By Long Luo

This article is the solution Just One Line Code with Detailed Explanation of Problem 342. Power of Four .

Math

If $n$ is a power of $4$, it must be $n=4^x,x\ge 0$.

Then:

$$4^x\equiv (3+1{)}^x\equiv 1^x\equiv 1(mod3)$$

If $n=2^x$ but $n\ne 4^x$, it must be $n=4^x\times 2$, which means $n\equiv 2(mod3)$.

Therefore, we can check whether $n=4^x$ by whether $n\equiv 1(mod3)$.

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class Solution {
    public boolean isPowerOfFour(int n) {
        return  (n & (n - 1)) == 0 && n % 3 == 1;
    }
}

Analysis

• Time Complexity: $O(1)$.
• Space Complexity: $O(1)$.

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