Tree: Depth-First Search - Count Complete Tree Nodes
What is the space complexity of the recursive countNodes function that uses height checks on left and right subtrees to count nodes in a complete binary tree?
What is the space complexity of the recursive countNodes function that uses height checks on left and right subtrees to count nodes in a complete binary tree?
medium🪤 Complexity Trap Q6 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze recursion depth
Recursion depth is O(log n) due to tree height.Step 2: Analyze work per call
Each call computes heights in O(log n), but height computations can be optimized to O(1) if cached; assuming naive implementation, total time is O((log n)^2), but space is dominated by recursion stack.Step 3: Space complexity
Space complexity is O(log n) due to recursion stack depth.Final Answer:
Option D -> Option DQuick Check:
Recursion stack space is logarithmic in n [OK]
Quick Trick: Recursion stack depth equals tree height -> O(log n) space [OK]
Common Mistakes:
MISTAKES- Confusing time and space complexity
- Assuming auxiliary space adds up multiplicatively
Trap Explanation:
PITFALL- Candidates often confuse auxiliary time with space; space is only recursion stack depth.
Interviewer Note:
CONTEXT- Tests understanding of recursion stack space versus auxiliary computations.
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