Why Bottom View of Binary Tree in DSA C#?

The Big Idea

What if you could instantly see the hidden branches of a tree just by looking from below? Discover how bottom view makes it possible!

The Scenario

Imagine you have a tall tree in your backyard and you want to see which branches are visible if you look at it from the bottom. You try to write down all the branches you see from the bottom, but the tree is so big and complicated that it's hard to keep track of which branches hide others.

The Problem

Trying to figure out the bottom view by just looking or drawing on paper is slow and confusing. You might miss some branches or count the same branch twice. It's easy to get mixed up about which branch is actually visible from the bottom because some branches overlap or hide others.

The Solution

The bottom view of a binary tree helps by giving a clear way to find exactly which nodes (branches) are visible from the bottom. It uses a smart method to check each node's position and height, so you only keep the nodes that are truly visible when looking up from the bottom.

Before vs After

✗ Before

void PrintBottomView(Node root) {
  // Manually guess which nodes are visible
  // No clear method, lots of confusion
}

✓ After

void PrintBottomView(Node root) {
  // Use horizontal distance and level tracking
  // Store nodes in a map to find bottom view
}

What It Enables

This concept lets you quickly and correctly find the exact nodes visible from the bottom of any binary tree, no matter how big or complex it is.

Real Life Example

In city planning, imagine buildings as nodes in a tree. The bottom view helps to know which buildings are visible when looking from street level, ignoring those hidden behind others.

Key Takeaways

Manual observation of bottom view is confusing and error-prone.

Bottom view uses position and level to find visible nodes from below.

It helps in clear, fast, and accurate visualization of tree structure.

Practice

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

easy

A. The nodes visible when the tree is viewed from the right side

B. The nodes visible when the tree is viewed from the top

C. The nodes visible when the tree is viewed from the left side

D. The 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:

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

4. Quick Check:

   Bottom view = nodes visible 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 C# data structure is best suited to store nodes by their horizontal distance when computing the bottom view of a binary tree?

easy

A. Dictionary

B. List<int>

C. Stack<int>

D. Queue<int>

Solution

1. Step 1: Identify the need to map horizontal distance to node value

   We need a structure to store nodes keyed by their horizontal distance for quick updates and lookups.

2. Step 2: Choose the appropriate data structure

   A Dictionary allows mapping horizontal distance (int) to node value (int) efficiently.

3. Final Answer:

   Dictionary<int, int> -> Option A

4. Quick Check:

   Use Dictionary for horizontal distance mapping [OK]

Hint: Use Dictionary to map horizontal distance to node value [OK]

Common Mistakes:

• Using List which doesn't map keys to values
• Using Stack or Queue which are not key-value stores
• Confusing data structure roles

3. Consider the following binary tree:

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

What is the bottom view of this tree?

medium

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

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

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

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

Solution

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

   Assign horizontal distances (HD) starting from root (20) at HD=0: - 20(0), 8(-1), 22(1), 5(-2), 3(0), 25(2), 10(-1), 14(1) For each HD, the bottom-most node is: HD -2: 5 HD -1: 10 (overwrites 8) HD 0: 3 (overwrites 20) HD 1: 14 (overwrites 22) HD 2: 25

2. Step 2: Collect bottom view nodes in order of HD

   Order HD from left to right: -2, -1, 0, 1, 2 Bottom view nodes: [5, 10, 3, 14, 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 distance and overwrite with lower nodes [OK]

Common Mistakes:

• Not updating nodes at same horizontal distance
• Confusing top view with bottom view
• Ignoring horizontal distance ordering

4. The following C# code attempts to compute the bottom view of a binary tree but has a bug. What is the error?

void BottomView(Node root) {
    if (root == null) return;
    var map = new Dictionary();
    var queue = new Queue<(Node node, int hd)>();
    queue.Enqueue((root, 0));
    while (queue.Count > 0) {
        var (node, hd) = queue.Dequeue();
        if (!map.ContainsKey(hd)) {
            map[hd] = node.data;
        }
        if (node.left != null) queue.Enqueue((node.left, hd - 1));
        if (node.right != null) queue.Enqueue((node.right, hd + 1));
    }
    foreach (var key in map.Keys.OrderBy(k => k)) {
        Console.Write(map[key] + " ");
    }
}

medium

A. It does not enqueue the root node

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

C. It uses a queue instead of a stack

D. It does not order the keys before printing

Solution

1. Step 1: Analyze how nodes are stored in the map

   The code adds node data to map only if the horizontal distance key is not present, so it keeps the first node encountered at that HD.

2. Step 2: Understand bottom view requires last node at each HD

   Bottom view needs the lowest node at each HD, so the map should update the value every time a node at the same HD is found, not only the first.

3. Final Answer:

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

4. Quick Check:

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

Hint: Update map value for each node at HD to get bottom view [OK]

Common Mistakes:

• Using if (!map.ContainsKey) instead of always updating
• Ignoring horizontal distance updates
• Not ordering keys before printing (though code does)

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

hard

A. Store pairs of (node value, depth) in the map and update only if new node's depth is greater

B. Store only node values and update map only if node value is greater

C. Use a stack instead of a queue to traverse nodes

D. Ignore depth and just print nodes in level order

Solution

1. Step 1: Recognize the need to track depth with node values

   To ensure the bottom view shows the node with greatest depth at each horizontal distance, we must store depth along with node value.

2. Step 2: Update map only if new node's depth is greater

   When visiting a node, compare its depth with stored depth for that horizontal distance; update only if current node is deeper.

3. Final Answer:

   Store pairs of (node value, depth) in the map and update only if new node's depth is greater -> Option A

4. Quick Check:

   Track depth and update map for deeper nodes [OK]

Hint: Keep depth info and update map only if deeper node found [OK]

Common Mistakes:

• Ignoring depth and overwriting incorrectly
• Comparing node values instead of depths
• Changing traversal order without depth tracking