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:
- 题意是判断一个32位的符号整数是不是4的次方
- 对于2的次方的判断是n&(n-1)== 0
10 => 2
100 => 4
1000 => 8
10000 => 16
100000 => 32
1000000 => 64
10000000 => 128
100000000 => 256
1000000000 => 512
10000000000 => 1024
100000000000 => 2048
1000000000000 => 4096
10000000000000 => 8192
100000000000000 => 16384
由图中观察可以看出来,4的次方,1都在从右往左数的奇数位,1,3,5等
所有从2的次方移除4的次方,与上01010101010101010101010101010101,十六进制是0x555555555
代码:
public class Solution {
public boolean isPowerOfFour(int num) {
return num > 0 && (num&(num -1)) == 0 && (num & 0x55555555) != 0;
}
}