# Eight different solutions with comments

• ``````//AC - direct iterative method;
bool isPowerOfThree(int n)
{
long a = 1;
while(a <= n)
{
if(a==n)
return true;
a *= 3;
}
return false;
}
``````

recursive solution

``````    bool isPowerOfThree(int n)
{
return n>0 && 1162261467%n==0;
}
``````

``````//AC - the following four methods are using mod;
//This process can be faster using hashmap or binary search;
bool isPowerOfThree(int n)
{
return (n == 1 || n == 3 || n == 9 || n == 27 || n == 81 || n == 243 || n == 729 || n == 2187 || n == 6561 || n == 19683 || n == 59049 || n == 177147 || n == 531441 || n == 1594323 || n == 4782969 || n == 14348907 || n == 43046721 || n == 129140163 || n == 387420489 || n == 1162261467);
}

bool isPowerOfThree(int n)
{
int maxPowerOfThree = (int)pow(3, (int)(log(INT_MAX)/log(3)));
return n>0 && maxPowerOfThree%n==0;
}

bool isPowerOfThree(int n)
{
return n>0 && (int)pow(3, 19)%n==0;
}

bool isPowerOfThree(int n)
{
return n>0 && 1162261467%n==0;
}
``````

``````//AC - the following two methods are using log;
bool isPowerOfThree(int n)
{
return fmod(log10(n)/log10(3), 1) == 0;
}

bool isPowerOfThree(int n)
{
double ret = log10(n)/log10(3);
return ret==(int)ret;
}``````

• Try for n =2. OJ gave error for this test case.

• Sorry to reply this late, I re-checked it and as for n=2 case the ret=log10(n)/log10(3)=0.630930 while (ret)=0 and quite clearly the equation is not equal so return false which means n=2 is not the power of three. Something wrong about this? I hope this can help. B.T.W. this technique has some mathematical logic behind, maybe you should do some reasoning to understand it.

• I don't quite understand your code

``````bool isPowerOfThree3(int n)
{
return n>0 && (int)pow(3, 19)%n==0;
}

bool isPowerOfThree4(int n)
{
return n>0 && 1162261467%n==0;
}
``````

why you use pow(3, 19)%n here? Thx

• In the assistance of the OJ, you can easily get it that the 19 is the biggest exponent of 3 which means here pow(3, 19) == 1162261467. B.T.W. you should post this question in comment section instead of answer.

• thanks for explanation

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