Tree: Depth-First Search - Count Complete Tree Nodes
What is the time complexity of the most efficient algorithm to count nodes in a complete binary tree with n nodes, which uses height comparisons and binary search on the last level?
What is the time complexity of the most efficient algorithm to count nodes in a complete binary tree with n nodes, which uses height comparisons and binary search on the last level?
medium🧠 Conceptual Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand the algorithm
The algorithm computes the height of left and right subtrees and uses binary search on the last level.Step 2: Analyze complexity
Height calculation takes O(log n), and binary search on last level also takes O(log n), resulting in O(log n * log n).Final Answer:
Option D -> Option DQuick Check:
Recall height and binary search costs [OK]
Quick Trick: Height checks plus binary search yield O(log² n) [OK]
Common Mistakes:
MISTAKES- Assuming linear time complexity
- Confusing with simple DFS traversal complexity
- Ignoring binary search on last level
Trap Explanation:
PITFALL- Option C (O(log n)) is too optimistic; binary search is nested within height checks.
Interviewer Note:
CONTEXT- Tests understanding of time complexity of optimized node counting.
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