Maximum Width of Binary Tree in DSA Rust - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does the "maximum width" of a binary tree mean?

The maximum width of a binary tree is the maximum over all levels of (rightmost node index - leftmost node index + 1), where indices are assigned in level order (root index 1, left child 2*i, right child 2*i + 1).

beginner

Why do we use a queue in the algorithm to find the maximum width of a binary tree?

A queue helps us visit nodes level by level (breadth-first). This way, we can track the minimum and maximum indices of nodes at each level to compute width as (max_index - min_index + 1).

intermediate

In Rust, which data structure is commonly used to implement a queue for level order traversal?

The VecDeque collection is commonly used as a queue in Rust because it allows efficient adding and removing from both ends.

advanced

How do we handle empty nodes or gaps when calculating the maximum width of a binary tree?

We assign position indices to nodes as if the tree was a complete binary tree. This helps us count the width including gaps between nodes.

intermediate

What is the time complexity of finding the maximum width of a binary tree using level order traversal?

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

What data structure is best suited for level order traversal to find maximum width?

A Linked List

B Stack

C HashMap

D Queue

Queue allows visiting nodes level by level, which is essential for calculating width at each level.

If at a level the minimum node index is 2 and maximum is 6, what is the width of that level?

A 5

B 2

C 3

D 10

Width of a level is maximum index - minimum index + 1 = 6 - 2 + 1 = 5.

Why do we assign position indices to nodes when calculating maximum width?

A To count gaps between nodes

B To sort nodes

C To track node values

D To find node depth

Position indices help include gaps between nodes to measure the true width.

What Rust collection is used for efficient queue operations in this algorithm?

A HashSet

B Vec

C VecDeque

D BTreeMap

VecDeque supports fast push and pop from both ends, ideal for queue.

What is the time complexity of the maximum width algorithm?

A O(log n)

B O(n)

C O(n^2)

D O(1)

Each node is visited once, so time complexity is O(n).

Explain how to find the maximum width of a binary tree using level order traversal.

Think about visiting nodes level by level and counting them.

Describe how position indices help in calculating the maximum width of a binary tree.

Imagine numbering nodes like seats in a row.

Practice

1. What does the "maximum width" of a binary tree represent?

easy

A. The total number of nodes in the tree

B. The height of the tree from root to the deepest leaf

C. The largest number of nodes present at any single level of the tree

D. The sum of values of all nodes at the widest level

Solution

1. Step 1: Understand the definition of width in a binary tree

   The width of a binary tree at a level is the count of nodes present at that level.

2. Step 2: Identify maximum width

   The maximum width is the largest such count among all levels.

3. Final Answer:

   The largest number of nodes present at any single level of the tree -> Option C

4. Quick Check:

   Width = max nodes at any level [OK]

Hint: Width means count of nodes at widest level [OK]

Common Mistakes:

• Confusing width with tree height
• Thinking width is sum of node values
• Mixing width with total nodes count

2. Which Rust data structure is most suitable to track nodes level by level when calculating maximum width of a binary tree?

easy

A. VecDeque (double-ended queue)

B. Vec (vector)

C. HashMap

D. BTreeSet

Solution

1. Step 1: Identify the need for level order traversal

   To find maximum width, we visit nodes level by level, which is a breadth-first search (BFS).

2. Step 2: Choose data structure for BFS

   BFS uses a queue to process nodes in FIFO order. Rust's VecDeque supports efficient push/pop from both ends.

3. Final Answer:

   VecDeque (double-ended queue) -> Option A

4. Quick Check:

   Use queue (VecDeque) for BFS traversal [OK]

Hint: Use VecDeque for efficient queue operations in BFS [OK]

Common Mistakes:

• Using Vec which is inefficient for queue operations
• Using HashMap which is unordered
• Using BTreeSet which is for sorted unique elements

3. Given the following Rust code snippet for maximum width calculation, what is the printed output?

struct TreeNode {
    val: i32,
    left: Option,
    right: Option,
}

fn max_width(root: Option) -> usize {
    use std::collections::VecDeque;
    if root.is_none() { return 0; }
    let mut queue = VecDeque::new();
    queue.push_back(root.unwrap());
    let mut max_width = 0;
    while !queue.is_empty() {
        let level_size = queue.len();
        max_width = max_width.max(level_size);
        for _ in 0..level_size {
            let node = queue.pop_front().unwrap();
            if let Some(left) = node.left {
                queue.push_back(left);
            }
            if let Some(right) = node.right {
                queue.push_back(right);
            }
        }
    }
    max_width
}

fn main() {
    let root = Some(Box::new(TreeNode {
        val: 1,
        left: Some(Box::new(TreeNode { val: 2, left: None, right: None })),
        right: Some(Box::new(TreeNode {
            val: 3,
            left: Some(Box::new(TreeNode { val: 4, left: None, right: None })),
            right: None,
        })),
    }));
    println!("{}", max_width(root));
}

medium

A. 3

B. 2

C. 4

D. 1

Solution

1. Step 1: Analyze the tree structure

   Level 1: Node 1 (1 node) Level 2: Nodes 2 and 3 (2 nodes) Level 3: Node 4 (1 node)

2. Step 2: Calculate maximum width

   Widths per level: 1, 2, 1 Maximum width is 2.

3. Final Answer:

   2 -> Option B

4. Quick Check:

   Max width = 2 nodes at level 2 [OK]

Hint: Count nodes per level, pick max count [OK]

Common Mistakes:

• Counting total nodes instead of per level
• Ignoring empty children in width calculation
• Confusing node values with count

4. The following Rust code attempts to compute the maximum width of a binary tree but has a bug. What is the bug?

fn max_width(root: Option) -> usize {
    use std::collections::VecDeque;
    if root.is_none() { return 0; }
    let mut queue = VecDeque::new();
    queue.push_back(root.unwrap());
    let mut max_width = 0;
    while !queue.is_empty() {
        let level_size = queue.len();
        max_width = max_width.max(level_size);
        for _ in 0..level_size {
            let node = queue.pop_front().unwrap();
            if node.left.is_some() {
                queue.push_back(node.left.unwrap());
            }
            if node.right.is_some() {
                queue.push_back(node.right.unwrap());
            }
        }
    }
    max_width
}

medium

A. Not handling empty tree case

B. Using VecDeque instead of Vec causes performance issues

C. Not updating max_width inside the loop

D. Calling unwrap() on Option without checking causes panic

Solution

1. Step 1: Identify unsafe unwrap calls

   Calling unwrap() on node.left or node.right without safely extracting causes panic if None.

2. Step 2: Correct approach

   Use if let Some(left) = node.left { queue.push_back(left); } to safely handle Options.

3. Final Answer:

   Calling unwrap() on Option without checking causes panic -> Option D

4. Quick Check:

   Unsafe unwrap causes runtime panic [OK]

Hint: Use if let to safely unwrap Options [OK]

Common Mistakes:

• Using unwrap() directly on Option fields
• Ignoring empty tree check (though present here)
• Confusing VecDeque with Vec performance

5. You want to find the maximum width of a binary tree where some levels have missing nodes between others (e.g., a sparse tree). Which approach correctly calculates the maximum width including gaps between nodes? A common method is to assign position indices to nodes as if the tree was a complete binary tree. Which Rust code snippet correctly updates the maximum width using position indices during level order traversal?

use std::collections::VecDeque;

fn max_width_with_positions(root: Option) -> usize {
    if root.is_none() { return 0; }
    let mut max_width = 0;
    let mut queue = VecDeque::new();
    queue.push_back((root.unwrap(), 0usize));
    while !queue.is_empty() {
        let level_length = queue.len();
        let first_index = queue.front().unwrap().1;
        let last_index;
        for i in 0..level_length {
            let (node, idx) = queue.pop_front().unwrap();
            let idx = idx - first_index; // normalize to prevent overflow
            if node.left.is_some() {
                queue.push_back((node.left.unwrap(), 2 * idx + 1));
            }
            if node.right.is_some() {
                queue.push_back((node.right.unwrap(), 2 * idx + 2));
            }
            if i == level_length - 1 {
                last_index = idx;
            }
        }
        max_width = max_width.max(last_index + 1);
    }
    max_width
}

hard

A. Normalize indices by subtracting first index at each level to avoid overflow

B. Use raw indices without normalization to get exact positions

C. Ignore indices and count nodes only for width

D. Use depth instead of indices for width calculation

Solution

1. Step 1: Understand position indexing

   Assigning indices as if complete binary tree helps measure width including gaps.

2. Step 2: Normalize indices to prevent overflow

   Subtracting first index at each level keeps indices small and prevents usize overflow.

3. Step 3: Calculate width as last_index - first_index + 1

   Using normalized indices, width = last_index + 1 at each level.

4. Final Answer:

   Normalize indices by subtracting first index at each level to avoid overflow -> Option A

5. Quick Check:

   Index normalization prevents overflow and calculates width correctly [OK]

Hint: Subtract first index each level to keep indices small [OK]

Common Mistakes:

• Not normalizing indices causing overflow
• Ignoring gaps by counting nodes only
• Using depth instead of position indices