Height of Binary Tree in DSA Python - 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. It measures how tall the tree is.

beginner

How do you calculate the height of an empty binary tree?

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

beginner

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

The height is 0 because there are no edges from the root to any leaf (the root itself is a leaf).

intermediate

Explain the recursive approach to find the height of a binary tree.

To find the height, recursively find the height of the left and right subtrees, then take the maximum of these two heights and add 1 for the current node.

intermediate

Why do we add 1 when calculating the height recursively?

We add 1 to count the edge from the current node to its child, moving one level down the tree.

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

A 2

B 1

C -1

D 0

A tree with only root has height 0 because there are no edges.

What is the height of an empty binary tree?

A 0

B -1

C 1

D Undefined

By definition, an empty tree has height -1.

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

A Recursive depth calculation

B Iterative level order traversal only

C Sorting nodes

D Counting leaf nodes

Recursion is commonly used to find height by checking left and right subtree heights.

If left subtree height is 3 and right subtree height is 5, what is the height at the current node?

A 6

B 4

C 5

D 3

Height is max(3,5) + 1 = 6.

What does the height of a binary tree represent?

A Number of nodes in the tree

B Number of leaf nodes

C Longest path from root to leaf in edges

D Number of children of root

Height is the longest path from root to leaf measured in edges.

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

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

Explain why the height of an empty tree is defined as -1.

Consider what height means in terms of edges.

Practice

1. What is the height of a binary tree with only one node (the root)?

easy

A. 2

B. 0

C. Undefined

D. 1

Solution

1. Step 1: Understand height definition

   The height of a binary tree is the number of nodes on the longest path from the root to a leaf.

2. Step 2: Apply to single node tree

   With only one node (root), the longest path has length 1.

3. Final Answer:

   1 -> Option D

4. Quick Check:

   Height of single node tree = 1 [OK]

Hint: Height counts nodes on longest root-to-leaf path [OK]

Common Mistakes:

• Thinking height is 0 for single node
• Confusing height with number of edges
• Assuming height is undefined for single node

2. Which of the following is the correct Python function header to calculate the height of a binary tree node named root?

easy

A. def height(root, node):

B. def height(root):

C. def height():

D. def height(tree_root):

Solution

1. Step 1: Identify function parameter

   The function needs one parameter representing the root node of the tree.

2. Step 2: Match parameter name and count

   def height(root): uses one parameter named root, which matches the question context.

3. Final Answer:

   def height(root): -> Option B

4. Quick Check:

   One parameter named root is correct [OK]

Hint: Function needs one parameter: the root node [OK]

Common Mistakes:

• Adding extra parameters unnecessarily
• No parameters in function
• Using unrelated parameter names

3. What will be the output of the following code snippet?

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

def height(root):
    if root is None:
        return 0
    left_height = height(root.left)
    right_height = height(root.right)
    return max(left_height, right_height) + 1

root = Node(10)
root.left = Node(20)
root.right = Node(30)
root.left.left = Node(40)
print(height(root))

medium

A. 3

B. 2

C. 4

D. 1

Solution

1. Step 1: Trace tree structure

   The tree has root 10, with left child 20 and right child 30. Node 20 has left child 40. The longest path is 10 -> 20 -> 40.

2. Step 2: Calculate height recursively

   Height is max height of left and right subtree plus 1. Left subtree height is 2 (20 -> 40), right subtree height is 1 (30). So total height = max(2,1)+1 = 3.

3. Final Answer:

   3 -> Option A

4. Quick Check:

   Longest path length = 3 [OK]

Hint: Count nodes on longest root-to-leaf path [OK]

Common Mistakes:

• Counting edges instead of nodes
• Ignoring one subtree height
• Returning wrong base case value

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

def height(root):
    if root is None:
        return -1
    left_height = height(root.left)
    right_height = height(root.right)
    return max(left_height, right_height) + 1

medium

A. Add else before recursive calls

B. Change max to min in return statement

C. Change base case return from -1 to 0

D. Remove +1 from return statement

Solution

1. Step 1: Understand base case meaning

   Height of empty tree (None) should be 0, not -1, to count nodes properly.

2. Step 2: Fix base case return value

   Changing return -1 to return 0 fixes height calculation to count nodes correctly.

3. Final Answer:

   Change base case return from -1 to 0 -> Option C

4. Quick Check:

   Base case height = 0 for empty tree [OK]

Hint: Base case for empty node should return 0 [OK]

Common Mistakes:

• Returning -1 causes height off by one
• Using min instead of max
• Forgetting to add 1 after recursion

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 will be the height of this tree?

    2
   / \
  3   4
     / \
    6   7
   /
  8

hard

A. 3

B. 4

C. 2

D. 1

Solution

1. Step 1: Identify even-valued nodes in tree

   Nodes with even values: 2 (root), 4, 6, 8. Nodes 3 and 7 are odd and ignored.

2. Step 2: Calculate height counting only even nodes

   Longest path with even nodes is 2 -> 4 -> 6 -> 8, but since 4 has children 6 and 7, and 7 is odd, it is ignored. The path length counting only even nodes is 4 nodes, but the height counts edges between nodes, so height is 3.

3. Step 3: Clarify height definition for this problem

   Height counts number of edges on longest path with even values only. The path is 2 -> 4 -> 6 -> 8, which has 3 edges, so height is 3.

4. Final Answer:

   3 -> Option A

5. Quick Check:

   Longest even-valued path edge count = 3 [OK]

Hint: Count only even nodes on longest root-to-leaf path, height = edges count [OK]

Common Mistakes:

• Counting odd nodes by mistake
• Confusing edges with nodes
• Ignoring subtree with even nodes