Bit Manipulation - Power of Four
What is the space complexity of the recursive approach to check if a number n is a power of four, assuming recursion divides n by 4 each call?
What is the space complexity of the recursive approach to check if a number n is a power of four, assuming recursion divides n by 4 each call?
medium🪤 Complexity Trap Q6 of Q15
Step-by-Step Solution
Solution:
Step 1: Determine recursion depth
Each call divides n by 4, so depth is log base 4 of n.Step 2: Express space complexity
Call stack uses O(log base 4 n) space, which is O(log n) when expressed in base 2 logs.Final Answer:
Option D -> Option DQuick Check:
Recursion depth equals log base 4 of n -> O(log n) space [OK]
Quick Trick: Recursion depth = log base 4 n -> O(log n) space [OK]
Common Mistakes:
MISTAKES- Forgetting recursion stack space
- Assuming O(1) space for recursion
Trap Explanation:
PITFALL- Candidates often ignore recursion stack space, assuming constant space.
Interviewer Note:
CONTEXT- Tests understanding of recursion space complexity
Master "Power of Four" in Bit Manipulation
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