Height of Binary Tree in DSA Javascript - Execution Trace

Concept Flow - Height of Binary Tree

Start at root node

↓

Is node null?

Yes→Return 0

No↓

Find height of left subtree

↓

Find height of right subtree

↓

Height = max(left, right) + 1

↓

Return height

The height is found by recursively checking left and right subtrees, then taking the larger height plus one.

Execution Sample

DSA Javascript

function height(node) {
  if (node === null) return 0;
  let leftHeight = height(node.left);
  let rightHeight = height(node.right);
  return Math.max(leftHeight, rightHeight) + 1;
}

This function calculates the height of a binary tree by recursively finding the height of left and right children.

Execution Table

Step	Operation	Node Visited	Left Height	Right Height	Height Computed	Tree State
1	Start at root	1	-	-	-	1 / \ 2 3 / \ 4 5
2	Go left	2	-	-	-	Same as above
3	Go left	4	-	-	-	Same as above
4	Check left child	null	-	-	0	Leaf reached
5	Check right child	null	-	-	0	Leaf reached
6	Compute height	4	0	0	1	Node 4 height = 1
7	Go right	5	-	-	-	Node 5 leaf
8	Check left child	null	-	-	0	Leaf reached
9	Check right child	null	-	-	0	Leaf reached
10	Compute height	5	0	0	1	Node 5 height = 1
11	Compute height	2	1	1	2	Node 2 height = 2
12	Go right	3	-	-	-	Node 3 leaf
13	Check left child	null	-	-	0	Leaf reached
14	Check right child	null	-	-	0	Leaf reached
15	Compute height	3	0	0	1	Node 3 height = 1
16	Compute height	1	2	1	3	Root node height = 3

💡 All nodes visited, height computed from bottom up

Variable Tracker

Variable	Start	After Step 6	After Step 10	After Step 11	After Step 15	After Step 16
node	1 (root)	4 (left leaf)	5 (right leaf of 2)	2 (left child of root)	3 (right child of root)	1 (root)
leftHeight	-	0	0	1	0	2
rightHeight	-	0	0	1	0	1
height	-	1	1	2	1	3

Key Moments - 3 Insights

Why do we return 0 when the node is null?

Returning 0 for null nodes means leaf nodes have height 1 (0 + 1). This is shown in steps 4, 5, 8, 9, 13, and 14 where null children return 0.

Why do we add 1 after taking max of left and right heights?

Adding 1 accounts for the current node's level. Steps 6, 10, 11, 15, and 16 show height computed as max(leftHeight, rightHeight) + 1.

How does recursion ensure all nodes are visited?

The function calls itself on left and right children until null is reached (leaf), ensuring bottom-up height calculation as seen in the step sequence.

Visual Quiz - 3 Questions

Look at the execution table, what is the height computed at step 11 for node 2?

A 1

B 3

C 2

D 0

💡 Hint

Check the 'Height Computed' column at step 11 in the execution table.

At which step does the function return height 1 for node 5?

A Step 10

B Step 6

C Step 15

D Step 16

💡 Hint

Look for node 5 in the 'Node Visited' column and check the height computed.

If the left subtree of node 2 was taller by 1, how would the height at root (step 16) change?

A It would remain 3

B It would become 4

C It would become 2

D It would become 5

💡 Hint

Height at root is max(leftHeight, rightHeight) + 1; increasing leftHeight by 1 increases root height by 1.

Concept Snapshot

Height of Binary Tree:
- Base case: null node height = 0
- Recursively find left and right subtree heights
- Height = max(leftHeight, rightHeight) + 1
- Returns height of tree from bottom up
- Used to measure tree depth

Full Transcript

The height of a binary tree is found by starting at the root and recursively checking the height of left and right children. If a node is null, it returns 0, meaning leaf nodes have height 1. For each node, the height is the maximum height of its left and right subtrees plus one for the current node. This process continues until all nodes are visited and the height of the root node is computed. The execution table shows each step visiting nodes, checking children, and computing heights. The variable tracker follows the node visited and height values at key steps. Key moments clarify why null returns 0 and why we add 1 after max. The visual quiz tests understanding of height values at specific steps and how changes affect the root height.

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