Bit Manipulation - Power of Four
You need to determine if a given positive integer can be expressed as 4 raised to some integer power (i.e., n = 4^k for k ≥ 0). Which approach guarantees an optimal O(1) time solution without loops or recursion?
Which approach guarantees an optimal O(1) time solution without loops or recursion?
easy🔍 Pattern Recognition Q11 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand the problem requirement
The problem asks for a constant-time check to determine if a number is a power of four, which means no loops or recursion.Step 2: Evaluate approaches for O(1) time
Using bitmasking to check if the number is a power of two and if the single set bit is in an even position is a known O(1) approach. Logarithm checks involve floating point operations and can have precision issues, so they are not guaranteed to be optimal or reliable in constant time. Iterative division and dynamic programming are not O(1).Final Answer:
Option C -> Option CQuick Check:
Bitmasking approach uses constant time bit operations [OK]
Quick Trick: Bitmasking checks power of two and bit position in O(1)
Common Mistakes:
MISTAKES- Confusing power of two check with power of four
- Using loops despite O(1) requirement
- Relying on floating point logarithm checks which can be imprecise
Trap Explanation:
PITFALL- Logarithm approach looks straightforward but can fail due to floating point precision and is not guaranteed O(1).
Interviewer Note:
CONTEXT- Tests if candidate can identify the optimal constant-time bit manipulation approach beyond brute force or floating point methods.
Master "Power of Four" in Bit Manipulation
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