Given an integer, write a function to determine if it is a power of three.

Follow up:

Could you do it without using any loop / recursion?

解决方法：

1、Recursive Solution

public boolean isPowerOfThree(int n) {    return n>0 && (n==1 || (n%3==0 && isPowerOfThree(n/3)));}

2、Iterative Solution

public boolean isPowerOfThree(int n) {    if(n>1)        while(n%3==0) n /= 3;    return n==1;}

数学方法

1、找到3的n次方的最大整数，检查是否为输入的整数倍

public boolean isPowerOfThree(int n) {    int maxPowerOfThree = (int)Math.pow(3, (int)(Math.log(0x7fffffff) / Math.log(3)));    return n>0 && maxPowerOfThree%n==0;}

或者更简单一点，3的n次方的最大值maxPowerOfThree = 1162261467。

public boolean isPowerOfThree(int n) {    return n > 0 && (1162261467 % n == 0);}

2、log10(n) / log10(3)返回整数

public boolean isPowerOfThree(int n) {    return (Math.log10(n) / Math.log10(3)) % 1 == 0;}

reference