Javascript Algorithm: Power of Three

The function takes an integer n as input and returns true if n is a power of three, and false otherwise.

To determine if an integer is a power of three, we can use the logarithmic property of the base-3 logarithm. If n is a power of three, then log3(n) is an integer, and we can check this by taking the logarithm of n to base 3 and checking if the result is an integer.

Here's how the algorithm works:

Check if the input n is less than or equal to zero. If so, return false because there is no power of three that equals zero or negative numbers.
Calculate the logarithm of n to base 3 using the change of base formula: log3(n) = log10(n) / log10(3). We use the Math.log10 function to calculate the base-10 logarithm, and then divide the result by the base-10 logarithm of 3 to obtain the base-3 logarithm.
Check if the result of the logarithm calculation is an integer. We do this by comparing the floor of the result to the result itself. If they are equal, the result is an integer, which means n is a power of three. Otherwise, it is not.

Time complexity

O(1)

It takes constant time to execute regardless of the size of the input.

This is because the algorithm performs a fixed number of arithmetic operations and comparisons, which take a constant amount of time on any input size.

Therefore, the time complexity does not depend on the magnitude of the input n.