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 (maximum position - minimum position + 1) of nodes at that level.
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intermediate
How can we keep track of node positions to calculate the maximum width in a binary tree?
We assign a position index to each node starting from 0 at the root. For any node at position p, its left child is at 2*p + 1 and right child at 2*p + 2. This helps measure the width by subtracting the minimum position from the maximum position at each level.
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intermediate
Why do we subtract the minimum position from the maximum position at each level when calculating width?
Subtracting the minimum position from the maximum position gives the number of positions spanned by nodes at that level. Adding 1 gives the total count of positions including gaps, which represents the width.
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beginner
What data structure is commonly used to traverse the tree level by level for width calculation?
A queue is used to perform a level order traversal (breadth-first search) to visit nodes level by level and track their positions.
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beginner
In Go, how do you represent a binary tree node for this problem?
A binary tree node is represented as a struct with an integer value and pointers to left and right child nodes, for example:
type TreeNode struct {
Val int
Left *TreeNode
Right *TreeNode
}
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What is the position of the right child if the parent node's position is 3?
✗ Incorrect
Right child position = 2 * parent_position + 2 = 2 * 3 + 2 = 8.
Which traversal method is best to calculate the maximum width of a binary tree?
✗ Incorrect
Level order traversal visits nodes level by level, which is needed to measure width at each level.
If a level has nodes at positions 4, 5, and 7, what is the width of that level?
✗ Incorrect
Width = max_position - min_position + 1 = 7 - 4 + 1 = 4.
What initial position index is assigned to the root node?
✗ Incorrect
The root node is assigned position 0 to start indexing from zero.
Why do we use a queue in the maximum width calculation algorithm?
✗ Incorrect
A queue helps traverse nodes level by level (breadth-first), which is essential for width calculation.
Explain how to calculate the maximum width of a binary tree using position indexing.
Think about numbering nodes and measuring gaps at each level.
You got /6 concepts.
Describe the role of a queue in finding the maximum width of a binary tree.
Consider how to visit nodes level by level.
You got /4 concepts.