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

可以通过循环或者递归的方法求出。

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class Solution(object):
    def isPowerOfFour(self, num):
        """
        :type num: int
        :rtype: bool
        """
        if (num <= 0):
            return False
        else:
            while (num > 1):
                if (num % 4 != 0):
                    return False
                num = num / 4
            return True

也可以利用位运算的方法。

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4: 100
3: 011
4 & 3 = 0
16: 10000
15: 01111
16 & 15 = 0

得到一个判断条件

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( (num-1) & num) == 0 and (num-1) % 3 == 0

如果满足这个判断条件，就是四的乘方了。