题目:

given an integer (signed 32 bits), write a function to check whether it is a power of 4.

Example:
Given num = 16, return true. Given num = 5, return false.

Follow up: Could you solve it without loops/recursion?

思路:

本题与power of two,power of three略有不同,不能简单的套用power of three的方法。可以分析2、4的幂都有哪些特征,可以从2进制角度考虑,

1:1

4:100

8:1000

16:10000

32:100000

64:1000000

总结规律发现满足2或4的幂必须num&(num-1) == 0,其次每4位用0101判断是否为4的幂

代码:

class Solution {
public:
    bool isPowerOfFour(int num) {
        return num > 0 && (num&(num-1)) == 0 && (num & 0x55555555) != 0;
        //0x55555555 is to get rid of those power of 2 but not power of 4
        //so that the single 1 bit always appears at the odd position 
        
    }
};