Bottom View of Binary Tree in DSA C# - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Bottom View for a Simple Binary Tree

What is the bottom view of the following binary tree after running the given code?

DSA C#

class Node {
    public int data;
    public Node left, right;
    public Node(int item) {
        data = item;
        left = right = null;
    }
}

class BinaryTree {
    Node root;

    public void BottomView() {
        var map = new SortedDictionary<int, int>();
        var queue = new Queue<(Node node, int hd)>();
        queue.Enqueue((root, 0));

        while (queue.Count > 0) {
            var (node, hd) = queue.Dequeue();
            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 val in map.Values) {
            Console.Write(val + " ");
        }
    }

    public void BuildTree() {
        root = new Node(20);
        root.left = new Node(8);
        root.right = new Node(22);
        root.left.left = new Node(5);
        root.left.right = new Node(3);
        root.right.right = new Node(25);
        root.left.right.left = new Node(10);
        root.left.right.right = new Node(14);
    }
}

var tree = new BinaryTree();
tree.BuildTree();
tree.BottomView();

A 20 8 3 14 25

B 5 8 10 14 25

C 5 10 3 14 25

D 5 10 3 22 25

💡 Hint

Think about horizontal distances and which nodes overwrite others in the bottom view.

The bottom view shows the last node visible at each horizontal distance from left to right.

Nodes at horizontal distances -2, -1, 0, 1, 2 are 5, 10, 3, 14, 25 respectively.

❓ Predict Output

intermediate

Bottom View Output with Different Tree Structure

What is the output of the bottom view for this binary tree after running the code?

DSA C#

class Node {
    public int data;
    public Node left, right;
    public Node(int item) {
        data = item;
        left = right = null;
    }
}

class BinaryTree {
    Node root;

    public void BottomView() {
        var map = new SortedDictionary<int, int>();
        var queue = new Queue<(Node node, int hd)>();
        queue.Enqueue((root, 0));

        while (queue.Count > 0) {
            var (node, hd) = queue.Dequeue();
            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 val in map.Values) {
            Console.Write(val + " ");
        }
    }

    public void BuildTree() {
        root = new Node(1);
        root.left = new Node(2);
        root.right = new Node(3);
        root.left.right = new Node(4);
        root.left.right.right = new Node(5);
        root.left.right.right.right = new Node(6);
    }
}

var tree = new BinaryTree();
tree.BuildTree();
tree.BottomView();

A 2 4 5 6

B 2 4 6 3

C 1 2 4 5 6 3

D 2 5 6 3

💡 Hint

Remember to update the bottom view map with the latest node at each horizontal distance.

The bottom view nodes at horizontal distances -1, 0, 1, 2 are 2, 4, 5, 6 respectively.

🔧 Debug

advanced

Identify the Error in Bottom View Implementation

The following code is intended to print the bottom view of a binary tree. What error will it cause when run?

DSA C#

class Node {
    public int data;
    public Node left, right;
    public Node(int item) {
        data = item;
        left = right = null;
    }
}

class BinaryTree {
    Node root;

    public void BottomView() {
        var map = new Dictionary<int, int>();
        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 val in map.Values) {
            Console.Write(val + " ");
        }
    }

    public void BuildTree() {
        root = new Node(10);
        root.left = new Node(20);
        root.right = new Node(30);
        root.left.left = new Node(40);
        root.left.right = new Node(60);
        root.right.left = new Node(90);
    }
}

var tree = new BinaryTree();
tree.BuildTree();
tree.BottomView();

A KeyNotFoundException when accessing map values

B SyntaxError due to tuple deconstruction in queue.Dequeue()

C NullReferenceException because root is not initialized

D The output will be incomplete because nodes are not overwritten for bottom view.

💡 Hint

Check how the map updates nodes at the same horizontal distance.

The code only inserts a node data if the horizontal distance is not already in the map.

This means the first node at each horizontal distance is kept, but bottom view requires the last node at that horizontal distance.

So the output will be incomplete or incorrect.

🧠 Conceptual

advanced

Understanding Horizontal Distance in Bottom View

In the bottom view of a binary tree, what does the horizontal distance (hd) represent?

A The vertical level of the node in the tree

B The distance of the node from the root node horizontally, where left child decreases hd by 1 and right child increases hd by 1

C The depth of the node from the root node

D The number of nodes in the subtree rooted at that node

💡 Hint

Think about how left and right children affect horizontal position.

Horizontal distance is a measure of how far left or right a node is from the root.

Left child decreases hd by 1, right child increases hd by 1.

🚀 Application

expert

Bottom View of Binary Tree with Duplicate Horizontal Distances

Given the following binary tree, what is the bottom view output after running the code?

DSA C#

class Node {
    public int data;
    public Node left, right;
    public Node(int item) {
        data = item;
        left = right = null;
    }
}

class BinaryTree {
    Node root;

    public void BottomView() {
        var map = new SortedDictionary<int, int>();
        var queue = new Queue<(Node node, int hd)>();
        queue.Enqueue((root, 0));

        while (queue.Count > 0) {
            var (node, hd) = queue.Dequeue();
            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 val in map.Values) {
            Console.Write(val + " ");
        }
    }

    public void BuildTree() {
        root = new Node(1);
        root.left = new Node(2);
        root.right = new Node(3);
        root.left.left = new Node(4);
        root.left.right = new Node(5);
        root.right.left = new Node(6);
        root.right.right = new Node(7);
        root.left.right.left = new Node(8);
        root.left.right.right = new Node(9);
    }
}

var tree = new BinaryTree();
tree.BuildTree();
tree.BottomView();

A 4 8 6 9 7

B 4 8 5 9 7

C 4 2 8 9 6 7

D 4 2 8 5 6 7

💡 Hint

Focus on which nodes overwrite others at the same horizontal distance during level order traversal.

The bottom view nodes at horizontal distances -2, -1, 0, 1, 2 are 4, 8, 6, 9, 7 respectively.

Nodes 2 and 3 are overwritten by nodes 8 and 9 respectively because they appear later in level order traversal at the same horizontal distance.

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