Tree Traversal Level Order BFS in DSA Java - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is Level Order Traversal in a tree?

Level Order Traversal visits nodes level by level from top to bottom and left to right within each level.

beginner

Which data structure is commonly used to implement Level Order Traversal (BFS) in a tree?

A queue is used to keep track of nodes to visit next in Level Order Traversal.

beginner

What is the time complexity of Level Order Traversal on a binary tree with n nodes?

The time complexity is O(n) because each node is visited exactly once.

intermediate

In Level Order Traversal, what happens when a node is dequeued?

When a node is dequeued, its value is processed (e.g., printed), and its children (left then right) are enqueued for future visits.

intermediate

Why is Level Order Traversal also called Breadth-First Search (BFS)?

Because it explores all nodes at the current depth before moving to nodes at the next depth, spreading out like a wave across the tree.

Which data structure is essential for implementing Level Order Traversal?

A Stack

B Queue

C Array

D HashMap

A queue helps process nodes in the order they are discovered, which is key for Level Order Traversal.

What is the order of visiting nodes in Level Order Traversal?

A Right subtree, root, left subtree

B Bottom to top, right to left

C Left subtree, root, right subtree

D Top to bottom, left to right

Level Order Traversal visits nodes level by level from top to bottom and left to right.

If a binary tree has 7 nodes, how many times will the queue enqueue nodes during Level Order Traversal?

A 14

B 6

C 7

D Depends on the tree shape

Each node is enqueued exactly once when it is discovered.

What is the first step in Level Order Traversal?

A Enqueue the root node

B Dequeue the root node

C Visit the left child

D Visit the right child

Traversal starts by adding the root node to the queue.

Which traversal method is Level Order Traversal most similar to?

A Breadth-First Search

B Depth-First Search

C Inorder Traversal

D Postorder Traversal

Level Order Traversal is another name for Breadth-First Search on trees.

Explain how Level Order Traversal works on a binary tree using a queue.

Think about visiting nodes level by level.

Describe the difference between Level Order Traversal and Depth-First Traversal.

Consider how nodes are visited in each method.

Practice

1. What does Level Order Traversal (BFS) of a binary tree do?

easy

A. Visits nodes in random order

B. Visits nodes in left subtree, then root, then right subtree

C. Visits nodes level by level from top to bottom, left to right

D. Visits nodes in right subtree, then root, then left subtree

Solution

1. Step 1: Understand Level Order Traversal

   Level order traversal visits nodes level by level starting from the root, moving left to right at each level.

2. Step 2: Compare with other traversals

   Other traversals like inorder or postorder do not visit nodes level-wise but follow subtree orders.

3. Final Answer:

   Visits nodes level by level from top to bottom, left to right -> Option C

4. Quick Check:

   Level Order = BFS = top-down, left-right [OK]

Hint: Level order means visit nodes by levels, left to right [OK]

Common Mistakes:

• Confusing level order with inorder or preorder traversal
• Thinking traversal is random
• Mixing left and right subtree orders

2. Which Java code snippet correctly initializes a queue for level order traversal of a binary tree?

easy

A. Queue<TreeNode> queue = new ArrayList<>();

B. Queue<TreeNode> queue = new LinkedList<>();

C. List<TreeNode> queue = new LinkedList<>();

D. Stack<TreeNode> queue = new Stack<>();

Solution

1. Step 1: Identify correct queue initialization

   Java's Queue interface is implemented by LinkedList, so Queue<TreeNode> queue = new LinkedList<>() is correct.

2. Step 2: Check other options

   ArrayList does not implement Queue, List is not a Queue, and Stack is LIFO, not FIFO needed for BFS.

3. Final Answer:

   Queue<TreeNode> queue = new LinkedList<>(); -> Option B

4. Quick Check:

   Queue for BFS = LinkedList implementation [OK]

Hint: Use LinkedList to implement Queue for BFS in Java [OK]

Common Mistakes:

• Using ArrayList instead of Queue
• Using Stack which is LIFO, not FIFO
• Declaring List instead of Queue

3. What is the output of the following Java code performing level order traversal on this tree?

    1
   / \
  2   3
 / \
4   5

// Code snippet:
Queue<TreeNode> queue = new LinkedList<>();
queue.add(root);
while (!queue.isEmpty()) {
  TreeNode node = queue.poll();
  System.out.print(node.val + " ");
  if (node.left != null) queue.add(node.left);
  if (node.right != null) queue.add(node.right);
}

medium

A. 1 2 3 4 5

B. 1 3 2 5 4

C. 4 5 2 3 1

D. 2 4 5 1 3

Solution

1. Step 1: Trace the queue operations

   Start with root (1). Print 1, add children 2 and 3. Then print 2, add 4 and 5. Then print 3 (no children). Then print 4 and 5.

2. Step 2: Write output sequence

   Output is: 1 2 3 4 5

3. Final Answer:

   1 2 3 4 5 -> Option A

4. Quick Check:

   Level order output = 1 2 3 4 5 [OK]

Hint: Print nodes as you dequeue in BFS order [OK]

Common Mistakes:

• Mixing preorder or inorder output with level order
• Adding children in wrong order
• Printing before adding children

4. Identify the bug in this Java code snippet for level order traversal:

Queue<TreeNode> queue = new LinkedList<>();
queue.add(root);
while (!queue.isEmpty()) {
  TreeNode node = queue.peek();
  System.out.print(node.val + " ");
  if (node.left != null) queue.add(node.left);
  if (node.right != null) queue.add(node.right);
}

medium

A. Using peek() instead of poll() causes infinite loop

B. Not checking if root is null

C. Adding children after printing node value

D. Queue should be Stack for BFS

Solution

1. Step 1: Understand peek() vs poll()

   peek() returns the front element but does not remove it, so the queue never empties.

2. Step 2: Effect on loop

   Since queue is never emptied, while loop runs infinitely printing the same node repeatedly.

3. Final Answer:

   Using peek() instead of poll() causes infinite loop -> Option A

4. Quick Check:

   poll() removes front, peek() does not [OK]

Hint: Use poll() to remove nodes, not peek() [OK]

Common Mistakes:

• Confusing peek() and poll()
• Ignoring null root check
• Using Stack instead of Queue

5. Given a binary tree, how can you modify level order traversal to print nodes level by level on separate lines in Java?

hard

A. Print nodes as they are dequeued without tracking levels

B. Use recursion to print nodes in preorder with newlines

C. Use a stack to reverse the order and print levels bottom-up

D. Use a queue and track the number of nodes at each level, printing a newline after each level

Solution

1. Step 1: Track nodes per level using queue size

   At each iteration, get the current queue size which equals nodes at that level. Process exactly that many nodes, then print newline.

2. Step 2: Print nodes level-wise

   This ensures nodes of one level print on one line, then move to next line for next level.

3. Final Answer:

   Use a queue and track the number of nodes at each level, printing a newline after each level -> Option D

4. Quick Check:

   Queue size = nodes per level for line breaks [OK]

Hint: Use queue size to separate levels during BFS [OK]

Common Mistakes:

• Using recursion which is not level order
• Using stack which reverses order
• Not tracking level size, so no line breaks