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What is the time complexity of the BFS-based serialization and deserialization of a binary tree with n nodes, assuming the tree is balanced? Consider both serialization and deserialization separately.

medium🪤 Complexity Trap Q13 of Q15
Tree: Depth-First Search - Serialize and Deserialize Binary Tree
What is the time complexity of the BFS-based serialization and deserialization of a binary tree with n nodes, assuming the tree is balanced? Consider both serialization and deserialization separately.
ASerialization: O(n log n), Deserialization: O(n log n)
BSerialization: O(n), Deserialization: O(n^2)
CSerialization: O(n), Deserialization: O(n)
DSerialization: O(n^2), Deserialization: O(n)
Step-by-Step Solution

  1. Step 1: Analyze serialization time

    Each node is enqueued and dequeued exactly once, so serialization is O(n).

  2. Step 2: Analyze deserialization time

    Deserialization processes each node once, reconstructing the tree in O(n) time.

  3. Final Answer:

    Option C -> Option C

  4. Quick Check:

    Both serialization and deserialization scale linearly with number of nodes [OK]
Quick Trick: Each node is processed once in BFS serialization/deserialization [OK]
Common Mistakes:
MISTAKES
  • Assuming deserialization is O(n^2) due to nested loops
  • Confusing tree height with number of nodes
  • Thinking serialization is O(n log n) due to queue operations
Trap Explanation:
PITFALL
  • Candidates often confuse BFS queue operations as more expensive or assume nested loops cause quadratic time.
Interviewer Note:
CONTEXT
  • Tests understanding of BFS traversal complexity and avoiding overestimating costs.
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