Zigzag Level Order Traversal in DSA C# - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is Zigzag Level Order Traversal in a binary tree?

It is a way to visit nodes level by level, but alternating the direction of traversal at each level. For example, left to right on one level, then right to left on the next.

beginner

Which data structure is commonly used to implement Zigzag Level Order Traversal?

A queue is used to process nodes level by level, and sometimes a stack or reversing the list is used to change the order of nodes on alternate levels.

intermediate

How do you decide the direction of traversal at each level in Zigzag Level Order Traversal?

You can use a boolean flag that flips after each level. If true, traverse left to right; if false, traverse right to left.

beginner

What is the time complexity of Zigzag Level Order Traversal?

The time complexity is O(n), where n is the number of nodes, because each node is visited exactly once.

intermediate

Show the output of Zigzag Level Order Traversal for this tree:
1
/ \
2 3
/ \ \
4 5 6

The output is [[1], [3, 2], [4, 5, 6]].
Level 0: left to right → 1
Level 1: right to left → 3, 2
Level 2: left to right → 4, 5, 6

What data structure is primarily used to keep track of nodes at each level during Zigzag Level Order Traversal?

A Stack

B Queue

C Linked List

D Hash Map

A queue is used to process nodes level by level in breadth-first order.

How do you alternate the direction of traversal in Zigzag Level Order Traversal?

A By using a boolean flag that flips after each level

B By sorting nodes at each level

C By using two queues simultaneously

D By reversing the entire tree

A boolean flag helps switch between left-to-right and right-to-left traversal after each level.

What is the output of Zigzag Level Order Traversal for a tree with only one node?

A [[node]]

B []

C [node]

D [[node, node]]

The output is a list containing one list with the single node.

What is the time complexity of Zigzag Level Order Traversal?

A O(log n)

B O(n^2)

C O(1)

D O(n)

Each node is visited once, so the time complexity is linear in the number of nodes.

Which of these is NOT a correct step in Zigzag Level Order Traversal?

A Use a queue to process nodes level by level

B Flip the traversal direction after each level

C Sort nodes at each level before adding to output

D Add nodes of the current level to output in the correct order

Sorting nodes at each level is not required or part of Zigzag Level Order Traversal.

Explain how Zigzag Level Order Traversal works step-by-step on a binary tree.

Think about how you visit nodes left to right, then right to left, and repeat.

Describe how you would implement Zigzag Level Order Traversal in C#.

Focus on the data structures and control flow needed.

Practice

1. What does the Zigzag Level Order Traversal of a binary tree do differently compared to a normal level order traversal?

easy

A. It alternates the direction of traversal at each level, left to right then right to left.

B. It visits nodes only on the left subtree.

C. It visits nodes in reverse order of their insertion.

D. It traverses nodes randomly without any order.

Solution

1. Step 1: Understand normal level order traversal

   Normal level order traversal visits nodes level by level from left to right.

2. Step 2: Identify zigzag difference

   Zigzag traversal alternates direction each level: first left to right, then right to left, and so on.

3. Final Answer:

   It alternates the direction of traversal at each level, left to right then right to left. -> Option A

4. Quick Check:

   Zigzag = alternate directions [OK]

Hint: Remember zigzag means direction flips every level [OK]

Common Mistakes:

• Thinking it only visits left subtree
• Assuming traversal is always left to right
• Confusing zigzag with reverse order

2. Which of the following C# code snippets correctly initializes a queue to perform a zigzag level order traversal?

easy

A. List<TreeNode> queue = new List<TreeNode>();

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

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

D. Dictionary queue = new Dictionary();

Solution

1. Step 1: Identify data structure for BFS

   Queue is used for breadth-first search to process nodes level by level.

2. Step 2: Check code snippet correctness

   Queue<TreeNode> queue = new Queue<TreeNode>(); correctly declares a Queue of TreeNode objects, suitable for traversal.

3. Final Answer:

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

4. Quick Check:

   Queue for BFS = Queue<TreeNode> queue = new Queue<TreeNode>(); [OK]

Hint: Use Queue for level order traversal in C# [OK]

Common Mistakes:

• Using Stack instead of Queue for BFS
• Using List which lacks FIFO behavior
• Using Dictionary which is not suitable here

3. Given the binary tree:

    1
   / \
  2   3
 / \   \
4   5   6

What is the output of zigzag level order traversal?

medium

A. [[1], [3, 2], [4, 5, 6]]

B. [[1], [2, 3], [4, 5, 6]]

C. [[1], [3, 2], [6, 5, 4]]

D. [[1, 2, 3], [4, 5, 6]]

Solution

1. Step 1: Traverse level 0 left to right

   Level 0 nodes: [1]

2. Step 2: Traverse level 1 right to left

   Level 1 nodes: [2, 3], reversed to [3, 2]

3. Step 3: Traverse level 2 left to right

   Level 2 nodes: [4, 5, 6]

4. Final Answer:

   [[1], [3, 2], [4, 5, 6]] -> Option A

5. Quick Check:

   Zigzag levels = [[1], [3, 2], [4, 5, 6]] [OK]

Hint: Alternate direction each level, reverse nodes on odd levels [OK]

Common Mistakes:

• Not reversing nodes on alternate levels
• Mixing node order in last level
• Confusing left and right child order

4. Consider this C# code snippet for zigzag traversal:

if (level % 2 == 0)
    result.Add(currentLevel);
else
    result.Add(currentLevel.Reverse().ToList());

What is the bug in this code?

medium

A. It reverses the list on even levels instead of odd levels.

B. It reverses the list on odd levels instead of even levels.

C. It reverses the original list causing side effects.

D. It does not reverse the list at all.

Solution

1. Step 1: Understand zigzag pattern

   Zigzag reverses nodes on odd levels (1, 3, 5...), not even levels (0, 2, 4...).

2. Step 2: Analyze code condition

   The condition correctly identifies even/odd levels for reversal.

3. Step 3: Identify the actual issue

   currentLevel.Reverse() (List<TreeNode>.Reverse) modifies the list in place and returns void, causing side effects and a compilation error on .ToList().

4. Final Answer:

   It reverses the original list causing side effects. -> Option C

5. Quick Check:

   List.Reverse() in-place modifies original [OK]

Hint: Reverse nodes only on odd levels (1, 3, 5...) [OK]

Common Mistakes:

• Reversing on even levels instead of odd
• Modifying original list causing bugs
• Not reversing at all

5. You want to perform zigzag level order traversal on a binary tree but only collect nodes with even values. Which modification is best to apply?

hard

A. Use a stack instead of a queue to collect only even nodes.

B. Reverse the entire result list after traversal to get even nodes first.

C. Skip reversing on odd levels to keep order consistent for even nodes.

D. Filter nodes by even value before adding them to the current level list during traversal.

Solution

1. Step 1: Identify filtering requirement

   We want only even-valued nodes in the output, so filter nodes during traversal.

2. Step 2: Apply filtering during level collection

   Filter nodes by checking if value is even before adding to current level list.

3. Step 3: Keep zigzag logic intact

   After filtering, apply zigzag reversal as usual on filtered nodes.

4. Final Answer:

   Filter nodes by even value before adding them to the current level list during traversal. -> Option D

5. Quick Check:

   Filter during traversal = Filter nodes by even value before adding them to the current level list during traversal. [OK]

Hint: Filter nodes while collecting each level, then zigzag [OK]

Common Mistakes:

• Reversing entire result instead of filtering
• Skipping reversal breaks zigzag pattern
• Using stack incorrectly for filtering