326. Power of Three

Description

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?

Solution

Math

利用log

If N is a power of 3:

It follows that 3^X == N
It follows that log (3^X) == log N
It follows that X log 3 == log N
It follows that X == (log N) / (log 3)

For the basis to hold, X must be an integer.
However, due to the fact that log(3) cannot be precisely represented on a binary computer; X is considered an integer if its decimal component falls within a guard range of +/-0.00000000000001. Static imports for log, abs and rint from java.lang.Math.

class Solution {
    public boolean isPowerOfThree(int n) {
        double a = Math.log(n) / Math.log(3);
        return Math.abs(a - Math.rint(a)) <= 0.00000000000001;
    }
}

Math

大写的服！

public boolean isPowerOfThree(int n) {
    // 1162261467 is 3^19,  3^20 is bigger than int  
    return ( n>0 && 1162261467%n==0);
}