Bottom View of Binary Tree in DSA Python - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a new node in the binary tree.

DSA Python

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

root = Node([1])

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

ANone

B10

C0

Droot

Attempts:

3 left

💡 Hint

Common Mistakes

Using None instead of a number for the node's data.

Using a variable name instead of a value.

The root node is created with the value 10.

2fill in blank

medium

Complete the code to assign the left child of the root node.

DSA Python

root.left = Node([1])

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

A20

B5

CNone

Droot

Attempts:

3 left

💡 Hint

Common Mistakes

Assigning None instead of a node.

Using the root variable instead of a value.

The left child of the root is assigned the value 20.

3fill in blank

hard

Fix the error in the function to print the bottom view of the binary tree.

DSA Python

def bottom_view(root):
    if root is None:
        return
    hd_node = dict()
    queue = [(root, 0)]
    while queue:
        node, hd = queue.pop(0)
        hd_node[[1]] = node.data
        if node.left:
            queue.append((node.left, hd - 1))
        if node.right:
            queue.append((node.right, hd + 1))
    for key in sorted(hd_node):
        print(hd_node[key], end=' ')

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

Ahd

Broot

Cnode

Dqueue

Attempts:

3 left

💡 Hint

Common Mistakes

Using the node object as a key instead of horizontal distance.

Using the root or queue variables incorrectly.

The horizontal distance (hd) is used as the key to update the bottom view map.

4fill in blank

hard

Fill both blanks to update the queue with child nodes and their horizontal distances.

DSA Python

if node.left:
    queue.append((node.left, hd [1] 1))
if node.right:
    queue.append((node.right, hd [2] 1))

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

A-

B+

C*

D//

Attempts:

3 left

💡 Hint

Common Mistakes

Adding 1 to left child horizontal distance.

Subtracting 1 from right child horizontal distance.

Left child horizontal distance is one less (hd - 1), right child is one more (hd + 1).

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension for bottom view filtering.

DSA Python

bottom_view_map = [1]: [2] for [3], [2] in hd_node.items()}

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

Ahd

Bvalue

Ckey

Dhd_node

Attempts:

3 left

💡 Hint

Common Mistakes

Using hd instead of key for dictionary keys.

Using hd_node instead of key, value in the loop.

The dictionary comprehension uses key and value from hd_node.items() to build the bottom view map.

Practice

1. What does the bottom view of a binary tree represent?

easy

A. Nodes visible when the tree is viewed from the right side

B. Nodes visible when the tree is viewed from the top

C. Nodes visible when the tree is viewed from the left side

D. Nodes visible when the tree is viewed from the bottom

Solution

1. Step 1: Understand the bottom view concept

   The bottom view shows nodes visible when looking at the tree from below, meaning the lowest nodes at each horizontal distance.

2. Step 2: Compare with other views

   Top view shows nodes from above, left and right views show nodes from sides, so bottom view is unique for bottom perspective.

3. Final Answer:

   Nodes visible when the tree is viewed from the bottom -> Option D

4. Quick Check:

   Bottom view = visible nodes from below [OK]

Hint: Bottom view shows lowest nodes at each horizontal distance [OK]

Common Mistakes:

• Confusing bottom view with top view
• Thinking bottom view shows all leaf nodes
• Mixing bottom view with side views

2. Which data structure is commonly used to track nodes and their horizontal distances when computing the bottom view of a binary tree?

easy

A. Hash Map (Dictionary)

B. Queue

C. Stack

D. Linked List

Solution

1. Step 1: Identify the need for horizontal distance mapping

   We need to map horizontal distances to nodes to know which node is visible at each position.

2. Step 2: Choose the data structure

   A hash map (dictionary) stores horizontal distance as key and node value as value, updating with the bottom-most node.

3. Final Answer:

   Hash Map (Dictionary) -> Option A

4. Quick Check:

   Use dictionary to map horizontal distance to node [OK]

Hint: Use dictionary to map horizontal distance to node [OK]

Common Mistakes:

• Using stack which is LIFO and not suitable here
• Using queue alone without mapping distances
• Using linked list which is inefficient for key-value mapping

3. What is the bottom view output of the following binary tree?

        20
       /  \
     8     22
    / \      \
   5   3      25
      / \     
     10  14

medium

A. [5, 10, 3, 14, 25]

B. [5, 8, 10, 14, 25]

C. [5, 10, 3, 22, 25]

D. [8, 10, 3, 14, 22]

Solution

1. Step 1: Assign horizontal distances and find bottom nodes

   Horizontal distances: 20(0), 8(-1), 22(1), 5(-2), 3(0), 25(2), 10(-1), 14(1). Bottom nodes at each distance: -2:5, -1:10, 0:3, 1:14, 2:25.

2. Step 2: List bottom view nodes in order of horizontal distance

   From left to right: 5, 10, 3, 14, 25.

3. Final Answer:

   [5, 10, 3, 14, 25] -> Option A

4. Quick Check:

   Bottom view nodes by horizontal distance = [5,10,3,14,25] [OK]

Hint: Track horizontal distances and update bottom nodes [OK]

Common Mistakes:

• Not updating bottom node when a lower node appears
• Mixing horizontal distances order
• Including nodes not visible from bottom

4. Consider this code snippet to compute bottom view of a binary tree:

def bottom_view(root):
    if not root:
        return []
    queue = [(root, 0)]
    hd_node = {}
    while queue:
        node, hd = queue.pop()
        hd_node[hd] = node.val
        if node.left:
            queue.append((node.left, hd - 1))
        if node.right:
            queue.append((node.right, hd + 1))
    return [hd_node[hd] for hd in sorted(hd_node)]

What is the main error in this code?

medium

A. Not checking if root is None

B. Using pop() removes last element, causing wrong traversal order

C. Not updating hd_node dictionary

D. Incorrect horizontal distance calculation

Solution

1. Step 1: Analyze queue usage and traversal order

   The code uses queue.pop() which removes last element (LIFO), making it behave like a stack, causing depth-first traversal instead of breadth-first.

2. Step 2: Understand impact on bottom view calculation

   Breadth-first traversal is needed to process nodes level by level to correctly update bottom nodes. Using pop() breaks this order.

3. Final Answer:

   Using pop() removes last element, causing wrong traversal order -> Option B

4. Quick Check:

   Use pop(0) or deque.popleft() for BFS [OK]

Hint: Use pop(0) for queue to maintain BFS order [OK]

Common Mistakes:

• Using pop() instead of pop(0) for queue
• Ignoring empty root check
• Incorrect horizontal distance updates

5. You have a binary tree where multiple nodes share the same horizontal distance and depth. How should you modify the bottom view algorithm to always show the node with the greatest depth at each horizontal distance?

hard

A. Store nodes in a list for each horizontal distance and pick the smallest value

B. Store only the first node encountered at each horizontal distance

C. Store both node value and depth in the dictionary, update only if new node depth is greater

D. Ignore depth and update dictionary with last visited node

Solution

1. Step 1: Understand the need to track depth

   To show the bottom-most node at each horizontal distance, we must know which node is deepest (greatest depth).

2. Step 2: Modify dictionary to store value and depth

   Store a tuple (node value, depth) for each horizontal distance. Update only if new node's depth is greater than stored depth.

3. Final Answer:

   Store both node value and depth in the dictionary, update only if new node depth is greater -> Option C

4. Quick Check:

   Track depth to update bottom view nodes correctly [OK]

Hint: Track depth with node to update bottom view correctly [OK]

Common Mistakes:

• Ignoring depth and overwriting nodes incorrectly
• Storing all nodes without filtering by depth
• Picking first or last node without depth check