Fastest sorting method for k numbers and N elements, k <<< N

Given the very limited number of item types ( 0, 1and 2) , you just need to count the number of occurrences of each type. Then to print the "sorted" array, you repeatedly print the number of occurrences of each label. running time isO(N)

int balls[N] = {...};  // array of balls: initialized to whatever
int sorted_balls[N];   // sorted array of balls (to be set below)
int counts[3] = {};    //   count of each label, zero initialized array.

// enumerate over the input array and count each label's occurance
for (int i = 0; i < N; i++)
{
    counts[balls[i]]++;
}

// sort the items by just printing each label the number of times it was counted above
int k = 0;
for (int j = 0; j < 3; j++)
{
    for (int x = 0; x < counts[j]; x++)
    {
        cout << j << ", ";   // print
        sorted_balls[k] = j; // store into the final sorted array
        k++;
    }
}