Tree: Depth-First Search - Symmetric Tree (DFS Approach)
What is the time complexity of the optimized recursive DFS approach to check if a binary tree with n nodes is symmetric?
What is the time complexity of the optimized recursive DFS approach to check if a binary tree with n nodes is symmetric?
medium🪤 Complexity Trap Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze traversal
The algorithm visits each node once, comparing mirrored nodes simultaneously.Step 2: Confirm no repeated work
Each node pair is compared once, so total work is proportional to n nodes.Final Answer:
Option C -> Option CQuick Check:
Linear time traversal of all nodes [OK]
Quick Trick: Each node visited once in mirrored pairs [OK]
Common Mistakes:
MISTAKES- Assuming quadratic due to recursion
- Confusing with balanced tree complexities
Trap Explanation:
PITFALL- Candidates often overestimate complexity thinking recursion causes repeated work, but each node is processed once.
Interviewer Note:
CONTEXT- Tests understanding of recursion time complexity in tree traversal
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