Height of Binary Tree in DSA Python - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

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

DSA Python

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

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

Aroot

Bleft_height

Cright_height

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using min instead of max

Returning left_height only

Returning right_height only

The height of a binary tree is 1 plus the maximum height of its left and right subtrees. So we take max(left_height, right_height).

2fill in blank

medium

Complete the code to check if the tree is empty and return height 0.

DSA Python

def height(root):
    if [1]:
        return 0
    # rest of the code

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

Aroot is None

Broot == None

Croot.left is None

Droot.right is None

Attempts:

3 left

💡 Hint

Common Mistakes

Using '==' instead of 'is' for None check

Checking left or right child instead of root

To check if the tree is empty, we check if root is None using 'is' keyword for identity comparison.

3fill in blank

hard

Fix the error in the recursive call to compute height of right subtree.

DSA Python

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

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

ANone

Broot.left

Croot

Droot.right

Attempts:

3 left

💡 Hint

Common Mistakes

Passing root.left instead of root.right

Passing root instead of child nodes

To get the height of the right subtree, we must call height on root.right.

4fill in blank

hard

Fill both blanks to compute height using recursion and return the correct value.

DSA Python

def height(root):
    if [1]:
        return 0
    left_height = height(root.left)
    right_height = height(root.right)
    return 1 + [2](left_height, right_height)

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

Aroot is None

Broot == None

Cmax

Dmin

Attempts:

3 left

💡 Hint

Common Mistakes

Using min instead of max

Using '==' instead of 'is' for None check

Check if root is None to handle empty tree, then return 1 plus max of left and right subtree heights.

5fill in blank

hard

Fill all three blanks to create a dictionary of node values and their heights for nodes with height > 1.

DSA Python

def height_dict(root):
    if root is None:
        return {}
    left = height_dict(root.left)
    right = height_dict(root.right)
    current_height = 1 + max([1], [2])
    result = {**left, **right}
    if current_height [3] 1:
        result[root.val] = current_height
    return result

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

Aheight(root.left)

Bheight(root.right)

C>

D>=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<' or '<=' instead of '>'

Mixing up left and right subtree heights

Calculate current height using height of left and right subtrees, then add node if height > 1.

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