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What is the time complexity of the optimal recursive approach to invert a binary tree with n nodes?

medium🪤 Complexity Trap Q5 of Q15
Tree: Depth-First Search - Invert Binary Tree
What is the time complexity of the optimal recursive approach to invert a binary tree with n nodes?
AO(n^2)
BO(n log n)
CO(n)
DO(log n)
Step-by-Step Solution
Solution:

  1. Step 1: Analyze traversal

    The algorithm visits each node exactly once to swap children.

  2. Step 2: Confirm linear time

    Since each node is processed once, total time is proportional to n.

  3. Final Answer:

    Option C -> Option C

  4. Quick Check:

    One visit per node -> O(n) time [OK]
Quick Trick: One pass over all nodes -> O(n) [OK]
Common Mistakes:
MISTAKES
  • Assuming O(n log n) due to recursion
  • Confusing with sorting complexities
Trap Explanation:
PITFALL
  • Candidates often overestimate complexity due to recursion overhead, picking O(n log n).
Interviewer Note:
CONTEXT
  • Tests understanding of recursion and traversal complexity
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