342 - Power of four

The problem statement

Given an integer n return true if its is a power of four. Otherwise, return false.

An integer n is a power of four, if there exists an integer x such that n === 4^x.

Understanding the problem

We can solve this problem with recursion:

1. 1 is a valid result for being a power of a number as the remainder will always be 0.
2. If n is <= 0 then we should return false as a negative number can't be a power of a number.
3. If dividing n by 4 results in a remainder then we should return false as it can't be divided equally.

Approaching the problem

Examples:

Example 1:

Input: n = 16

Output: true

Example 2:

Input: n = 5

Output: false

Example 3:

Input: n = 1

Output: true

Code solution

Log(n)

function isPowerOfFour(n: number): boolean {
  if (n === 1) return true;
  if (n <= 0 || n % 4 != 0) return false;
  return isPowerOfFour(n / 4);
}

Key Takeaways

1. 1 is always a factor of a number.
2. Anything to the power of 0 is 1.