Tree Terminology Root Leaf Height Depth Level in DSA Python - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create the root node of a tree with value 10.

DSA Python

root = TreeNode([1])

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

A'root'

B10

CNone

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using a string instead of an integer for the root value.

The root node is created with the value 10, which is the starting point of the tree.

2fill in blank

medium

Complete the code to check if a node is a leaf (has no children).

DSA Python

is_leaf = node.left is [1] and node.right is None

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

AFalse

B0

CTrue

DNone

Attempts:

3 left

💡 Hint

Common Mistakes

Using True or False instead of None to check for children.

A leaf node has no left or right children, so both should be None.

3fill in blank

hard

Fix the error in the code to calculate the height of a tree node.

DSA Python

height = 1 + max([1](node.left), height(node.right)) if node else -1

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

Aheight

Blen

Cheight_of

Attempts:

3 left

💡 Hint

Common Mistakes

Using built-in functions like len instead of the recursive function name.

The function calls itself recursively as 'height' to calculate the height of left and right subtrees.

4fill in blank

hard

Fill in the blank to calculate the depth of a node in a tree.

DSA Python

def depth(node, root, current_depth=0):
    if node == root:
        return current_depth
    return depth(node, root.parent, current_depth [1] 1)

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

A+

B-

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Subtracting 1 instead of adding 1 to current_depth.

Depth increases by 1 as we move from the root to the node, so we add 1 to current_depth.

5fill in blank

hard

Fill all three blanks to create a dictionary mapping each node's level to a list of node values at that level.

DSA Python

levels = {}
for node in nodes:
    level = node.depth
    if level not in levels:
        levels[[1]] = []
    levels[[2]].append([3])

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

Alevel

Bnode

Cnode.value

Dlevels

Attempts:

3 left

💡 Hint

Common Mistakes

Using the node object instead of its value.

Using wrong keys for the dictionary.

We use the node's level as the key and append the node's value to the list at that level.

Practice

1. In a tree data structure, which node is called the root?

easy

A. A node at the lowest level

B. The topmost node with no parent

C. Any node with no children

D. A node with exactly two children

Solution

1. Step 1: Understand the root node definition

   The root node is the starting point of the tree and has no parent node above it.

2. Step 2: Compare options with definition

   The topmost node with no parent matches this definition exactly. Other options describe leaf nodes or other properties.

3. Final Answer:

   The topmost node with no parent -> Option B

4. Quick Check:

   Root = topmost node with no parent [OK]

Hint: Root is always the top node without a parent [OK]

Common Mistakes:

• Confusing root with leaf node
• Thinking root has children always
• Mixing root with internal nodes

2. Which of the following is the correct way to represent the leaf node in a tree?

easy

A. A node with no children

B. A node with exactly one child

C. The root node

D. A node with at least one child

Solution

1. Step 1: Define leaf node

   A leaf node is a node that has no children; it is at the end of a branch.

2. Step 2: Match definition with options

   A node with no children states a node with no children, which matches the leaf node definition.

3. Final Answer:

   A node with no children -> Option A

4. Quick Check:

   Leaf = node with no children [OK]

Hint: Leaf nodes have zero children [OK]

Common Mistakes:

• Thinking leaf nodes have children
• Confusing leaf with root
• Assuming leaf nodes must have one child

3. Consider the following tree structure:

       A
      / \
     B   C
    /   / \
   D   E   F

What is the height of node C?

medium

A. 0

B. 2

C. 3

D. 1

Solution

1. Step 1: Understand height of a node

   Height is the number of edges on the longest path from the node down to a leaf.

2. Step 2: Calculate height of node C

   Node C has children E and F, both leaves with height 0. So height of C = 1 + max(0,0) = 1.

3. Step 3: Verify options

   1 says 1, but height counts edges down, so height is 1. 2 says 2, which is incorrect. 0 is 0, which is leaf height.

4. Final Answer:

   1 -> Option D

5. Quick Check:

   Height of C = 1 edge to leaf [OK]

Hint: Height counts edges down to farthest leaf [OK]

Common Mistakes:

• Confusing height with depth
• Counting nodes instead of edges
• Assuming leaf height is 1

4. Given the tree below:

       X
      / \
     Y   Z
    / 
   W  

What is the depth of node W?
Note: Depth is the number of edges from the root to the node.

medium

A. 2

B. 1

C. 0

D. 3

Solution

1. Step 1: Understand depth definition

   Depth is the number of edges from the root node to the target node.

2. Step 2: Trace path from root to W

   Path: X (root) -> Y -> W. Number of edges = 2.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Depth of W = 2 edges from root [OK]

Hint: Count edges from root to node for depth [OK]

Common Mistakes:

• Counting nodes instead of edges
• Confusing depth with height
• Starting count from 1 instead of 0

5. In a tree, the level of a node is defined as its depth plus one. Given the tree:

        M
       / \
      N   O
     / \
    P   Q

What is the level of node Q?

hard

A. 1

B. 2

C. 3

D. 4

Solution

1. Step 1: Find depth of node Q

   Path from root M to Q is M -> N -> Q, which has 2 edges, so depth = 2.

2. Step 2: Calculate level using formula

   Level = depth + 1 = 2 + 1 = 3.

3. Final Answer:

   3 -> Option C

4. Quick Check:

   Level = depth + 1 = 3 [OK]

Hint: Level = depth + 1 always [OK]

Common Mistakes:

• Using depth as level directly
• Counting nodes incorrectly
• Confusing level with height