Right Side View of Binary Tree in DSA Java - Time & Space Complexity

Time Complexity: Right Side View of Binary Tree

O(n)

Understanding Time Complexity

We want to understand how the time needed to find the right side view of a binary tree changes as the tree grows.

Specifically, how does the number of nodes affect the work done?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public List<Integer> rightSideView(TreeNode root) {
    List<Integer> result = new ArrayList<>();
    if (root == null) return result;
    Queue<TreeNode> queue = new LinkedList<>();
    queue.offer(root);
    while (!queue.isEmpty()) {
        int size = queue.size();
        for (int i = 0; i < size; i++) {
            TreeNode node = queue.poll();
            if (i == size - 1) result.add(node.val);
            if (node.left != null) queue.offer(node.left);
            if (node.right != null) queue.offer(node.right);
        }
    }
    return result;
}

This code finds the right side view of a binary tree by visiting nodes level by level and recording the last node at each level.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Visiting each node once in a breadth-first manner using a queue.
• How many times: Each node is processed exactly one time.

How Execution Grows With Input

As the number of nodes increases, the code visits each node once, so the work grows directly with the number of nodes.

Input Size (n)	Approx. Operations
10	About 10 visits
100	About 100 visits
1000	About 1000 visits

Pattern observation: The work grows linearly as the tree size grows.

Final Time Complexity

Time Complexity: O(n)

This means the time to find the right side view grows directly with the number of nodes in the tree.

Common Mistake

[X] Wrong: "Since we only take one node per level, the time complexity is O(h), where h is the tree height."

[OK] Correct: Even though we record one node per level, we still visit all nodes to find those rightmost nodes, so the time depends on total nodes, not just height.

Interview Connect

Understanding this helps you explain how tree traversal works and how to analyze algorithms that visit all nodes efficiently.

Self-Check

"What if we changed the traversal to depth-first search instead of breadth-first search? How would the time complexity change?"

Practice

1. What does the "Right Side View of Binary Tree" represent?

easy

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

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

C. All leaf nodes of the binary tree

D. All nodes at the deepest level of the tree

Solution

1. Step 1: Understand the view perspective

   The right side view shows nodes visible when looking at the tree from the right side.

2. Step 2: Differentiate from other views

   Unlike left side or leaf nodes, right side view includes the rightmost node at each level.

3. Final Answer:

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

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
• Thinking it shows all leaf nodes
• Assuming it shows all nodes at deepest level

2. Which of the following Java method signatures is correct for a function that returns the right side view of a binary tree as a list of integers?

easy

A. public int rightSideView(TreeNode root)

B. public void rightSideView(TreeNode root)

C. public List<Integer> rightSideView(TreeNode root)

D. public TreeNode rightSideView(List<Integer> root)

Solution

1. Step 1: Identify return type for right side view

   The right side view returns a list of integers representing node values visible from the right side.

2. Step 2: Match method signature

   Method should return List<Integer> and accept TreeNode root as input.

3. Final Answer:

   public List<Integer> rightSideView(TreeNode root) -> Option C

4. Quick Check:

   Return list of integers = public List<Integer> rightSideView(TreeNode root) [OK]

Hint: Return a list of node values, input is root node [OK]

Common Mistakes:

• Returning int instead of list
• Using void return type
• Incorrect parameter types

3. What is the output of the following code snippet for the right side view of the binary tree?

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

public List<Integer> rightSideView(TreeNode root) {
  List<Integer> result = new ArrayList<>();
  if (root == null) return result;
  Queue<TreeNode> queue = new LinkedList<>();
  queue.add(root);
  while (!queue.isEmpty()) {
    int size = queue.size();
    for (int i = 0; i < size; i++) {
      TreeNode node = queue.poll();
      if (node.left != null) queue.add(node.left);
      if (node.right != null) queue.add(node.right);
      if (i == size - 1) result.add(node.val);
    }
  }
  return result;
}

// Tree structure:
//      1
//     / \
//    2   3
//     \   \
//      5   4

TreeNode 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);
System.out.println(rightSideView(root));

medium

A. [1, 2, 4]

B. [1, 2, 5]

C. [1, 3, 5]

D. [1, 3, 4]

Solution

1. Step 1: Traverse level by level and identify rightmost nodes

   Level 1: Node 1 (only node), Level 2: Nodes 2 and 3, rightmost is 3, Level 3: Nodes 5 and 4, rightmost is 4.

2. Step 2: Collect rightmost nodes in order

   Right side view list is [1, 3, 4].

3. Final Answer:

   [1, 3, 4] -> Option D

4. Quick Check:

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

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

Common Mistakes:

• Choosing leftmost nodes instead of rightmost
• Adding all nodes instead of only rightmost
• Confusing order of nodes

4. Identify the bug in the following code for computing the right side view of a binary tree:

public List<Integer> rightSideView(TreeNode root) {
  List<Integer> result = new ArrayList<>();
  if (root == null) return result;
  Queue<TreeNode> queue = new LinkedList<>();
  queue.add(root);
  while (!queue.isEmpty()) {
    int size = queue.size();
    for (int i = 0; i <= size; i++) {
      TreeNode node = queue.poll();
      if (node.left != null) queue.add(node.left);
      if (node.right != null) queue.add(node.right);
      if (i == size - 1) result.add(node.val);
    }
  }
  return result;
}

medium

A. The null check for root is missing

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

C. The queue should be a Stack instead of a Queue

D. The result list should be a Set to avoid duplicates

Solution

1. Step 1: Analyze the for loop condition

   The for loop runs from i = 0 to i <= size, which causes one extra iteration and poll from empty queue.

2. Step 2: Correct the loop boundary

   The loop should run i < size to process exactly 'size' nodes per level.

3. Final Answer:

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

4. Quick Check:

   Loop boundary off by one = The for loop condition should be i < size, not i <= size [OK]

Hint: Use i < size for loops over queue size [OK]

Common Mistakes:

• Using <= instead of < in loop condition
• Replacing queue with stack incorrectly
• Ignoring null root check
• Using Set instead of List unnecessarily

5. Given a binary tree, how would you modify the standard right side view algorithm to return the right side view in reverse order (bottom to top)?

hard

A. All of the above approaches can achieve the reverse right side view

B. Traverse the tree from bottom to top using recursion and add rightmost nodes

C. Use a stack to store rightmost nodes during BFS and pop them to reverse order

D. Collect rightmost nodes top to bottom, then reverse the list before returning

Solution

1. Step 1: Understand the standard right side view

   Standard approach collects rightmost nodes level by level from top to bottom.

2. Step 2: Consider ways to reverse order

   We can reverse the collected list, use recursion bottom-up, or use a stack to reverse order after BFS.

3. Step 3: Confirm all methods are valid

   Each method correctly produces the right side view in reverse order.

4. Final Answer:

   All of the above approaches can achieve the reverse right side view -> Option A

5. Quick Check:

   Multiple valid methods = All of the above approaches can achieve the reverse right side view [OK]

Hint: Reverse collected list or use stack/recursion [OK]

Common Mistakes:

• Thinking only one method works
• Ignoring simple list reversal
• Confusing traversal order