Why Right Side View of Binary Tree in DSA C#?

The Big Idea

Discover how to see the hidden right side of a tree clearly without guessing!

The Scenario

Imagine you are standing on the right side of a tall tree and want to see which branches are visible from your view. If you try to write down the visible branches by looking at the tree from the front or top, it becomes confusing and you might miss some branches.

The Problem

Manually checking each branch from different angles is slow and error-prone. You might write down branches that are hidden behind others or miss the ones that are actually visible from the right side. This makes it hard to get a clear picture of the tree's right side.

The Solution

The "Right Side View of Binary Tree" concept helps you automatically find the branches visible from the right side by looking level by level and picking the last branch at each level. This way, you get a clear list of visible branches without confusion or missing any.

Before vs After

✗ Before

void PrintRightSide(TreeNode root) {
  // Manually guess which nodes are visible
  Console.WriteLine(root.val);
  if (root.right != null) Console.WriteLine(root.right.val);
  else if (root.left != null) Console.WriteLine(root.left.val);
}

✓ After

List<int> RightSideView(TreeNode root) {
  var result = new List<int>();
  var queue = new Queue<TreeNode>();
  if (root == null) return result;
  queue.Enqueue(root);
  while(queue.Count > 0) {
    int levelSize = queue.Count;
    for(int i=0; i<levelSize; i++) {
      var node = queue.Dequeue();
      if(i == levelSize - 1) result.Add(node.val);
      if(node.left != null) queue.Enqueue(node.left);
      if(node.right != null) queue.Enqueue(node.right);
    }
  }
  return result;
}

What It Enables

This concept enables you to quickly and accurately see the right side outline of any binary tree, which helps in understanding its shape and structure from that perspective.

Real Life Example

In a city skyline, if you want to see which buildings are visible from the right side street, this method helps you list only those buildings that are not hidden behind others, giving a clear view of the skyline.

Key Takeaways

Manually finding right side view is confusing and error-prone.

Right Side View uses level order traversal to pick last nodes at each level.

This gives a clear and accurate list of visible nodes from the right side.

Practice

1. What does the "Right Side View of Binary Tree" represent?
RightSideView(root) returns which nodes?

easy

A. All nodes at the deepest level of the tree

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

C. All leaf nodes of the binary tree

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

Solution

1. Step 1: Understand the problem context

   The right side view means seeing the tree from the right side, so only nodes visible from that angle are included.

2. Step 2: Identify what nodes are visible

   These are the rightmost nodes at each level of the tree, as nodes behind them are hidden.

3. Final Answer:

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

4. Quick Check:

   Right side view = rightmost nodes [OK]

Hint: Right side view shows rightmost nodes at each level [OK]

Common Mistakes:

• Confusing right side view with left side view
• Including all leaf nodes instead of rightmost nodes
• Thinking it returns all nodes at the deepest level

2. Which of the following C# method signatures correctly represents a function to get the right side view of a binary tree?
class Solution { public IList<int> RightSideView(TreeNode root) { ... } }

easy

A. public List<TreeNode> RightSideView(int root)

B. public IList<int> RightSideView(TreeNode root)

C. public int RightSideView(TreeNode root)

D. public void RightSideView(TreeNode root)

Solution

1. Step 1: Analyze the return type

   The method should return a list of integers representing node values visible from the right side, so IList<int> is appropriate.

2. Step 2: Check parameter and method signature

   The parameter should be the root node of type TreeNode, and the method should return the list, not void or a single int.

3. Final Answer:

   public IList<int> RightSideView(TreeNode root) -> Option B

4. Quick Check:

   Return list of int values from TreeNode root [OK]

Hint: Return list of int, input is TreeNode root [OK]

Common Mistakes:

• Returning void instead of a list
• Returning a single int instead of a list
• Wrong parameter type like int instead of TreeNode

3. What is the output of the following code?

class TreeNode {
  public int val;
  public TreeNode left, right;
  public TreeNode(int v) { val = v; }
}

var root = new TreeNode(1);
root.left = new TreeNode(2);
root.right = new TreeNode(3);
root.left.right = new TreeNode(5);
root.right.right = new TreeNode(4);

var result = RightSideView(root);
Console.WriteLine(string.Join(", ", result));

IList<int> RightSideView(TreeNode root) {
  var view = new List<int>();
  var queue = new Queue<TreeNode>();
  if (root != null) queue.Enqueue(root);
  while (queue.Count > 0) {
    int size = queue.Count;
    for (int i = 0; i < size; i++) {
      var node = queue.Dequeue();
      if (node.left != null) queue.Enqueue(node.left);
      if (node.right != null) queue.Enqueue(node.right);
      if (i == size - 1) view.Add(node.val);
    }
  }
  return view;
}

medium

A. [1, 3, 4]

B. [1, 2, 5]

C. [1, 3, 5]

D. [1, 2, 4]

Solution

1. Step 1: Trace the tree levels and nodes

   Level 1: Node 1; Level 2: Nodes 2 and 3; Level 3: Nodes 5 and 4.

2. Step 2: Identify rightmost nodes at each level

   Level 1 rightmost: 1; Level 2 rightmost: 3; Level 3 rightmost: 4.

3. Final Answer:

   [1, 3, 4] -> Option A

4. Quick Check:

   Rightmost nodes per level = [1, 3, 4] [OK]

Hint: Pick last node at each level in BFS order [OK]

Common Mistakes:

• Choosing leftmost nodes instead of rightmost
• Mixing node values from different levels
• Forgetting to add last node of each level

4. Find the error in this code snippet for right side view:

IList<int> RightSideView(TreeNode root) {
  var view = new List<int>();
  var queue = new Queue<TreeNode>();
  if (root != null) queue.Enqueue(root);
  while (queue.Count > 0) {
    int size = queue.Count;
    for (int i = 0; i <= size; i++) {
      var node = queue.Dequeue();
      if (node.left != null) queue.Enqueue(node.left);
      if (node.right != null) queue.Enqueue(node.right);
      if (i == size - 1) view.Add(node.val);
    }
  }
  return view;
}

medium

A. The root node should not be enqueued initially

B. The queue should be a Stack instead

C. The for loop condition should be i < size, not i <= size

D. The view list should be cleared inside the while loop

Solution

1. Step 1: Check the for loop boundary

   The for loop runs from i = 0 to i <= size, which means it runs size+1 times, causing an error when dequeueing.

2. Step 2: Correct the loop condition

   It should run exactly size times, so condition must be i < size to avoid dequeueing from empty queue.

3. Final Answer:

   The for loop condition should be i < size, not i <= size -> Option C

4. Quick Check:

   Loop runs size times, not size+1 [OK]

Hint: For loops over queue size use i < size, not i <= size [OK]

Common Mistakes:

• Using <= instead of < in loop condition
• Using stack instead of queue for BFS
• Clearing result list inside loop mistakenly

5. Given a binary tree where some nodes have only left children and others only right children, how would the right side view behave?
Example tree:

    1
   / 
  2   
   \   
    3
     \
      4

What is the right side view output?

hard

A. [1, 3, 4]

B. [4]

C. [1, 4]

D. [1, 2, 3, 4]

Solution

1. Step 1: Visualize the tree and levels

   Level 1: Node 1; Level 2: Node 2; Level 3: Node 3; Level 4: Node 4.

2. Step 2: Determine rightmost nodes at each level

   At level 2, node 2 is on the left, but node 3 is the right child of 2 and is visible from the right side. So the rightmost nodes per level are 1, 3, and 4.

3. Final Answer:

   [1, 3, 4] -> Option A

4. Quick Check:

   Right side view includes nodes visible from right side, skipping node 2 at level 2 [OK]

Hint: Right side view picks rightmost nodes at each level, even in skewed trees [OK]

Common Mistakes:

• Skipping nodes with only left children
• Assuming only right children appear in right side view
• Returning all nodes instead of rightmost nodes