Power of Two

Problem Statement

Given an integer n, return true if it is a power of two. Otherwise, return false. An integer n is a power of two if there exists an integer x such that n == 2^x.

Example: n = 16 → Output: true (16 = 2^4)
n = 3 → Output: false

Approach 1: Logarithmic Check

Explanation: Use logarithm base 2 to check if n is a power of two. If log2(n) is an integer, n is a power of two.

Time Complexity: O(1)

Space Complexity: O(1)

if n <= 0:
    return false
x = log2(n)
if x == floor(x):
    return true
else:
    return false

Approach 2: Iterative Power Check

Explanation: Iterate through possible powers of 2 (up to 2^30) and check if any match n.

Time Complexity: O(log n)

Space Complexity: O(1)

for x in range(0, 31):
    if 2^x == n:
        return true
return false

Approach 3: Bit Manipulation

Explanation: A power of two has exactly one bit set in its binary representation. Check if n has only one set bit using bit counting.

Time Complexity: O(1)

Space Complexity: O(1)

if n <= 0:
    return false
return popcount(n) == 1