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What is the time complexity of the BFS-based algorithm to compute the maximum depth of a binary tree with n nodes?

medium🪤 Complexity Trap Q5 of Q15
Tree: Depth-First Search - Maximum Depth of Binary Tree
What is the time complexity of the BFS-based algorithm to compute the maximum depth of a binary tree with n nodes?
AO(log n)
BO(n)
CO(n^2)
DO(n log n)
Step-by-Step Solution
Solution:

  1. Step 1: Analyze BFS traversal

    BFS visits each node exactly once.

  2. Step 2: Count operations per node

    Each node enqueued and dequeued once, so total O(n).

  3. Final Answer:

    Option B -> Option B

  4. Quick Check:

    Linear time for visiting all nodes [OK]
Quick Trick: BFS visits all nodes once -> O(n) [OK]
Common Mistakes:
MISTAKES
  • Assuming O(n^2) due to nested loops
  • Confusing with balanced tree height
  • Thinking BFS is O(log n)
Trap Explanation:
PITFALL
  • Candidates often mistake BFS as O(n^2) due to nested loops over levels and nodes.
Interviewer Note:
CONTEXT
  • Tests understanding of BFS time complexity on trees.
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