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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?
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Practice Questions
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Q1
What is the space complexity of a breadth-first traversal of a binary tree?
O(n)
O(log n)
O(1)
O(n log n)
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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.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the space complexity of a breadth-first traversal of a binary tree?
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.
Steps: 6
Show Steps
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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