C++: Bjorklund’s Algorithm

#!c++
 
std::string bjorklund(int beats, int steps)
{
    //We can only have as many beats as we have steps (0 <= beats <= steps)
    if (beats > steps)
        beats = steps;
 
    //Each iteration is a process of pairing strings X and Y and the remainder from the pairings
    //X will hold the "dominant" pair (the pair that there are more of)
    std::string x = "1";
    int x_amount = beats;
 
    std::string y = "0";
    int y_amount = steps - beats;
 
    do
    {
        //Placeholder variables
        int x_temp = x_amount;
        int y_temp = y_amount;
        std::string y_copy = y;
 
        //Check which is the dominant pair 
        if (x_temp >= y_temp)
        {
            //Set the new number of pairs for X and Y
            x_amount = y_temp;
            y_amount = x_temp - y_temp;
 
            //The previous dominant pair becomes the new non dominant pair
            y = x;
        }
        else
        {
            x_amount = x_temp;
            y_amount = y_temp - x_temp;
        }
 
        //Create the new dominant pair by combining the previous pairs
        x = x + y_copy;
    } while (x_amount > 1 && y_amount > 1);//iterate as long as the non dominant pair can be paired (if there is 1 Y left, all we can do is pair it with however many Xs are left, so we're done)
 
    //By this point, we have strings X and Y formed through a series of pairings of the initial strings "1" and "0"
    //X is the final dominant pair and Y is the second to last dominant pair
    std::string rhythm;
    for (int i = 1; i <= x_amount; i++)
        rhythm += x;
    for (int i = 1; i <= y_amount; i++)
        rhythm += y;
    return rhythm;
}