Recall & Review
beginner
What does the "maximum width" of a binary tree mean?
The maximum width of a binary tree is the maximum value of (maximum node index - minimum node index + 1) across all levels, where indices are assigned as in a complete binary tree.
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intermediate
How can we keep track of node positions to calculate the maximum width of a binary tree?
We assign an index to each node as if the tree was a complete binary tree. The root is index 0, left child is 2 * parent_index + 1, right child is 2 * parent_index + 2. This helps calculate width by subtracting minimum from maximum indices at each level.
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intermediate
Why do we subtract the minimum index from the maximum index at each level when finding the width?
The width of a level is calculated as (maximum index - minimum index + 1). Subtracting minimum from maximum and adding 1 accounts for all positions from leftmost to rightmost node, including gaps.
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beginner
What data structure is commonly used to traverse the binary tree level by level for width calculation?
A queue is used for level order traversal (breadth-first search) to visit nodes level by level and track their indices.
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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 during the traversal.
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What is the index of the right child if the parent node has index 3?
✗ Incorrect
Right child index = 2 * parent_index + 2 = 2 * 3 + 2 = 8.
Which traversal method is best suited to calculate the maximum width of a binary tree?
✗ Incorrect
Level order traversal visits nodes level by level, which is needed to calculate width at each level.
If a level has nodes with indices 4, 5, and 7, what is the width of that level?
✗ Incorrect
Width = max_index - min_index + 1 = 7 - 4 + 1 = 4.
What does the maximum width of a binary tree include?
✗ Incorrect
Maximum width counts nodes plus empty positions (gaps) between nodes at the widest level.
What is the initial index assigned to the root node when calculating maximum width?
✗ Incorrect
The root node is assigned index 0 to start the indexing system.
Explain how to calculate the maximum width of a binary tree using level order traversal and node indexing.
Think about numbering nodes like positions in a complete binary tree.
You got /4 concepts.
Describe why indexing nodes helps in finding the maximum width of a binary tree including gaps between nodes.
Imagine nodes placed on a number line with spaces.
You got /4 concepts.