What is the space complexity of a breadth-first traversal of a binary tree?

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Question: What is the space complexity of a breadth-first traversal of a binary tree?

Options:

Correct Answer: O(n)

Solution:

The space complexity of a breadth-first traversal is O(n) because it needs to store all nodes at the current level in the queue.

What is the space complexity of a breadth-first traversal of a binary tree?

What is the space complexity of a breadth-first traversal of a binary tree?

Step 1: Understand what breadth-first traversal means. It is a way to visit all the nodes in a binary tree level by level, starting from the root.
Step 2: Recognize that during this traversal, we use a queue to keep track of the nodes we need to visit next.
Step 3: Realize that at any given time, the queue can hold all the nodes at the current level of the tree.
Step 4: In a binary tree, the maximum number of nodes at any level can be up to n/2, where n is the total number of nodes in the tree.
Step 5: Therefore, the space needed for the queue can grow to O(n) in the worst case, when the tree is completely filled.
Step 6: Conclude that the space complexity of a breadth-first traversal of a binary tree is O(n).

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