined) return 1;

D. if (node === undefined) return 0;

Solution

1. Step 1: Understand the base case for empty subtree

   When the node is null (no node), height is defined as -1 to count edges properly.

2. Step 2: Why -1 instead of 0?

   Returning -1 for null ensures leaf nodes have height 0 (0 edges below them), matching edge count definition.

3. Final Answer:

   if (node === null) return -1; -> Option A

4. Quick Check:

   Empty node height = -1 for correct edge count [OK]

Hint: Use -1 for null node to count edges correctly [OK]

Common Mistakes:

• Returning 0 for null node causes off-by-one height
• Checking undefined instead of null for nodes
• Confusing node absence with leaf node

3. What is the output of the following code snippet?

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

function height(node) {
  if (node === null) return -1;
  return 1 + Math.max(height(node.left), height(node.right));
}

const root = new Node(10);
root.left = new Node(5);
root.right = new Node(15);
root.left.left = new Node(3);
root.left.left.left = new Node(1);

console.log(height(root));

medium

A. 5

B. 3

C. 4

D. 2

Solution

1. Step 1: Trace the tree structure and count edges

   The longest path is from root (10) to left-left-left (1): edges are 10->5, 5->3, 3->1, total 3 edges.

2. Step 2: Calculate height using the function logic

   Function returns 1 + max height of children. For leaf node (1), height = 0. So total height = 3 edges means function returns 3.

3. Final Answer:

   3 -> Option B

4. Quick Check:

   Longest path edges = 3 [OK]

Hint: Count edges on longest path, not nodes [OK]

Common Mistakes:

• Counting nodes instead of edges for height
• Misreading tree structure and missing deepest node
• Confusing return value for leaf node height

4. Find the error in this height function and select the correct fix:

function height(node) {
  if (node === null) return 0;
  return Math.max(height(node.left), height(node.right));
}

medium

A. Change base case to return -1 instead of 0

B. Return sum instead of max of left and right heights

C. Add +1 before Math.max to count current node

D. No error, function is correct

Solution

1. Step 1: Analyze the base case and recursive return

   Base case returns 0 for null, which is acceptable if counting nodes, but function misses adding 1 for current node.

2. Step 2: Identify missing increment for current node

   Function returns max height of children but does not add 1 for current node, so height is underestimated by 1.

3. Final Answer:

   Add +1 before Math.max to count current node -> Option C

4. Quick Check:

   Height = 1 + max(child heights) [OK]

Hint: Add +1 to include current node in height [OK]

Common Mistakes:

• Forgetting to add 1 for current node
• Changing base case unnecessarily
• Returning sum instead of max height

5. Given a binary tree where some nodes have only one child, how does the height calculation change if you want to count the number of nodes on the longest path instead of edges? Choose the correct modification to the recursive height function.

function height(node) {
  if (node === null) return ?;
  return ? + Math.max(height(node.left), height(node.right));
}

hard

A. Return 0 for null; add 1 before Math.max to count nodes

B. Return -1 for null; add 1 before Math.max to count nodes

C. Return 1 for null; add 0 before Math.max to count nodes

D. Return 0 for null; add 0 before Math.max to count nodes

Solution

1. Step 1: Understand difference between counting edges and nodes

   Counting nodes means height of empty tree is 0, and each node adds 1 to path length.

2. Step 2: Adjust base case and recursive addition accordingly

   Return 0 for null node (no nodes), and add 1 for current node to count nodes on path.

3. Final Answer:

   Return 0 for null; add 1 before Math.max to count nodes -> Option A

4. Quick Check:

   Height counts nodes: base=0, add 1 per node [OK]

Hint: Use 0 base and add 1 to count nodes, not edges [OK]

Common Mistakes:

• Using -1 base for node count causes off-by-one
• Not adding 1 for current node
• Confusing edges count with nodes count