Zigzag Level Order Traversal in DSA Rust - 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).

beginner

In Zigzag Level Order Traversal, what determines the direction of traversal at each level?

The level number (starting from 0). Even levels are traversed left to right, odd levels right to left.

intermediate

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

How does Zigzag Level Order Traversal differ from normal Level Order Traversal?

Normal level order visits nodes left to right at every level. Zigzag alternates direction at each level, switching between left to right and right to left.

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

A Linked List

B Queue

C HashMap

D Stack or Deque

Stacks or deques help reverse the order of nodes at alternate levels, which is essential for zigzag traversal.

In Zigzag Level Order Traversal, which level is traversed from right to left?

A Odd-numbered levels

B Level 0

C All levels

D Even-numbered levels

Odd-numbered levels (1, 3, 5, ...) are traversed from right to left.

What is the output of Zigzag Level Order Traversal for a tree with root 1 and children 2 (left) and 3 (right)?

A [[1], [2, 3]]

B [[1, 2, 3]]

C [[1], [3, 2]]

D [[3, 2], [1]]

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

What is the space complexity of Zigzag Level Order Traversal?

A O(n)

B O(1)

C O(log n)

D O(n^2)

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

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

A Traverse nodes level by level

B Visit nodes randomly

C Use stacks or deque to manage order

D Alternate direction of traversal at each level

Nodes are visited level by level, not randomly.

Explain how Zigzag Level Order Traversal works and why alternating direction is important.

Think about visiting nodes left to right on one level, then right to left on the next.

Describe the data structures and steps needed to implement Zigzag Level Order Traversal in Rust.

Focus on how to store nodes and control traversal direction.

Practice

1. What does Zigzag Level Order Traversal of a binary tree mean?

easy

A. Traverse nodes only from right to left at all levels

B. Traverse nodes only from left to right at all levels

C. Traverse nodes randomly without any order

D. Traverse nodes level by level, alternating direction each level

Solution

1. Step 1: Understand level order traversal

   Level order traversal means visiting nodes level by level from top to bottom.

2. Step 2: Add zigzag pattern

   Zigzag means alternating the direction of traversal at each level: left to right, then right to left, and so on.

3. Final Answer:

   Traverse nodes level by level, alternating direction each level -> Option D

4. Quick Check:

   Zigzag = alternate directions [OK]

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

Common Mistakes:

• Thinking traversal is always left to right
• Confusing zigzag with preorder or inorder traversal
• Ignoring direction change at alternate levels

2. Which Rust data structure is best to use for implementing Zigzag Level Order Traversal?

easy

A. HashMap for storing node values

B. VecDeque for efficient front and back operations

C. BinaryHeap for priority ordering

D. LinkedList for random access

Solution

1. Step 1: Identify needed operations

   Zigzag traversal requires adding and removing nodes from both ends efficiently.

2. Step 2: Choose suitable Rust structure

   VecDeque supports push/pop from front and back efficiently, ideal for zigzag traversal.

3. Final Answer:

   VecDeque for efficient front and back operations -> Option B

4. Quick Check:

   VecDeque = double-ended queue [OK]

Hint: Use VecDeque for double-ended queue operations [OK]

Common Mistakes:

• Using HashMap which is unordered
• Using BinaryHeap which is for priority, not order
• Using LinkedList which is inefficient in Rust

3. What is the output of the zigzag level order traversal for this tree?

    1
   / \
  2   3
 / \   \
4   5   6

medium

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

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

C. [[1], [2, 3], [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: [3, 2]

3. Step 3: Traverse level 2 left to right

   Level 2 nodes: [4, 5, 6]

4. Final Answer:

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

5. Quick Check:

   Zigzag levels alternate direction [OK]

Hint: Alternate direction each level when listing nodes [OK]

Common Mistakes:

• Not reversing order on alternate levels
• Mixing node values in wrong order
• Ignoring missing children in traversal

4. Given this Rust code snippet for zigzag traversal, what is the bug?

let mut left_to_right = true;
while !queue.is_empty() {
    let level_size = queue.len();
    let mut level_nodes = Vec::new();
    for _ in 0..level_size {
        let node = queue.pop_front().unwrap();
        if left_to_right {
            level_nodes.push(node.val);
        } else {
            level_nodes.insert(0, node.val);
        }
        if let Some(left) = node.left {
            queue.push_back(left);
        }
        if let Some(right) = node.right {
            queue.push_back(right);
        }
    }
    left_to_right = !left_to_right;
}

medium

A. Inserting at index 0 in Vec is inefficient; use a deque instead

B. The queue should be cleared each iteration

C. left_to_right flag is never toggled

D. Nodes are pushed to queue incorrectly

Solution

1. Step 1: Analyze insertion in level_nodes

   Inserting at index 0 in a Vec shifts all elements, causing inefficiency.

2. Step 2: Suggest better data structure

   Using a VecDeque allows efficient push_front operations for reverse order.

3. Final Answer:

   Inserting at index 0 in Vec is inefficient; use a deque instead -> Option A

4. Quick Check:

   Vec insert(0) is slow; VecDeque better [OK]

Hint: Avoid Vec insert(0); prefer VecDeque for front insertions [OK]

Common Mistakes:

• Thinking queue needs clearing each level
• Missing toggle of left_to_right flag
• Incorrectly pushing children nodes

5. How would you modify a zigzag level order traversal to return the sum of values at each level instead of nodes themselves?

hard

A. Use a stack instead of queue to store nodes

B. Add node values directly to a global sum without level separation

C. Sum values in level_nodes vector before adding to result

D. Reverse the tree before traversal

Solution

1. Step 1: Collect node values per level

   During traversal, store node values in a temporary vector for each level.

2. Step 2: Calculate sum of level nodes

   Sum all values in the vector before adding the sum to the final result list.

3. Final Answer:

   Sum values in level_nodes vector before adding to result -> Option C

4. Quick Check:

   Sum per level = sum(level_nodes) [OK]

Hint: Sum nodes per level before storing result [OK]

Common Mistakes:

• Summing all nodes without level grouping
• Using stack breaks level order logic
• Reversing tree changes structure, not traversal