Bottom View of Binary Tree in DSA C++ - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the bottom view of a binary tree?

The bottom view of a binary tree is the set of nodes visible when the tree is seen from the bottom. It shows the last node at each horizontal distance from the root.

beginner

How do we assign horizontal distances to nodes in a binary tree for bottom view?

We assign horizontal distance (HD) starting with root as 0. Left child has HD = parent HD - 1, right child has HD = parent HD + 1.

intermediate

Which data structure is commonly used to track nodes and their horizontal distances in bottom view?

A map or dictionary is used to store the latest node at each horizontal distance. A queue is used for level order traversal.

intermediate

In bottom view, if multiple nodes share the same horizontal distance, which node is visible?

The node that appears last in level order traversal (lowest level) at that horizontal distance is visible in the bottom view.

intermediate

What is the time complexity of computing the bottom view of a binary tree?

The time complexity is O(n), where n is the number of nodes, because each node is visited once during level order traversal.

What horizontal distance is assigned to the root node in bottom view calculation?

A 1

B 0

C -1

D Depends on tree height

The root node is always assigned horizontal distance 0.

Which traversal method is best suited to compute the bottom view of a binary tree?

A Level order traversal

B Inorder traversal

C Postorder traversal

D Preorder traversal

Level order traversal visits nodes level by level, which helps track the bottom-most nodes at each horizontal distance.

If two nodes have the same horizontal distance, which one appears in the bottom view?

A The node at the lower level

B The node at the higher level

C The leftmost node

D The rightmost node

The node at the lower level (deeper in the tree) is visible in the bottom view.

What data structure is used to store the nodes visible in the bottom view?

A Stack

B Linked list

C Queue

D Map or dictionary

A map or dictionary stores the latest node at each horizontal distance.

What is the overall time complexity to find the bottom view of a binary tree with n nodes?

A O(n log n)

B O(log n)

C O(n)

D O(n^2)

Each node is visited once, so the time complexity is O(n).

Explain how to compute the bottom view of a binary tree step-by-step.

Think about horizontal distances and level order traversal.

Describe why level order traversal is important for the bottom view of a binary tree.

Consider how nodes at different depths affect visibility.

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