Zigzag Level Order Traversal in DSA Go - 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.

intermediate

Why do we use two stacks or a deque in Zigzag Level Order Traversal?

To keep track of nodes in the current level and the next level while controlling the order of traversal direction (left to right or right to left).

intermediate

In Zigzag Level Order Traversal, what determines the order of adding child nodes to the next level?

The current traversal direction. If going left to right, add left child first then right child. If right to left, add right child first then left child.

beginner

What is the time complexity of Zigzag Level Order Traversal?

O(n), where n is the number of nodes in the tree, because each node is visited exactly once.

beginner

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 1: left to right → [1]
Level 2: right to left → [3, 2]
Level 3: left to right → [4, 5, 6]

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

A Queue or deque

B Stack or deque

C Hash map

D Linked list

Stacks or deques help alternate the order of traversal by controlling the order of node processing.

In Zigzag traversal, if the current level is traversed left to right, how are child nodes added for the next level?

A Right child first, then left child

B Only left child

C Only right child

D Left child first, then right child

When traversing left to right, add left child first to maintain correct order for next level.

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

A []

B [[]]

C [[node_value]]

D [node_value]

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

What is the main difference between normal level order traversal and zigzag level order traversal?

A Zigzag alternates direction each level, normal always left to right

B Zigzag uses recursion, normal uses iteration

C Zigzag only visits leaf nodes

D Normal traversal uses stacks, zigzag uses queues

Zigzag traversal changes direction at each level, normal traversal always goes left to right.

What is the space complexity of Zigzag Level Order Traversal?

A O(n)

B O(log n)

C O(1)

D O(n^2)

Space complexity is O(n) because we store nodes of each level in data structures.

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

Think about how you would walk through the tree visiting nodes in a zigzag pattern.

Describe the data structures and logic needed to implement Zigzag Level Order Traversal efficiently.

Focus on how to keep track of nodes and direction for each level.

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, switching between left-to-right and right-to-left.

B. It only traverses the left subtree of the tree.

C. It visits nodes in a random order at each level.

D. It traverses nodes only in right-to-left order for all levels.

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 changes direction every level: first left-to-right, then right-to-left, and so on.

3. Final Answer:

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

4. Quick Check:

   Zigzag = alternate directions [OK]

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

Common Mistakes:

• Thinking traversal is always left-to-right
• Confusing zigzag with random order
• Ignoring direction change at each level

2. Which of the following Go code snippets correctly initializes a queue for level order traversal in Zigzag Level Order Traversal?

easy

A. queue := make([]int, 0)

B. queue := []int{root}

C. queue := map[int]*TreeNode{}

D. queue := []*TreeNode{root}

Solution

1. Step 1: Identify the queue type needed

   Queue should hold pointers to TreeNode structs, so []*TreeNode is correct.

2. Step 2: Check each option's correctness

   queue := []*TreeNode{root} uses []*TreeNode with root node, correct for traversal. Options A and B use int slices, wrong type. queue := map[int]*TreeNode{} uses map, not queue.

3. Final Answer:

   queue := []*TreeNode{root} -> Option D

4. Quick Check:

   Queue holds TreeNode pointers = queue := []*TreeNode{root} [OK]

Hint: Queue must hold TreeNode pointers, not ints or maps [OK]

Common Mistakes:

• Using int slices instead of TreeNode pointers
• Using map instead of slice for queue
• Not initializing queue with root node

3. Given the binary tree:

    1
   / \
  2   3
 / \   \
4   5   6

What is the output of Zigzag Level Order Traversal?

medium

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

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

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

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

Solution

1. Step 1: Traverse level 0 and 1 with direction

   Level 0: left-to-right -> [1]. Level 1: right-to-left -> [3, 2].

2. Step 2: Traverse level 2 left-to-right

   Level 2 nodes: 4, 5, 6 from left to right -> [4, 5, 6].

3. Final Answer:

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

4. Quick Check:

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

Hint: Alternate direction each level, left-to-right then right-to-left [OK]

Common Mistakes:

• Not reversing nodes on odd levels
• Reversing nodes on even levels incorrectly
• Mixing node order at last level

4. Consider this Go code snippet for Zigzag Level Order Traversal:

for len(queue) > 0 {
    levelSize := len(queue)
    var level []int
    for i := 0; i < levelSize; i++ {
        node := queue[0]
        queue = queue[1:]
        level = append(level, node.Val)
        if node.Left != nil {
            queue = append(queue, node.Left)
        }
        if node.Right != nil {
            queue = append(queue, node.Right)
        }
    }
    if leftToRight {
        result = append(result, level)
    } else {
        reverse(level)
        result = append(result, level)
    }
    leftToRight = !leftToRight
}

What is the main bug in this code?

medium

A. The reverse function is called but not defined or implemented.

B. The queue is not updated correctly after popping the first element.

C. The variable leftToRight is never initialized before use.

D. The level slice is appended before processing child nodes.

Solution

1. Step 1: Check queue update correctness

   Queue is updated by slicing off first element correctly, no bug here.

2. Step 2: Verify reverse function usage

   reverse(level) is called but no definition or implementation is shown, causing compile error.

3. Final Answer:

   The reverse function is called but not defined or implemented. -> Option A

4. Quick Check:

   Undefined reverse function causes error [OK]

Hint: Ensure all helper functions like reverse are implemented [OK]

Common Mistakes:

• Assuming reverse is built-in in Go
• Ignoring initialization of leftToRight (usually done before loop)
• Misunderstanding queue slicing syntax

5. You want to implement Zigzag Level Order Traversal but optimize space by avoiding reversing slices. Which approach is best?

hard

A. Use a queue and reverse the slice after each level as usual.

B. Use two stacks to alternate pushing nodes in correct order per level.

C. Use recursion with a global list and reverse at the end.

D. Traverse all nodes left-to-right and then reverse the entire result.

Solution

1. Step 1: Understand reversing cost

   Reversing slices after each level adds extra time and space overhead.

2. Step 2: Use two stacks for order control

   Two stacks let you push child nodes in order that naturally produces zigzag traversal without reversing.

3. Final Answer:

   Use two stacks to alternate pushing nodes in correct order per level. -> Option B

4. Quick Check:

   Two stacks avoid reversing slices [OK]

Hint: Two stacks method avoids reversing slices [OK]

Common Mistakes:

• Relying on reversing slices every level
• Using recursion without order control
• Reversing entire result instead of per level