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What is the time complexity of the bit manipulation approach using n & (n - 1) to check if a number is a power of two, assuming n is a 32-bit integer?

medium🪤 Complexity Trap Q13 of Q15

Bit Manipulation - Power of Two

What is the time complexity of the bit manipulation approach using n & (n - 1) to check if a number is a power of two, assuming n is a 32-bit integer?

AO(n), where n is the input number

BO(n log n), due to repeated bit operations

CO(1), constant time since integer size is fixed

DO(log n), proportional to the number of bits in n

Step-by-Step Solution

Solution:

Step 1: Identify the operation cost
The operation n & (n - 1) runs in constant time on fixed-width integers, such as 32-bit integers.
Step 2: Consider input size in bits
Since the integer size is fixed (32 bits), the operation is O(1) constant time.
Final Answer:
Option C -> Option C
Quick Check:
Bitwise operations on fixed-width integers are constant time [OK]

Quick Trick: Bit ops on fixed-width integers are O(1) [OK]

Common Mistakes:

MISTAKES

Assuming O(log n) for fixed-width integers
Confusing numeric value with bit length

Trap Explanation:

PITFALL

Bitwise operations on fixed-width integers do not depend on numeric value size.

Interviewer Note:

CONTEXT

Tests understanding of complexity in bit manipulation relative to fixed integer sizes.

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