Python - Given an integer 'n', check if it is a power of 4, and return True, otherwise False.

When it is required to check if a given variable is a power of 4, we can use different approaches. A power of 4 means the number can be expressed as 4^k where k is a non-negative integer (1, 4, 16, 64, 256, etc.).

Method 1: Using Division and Modulus

This method repeatedly divides the number by 4 and checks if there's any remainder ?

def check_power_of_4(num):
    if num == 0:
        return False
    while num != 1:
        if num % 4 != 0:
            return False
        num = num // 4
    return True

# Test the function
test_num = 64
print("The number to be checked is:", test_num)

if check_power_of_4(test_num):
    print(test_num, "is a power of 4")
else:
    print(test_num, "is not a power of 4")

The number to be checked is: 64
64 is a power of 4

Method 2: Using Logarithms

We can use logarithms to check if log₄(n) is an integer ?

import math

def is_power_of_4_log(num):
    if num <= 0:
        return False
    
    log_result = math.log(num, 4)
    return log_result == int(log_result)

# Test with multiple numbers
test_numbers = [1, 4, 16, 64, 100, 256]

for num in test_numbers:
    result = is_power_of_4_log(num)
    print(f"{num} is {'a' if result else 'not a'} power of 4")

1 is a power of 4
4 is a power of 4
16 is a power of 4
64 is a power of 4
100 is not a power of 4
256 is a power of 4

Method 3: Using Bit Manipulation

For powers of 4, we can use bitwise operations. A number is a power of 4 if it's a power of 2 and has bits set only at even positions ?

def is_power_of_4_bitwise(num):
    if num <= 0:
        return False
    
    # Check if it's a power of 2 and has bits at even positions
    return (num & (num - 1)) == 0 and (num & 0x55555555) != 0

# Test the function
test_cases = [1, 4, 8, 16, 32, 64, 128, 256]

for num in test_cases:
    result = is_power_of_4_bitwise(num)
    print(f"{num}: {'Power of 4' if result else 'Not power of 4'}")

1: Power of 4
4: Power of 4
8: Not power of 4
16: Power of 4
32: Not power of 4
64: Power of 4
128: Not power of 4
256: Power of 4

Comparison

How It Works

The division method works by repeatedly dividing the number by 4. If at any point there's a remainder, the number is not a power of 4. The logarithm method calculates log₄(n) and checks if the result is an integer. The bitwise method uses the fact that powers of 4 have specific bit patterns.

Conclusion

Use the division method for clarity and educational purposes. The bitwise approach is most efficient for performance-critical applications. The logarithm method provides a mathematical solution but may have floating-point precision issues.