Power of Four
The problem asks you to determine whether a given integer ( n ) is a power of four. You can do this by following a simple approach.
 Check if ( n ) is Positive: Since powers of four are positive, return
false
if ( n ) is less than or equal to zero.  Check if ( n ) is Power of Two: A number that is a power of four must also be a power of two. You can check this by ensuring that ( n ) has exactly one ‘1’ bit in its binary representation.
 Check if the ‘1’ Bit is in the Right Position: Since powers of four have the ‘1’ bit in odd positions (counting from right to left and starting from 0), you can check this condition to ensure that ( n ) is a power of four.
Here’s the code:


Explanation:
 The first condition checks if ( n ) is positive.
 The second condition uses bitwise operations to check if ( n ) is a power of two.
 The third condition uses a bitmask (
0x55555555
) to check if the ‘1’ bit is in the correct position. In binary, this mask has ‘1’ bits at all odd positions, allowing us to check if ( n ) is a power of four.
This approach ensures an efficient and correct solution for the given problem.


Problem Classification
This problem falls under the following categories:
Mathematical Problems: The problem involves performing mathematical operations to determine if a number is a power of four.
Number Theory: Specifically, it is related to properties of numbers and their powers.
Logarithms: The simplest solution involves using logarithms to determine if a number is a power of four.
Binary Representation: Another approach involves using the binary representation of the number.
Problem Solving: This is a problemsolving task that involves applying the correct mathematical rules and logic to solve the problem.
Boolean Logic: The final output is a Boolean value (true or false) depending on whether the number is a power of four.
Language Agnostic Coding Drills
Understanding and Checking Conditions: The first step is to understand that a number can only be a power of four if it’s positive. Therefore, the first check in our solution should be to verify that the input number is greater than zero.
Drill: Write a function that takes an integer as input and returns true if the number is greater than zero, false otherwise.
Working with Logarithms: The concept of logarithms is crucial to solve this problem. If the logarithm to the base 4 of a number is an integer, that number is a power of four.
Drill: Write a function that takes a positive integer as input and calculates its logarithm to the base 4. The function should return the result.
Checking for Integer Results: If the result of the logarithm operation is an integer, the original number is a power of four.
Drill: Extend the function from the previous step. After calculating the logarithm, check whether the result is an integer or not. Return True if it’s an integer, False otherwise.
Combine Above Steps: After understanding and coding the above drills, we are now ready to solve the problem. We need to combine these steps into a single solution, checking first if the number is positive and then whether the logarithm of the number to the base 4 is an integer.
In the final solution, we should ensure we correctly handle all potential edge cases, such as the input being zero or negative.
Targeted Drills in Python
 Understanding and Checking Conditions


 Working with Logarithms


 Checking for Integer Results


 Combine Above Steps


With these drills, you should be able to understand each step involved in the final solution and practice the concepts of checking conditions and working with logarithms.