Bottom View of Binary Tree in DSA C++ - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to declare the map that stores the bottom view nodes with their horizontal distance.

DSA C++

std::map<int, int> [1];

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

AlevelMap

BtopViewMap

CbottomViewMap

DnodeMap

Attempts:

3 left

💡 Hint

Common Mistakes

Using a map name related to top view instead of bottom view.

Using an unrelated variable name.

The map named bottomViewMap stores the horizontal distance as key and node's data as value for bottom view.

2fill in blank

medium

Complete the code to insert or update the bottom view map with the current node's data at its horizontal distance.

DSA C++

bottomViewMap[[1]] = node->data;

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

Aindex

Bdepth

Clevel

DhorizontalDistance

Attempts:

3 left

💡 Hint

Common Mistakes

Using level or depth instead of horizontal distance as key.

Using an undefined variable.

The horizontal distance is used as the key to store the node's data in the bottom view map.

3fill in blank

hard

Fix the error in the queue push operation to add the left child with updated horizontal distance.

DSA C++

if (node->left) q.push(std::make_pair(node->left, [1]));

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

AhorizontalDistance - 1

BhorizontalDistance + 1

ChorizontalDistance

Dlevel - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Increasing horizontal distance for left child.

Using the same horizontal distance as parent.

The left child is at horizontal distance one less than the current node, so horizontalDistance - 1 is correct.

4fill in blank

hard

Fill both blanks to correctly push the right child with updated horizontal distance and the current level incremented.

DSA C++

if (node->right) q.push(std::make_pair([1], [2]));

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Anode->right

BhorizontalDistance + 1

Clevel + 1

Dnode->left

Attempts:

3 left

💡 Hint

Common Mistakes

Using left child instead of right child.

Not updating horizontal distance correctly.

The right child node pointer and its horizontal distance (parent's + 1) are pushed into the queue.

5fill in blank

hard

Fill all three blanks to print the bottom view nodes in order of their horizontal distance.

DSA C++

for (auto [1] : bottomViewMap) {
    std::cout << [2] << " ";
}
std::cout << [3];

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

Aentry

Bentry.second

Cstd::endl

Dentry.first

Attempts:

3 left

💡 Hint

Common Mistakes

Printing the key (entry.first) instead of the node data.

Forgetting to print a newline at the end.

We iterate over each entry in the map, print the node data (entry.second), and end with a newline (std::endl).

Practice

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

easy

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

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 right side

Solution

1. Step 1: Understand the bottom view concept

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

2. Step 2: Compare with other views

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

3. Final Answer:

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

4. Quick Check:

   Bottom view = nodes visible from bottom [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 of the following C++ STL containers is most suitable to store nodes by their horizontal distance for bottom view calculation?

easy

A. std::vector<int>

B. std::map

C. std::stack<int>

D. std::queue<int>

Solution

1. Step 1: Identify data structure needs

   We need to map horizontal distances (int) to node values (int) and keep them sorted by horizontal distance.

2. Step 2: Choose container

   std::map keeps keys sorted and allows key-value pairs, perfect for horizontal distance mapping.

3. Final Answer:

   std::map -> Option B

4. Quick Check:

   Use map for sorted key-value pairs [OK]

Hint: Use map to keep horizontal distances sorted [OK]

Common Mistakes:

• Using vector which is index-based, not key-based
• Using stack or queue which don't map keys to values
• Not sorting horizontal distances

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

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

medium

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

B. [5, 10, 14, 22, 25]

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

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

Solution

1. Step 1: Assign horizontal distances (HD) to nodes

   Root 20 at HD=0; 8 at HD=-1; 22 at HD=1; 5 at HD=-2; 3 at HD=0; 25 at HD=2; 10 at HD=-1; 14 at HD=1.

2. Step 2: Determine bottom view nodes by HD

   At HD=-2: 5; HD=-1: 10 (lower than 8); HD=0: 3 (lower than 20); HD=1: 14 (lower than 22); HD=2: 25.

3. Final Answer:

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

4. Quick Check:

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

Hint: Track horizontal distances and pick lowest nodes [OK]

Common Mistakes:

• Choosing top nodes instead of bottom nodes
• Mixing horizontal distances incorrectly
• Ignoring nodes at same horizontal distance but lower level

4. Consider this code snippet for bottom view calculation. What is the error?

void bottomView(Node* root) {
  if (!root) return;
  std::map hdNodeMap;
  std::queue> q;
  q.push({root, 0});
  while (!q.empty()) {
    auto p = q.front(); q.pop();
    Node* node = p.first;
    int hd = p.second;
    if (hdNodeMap.find(hd) == hdNodeMap.end()) {
      hdNodeMap[hd] = node->data;
    }
    if (node->left) q.push({node->left, hd - 1});
    if (node->right) q.push({node->right, hd + 1});
  }
  for (auto it : hdNodeMap) {
    std::cout << it.second << " ";
  }
}

medium

A. It stores only the first node at each horizontal distance, not the bottom-most

B. It uses queue incorrectly for BFS traversal

C. It does not check for null root

D. It prints nodes in reverse horizontal order

Solution

1. Step 1: Analyze node storage logic

   The code stores node data only if horizontal distance is not already in map, so it keeps first node encountered at that HD.

2. Step 2: Understand bottom view requirement

   Bottom view requires the lowest node at each HD, so we must update map with nodes at lower levels, not just first.

3. Final Answer:

   It stores only the first node at each horizontal distance, not the bottom-most -> Option A

4. Quick Check:

   Bottom view needs last node at HD, not first [OK]

Hint: Update map with latest node at each horizontal distance [OK]

Common Mistakes:

• Not updating map for lower level nodes
• Assuming BFS order guarantees bottom view
• Ignoring horizontal distance updates

5. Given a binary tree, how would you modify the bottom view algorithm to handle nodes with the same horizontal distance and depth, ensuring the rightmost node is chosen in the bottom view?

hard

A. Use a queue for BFS and update map only if node depth is greater, replacing existing node

B. Use DFS and store only the first node encountered at each horizontal distance

C. Use a stack and update map only if node depth is less than current stored depth

D. Use BFS and update map only if node depth is greater or equal, replacing existing node

Solution

1. Step 1: Understand the problem with same HD and depth

   When nodes share horizontal distance and depth, bottom view should show the rightmost node.

2. Step 2: Modify BFS approach

   Use BFS to traverse level by level, and update map if current node's depth is greater or equal to stored node's depth, ensuring rightmost node replaces leftmost at same depth.

3. Step 3: Implement depth tracking

   Track depth along with horizontal distance, update map accordingly during BFS.

4. Final Answer:

   Use BFS and update map only if node depth is greater or equal, replacing existing node -> Option D

5. Quick Check:

   Update map on equal or greater depth for rightmost node [OK]

Hint: Update map if depth >= current to keep rightmost node [OK]

Common Mistakes:

• Ignoring depth when updating map
• Using DFS which doesn't guarantee level order
• Not handling equal depth nodes properly