javaalgorithmmathnumberscubes

Fast way to check if long integer is a cube (in Java)

I am writing a program in which I am required to check if certain large numbers (permutations of cubes) are cubic (equal to n^3 for some n).

At the moment I simply use the method

static boolean isCube(long input) {
    double cubeRoot = Math.pow(input,1.0/3.0);
    return Math.round(cubeRoot) == cubeRoot;
}

but this is very slow when working with large numbers (10+ digits). Is there a faster way to determine if integer numbers are cubes?

Solution

  • There are only 2^21 cubes that don't overflow a long (2^22 - 1 if you allow negative numbers), so you could just use a HashSet lookup.