Performance issue with generation of random unique numbers

Question

I have a situation where by I need to create tens of thousands of unique numbers. However these numbers must be 9 digits and cannot contain any 0\'s. My current approach is

Answer 1

Try avoiding checks making sure that you always pick up a unique number:

static char[] base9 = "123456789".ToCharArray();

static string ConvertToBase9(int value) {
    int num = 9;
    char[] result = new char[9];
    for (int i = 8; i >= 0; --i) { 
        result[i] = base9[value % num];
        value = value / num;
    }
    return new string(result);
}

public static void generateIdentifiers(int quantity) {
    var uniqueIdentifiers = new List(quantity);
    // we have 387420489 (9^9) possible numbers of 9 digits in base 9.
    // if we choose a number that is prime to that we can easily get always
    // unique numbers
    Random random = new Random();
    int inc = 386000000;
    int seed = random.Next(0, 387420489);
    while (uniqueIdentifiers.Count < quantity) {
        uniqueIdentifiers.Add(ConvertToBase9(seed));
        seed += inc;
        seed %= 387420489;
    }
}

I'll try to explain the idea behind with small numbers...

Suppose you have at most 7 possible combinations. We choose a number that is prime to 7, e.g. 3, and a random starting number, e.g. 4.

At each round, we add 3 to our current number, and then we take the result modulo 7, so we get this sequence:

4 -> 4 + 3 % 7 = 0
0 -> 0 + 3 % 7 = 3
3 -> 3 + 3 % 7 = 6
6 -> 6 + 6 % 7 = 5

In this way, we generate all the values from 0 to 6 in a non-consecutive way. In my example, we are doing the same, but we have 9^9 possible combinations, and as a number prime to that I choose 386000000 (you just have to avoid multiples of 3).

Then, I pick up the number in the sequence and I convert it to base 9.

I hope this is clear :)

I tested it on my machine, and generating 400k unique values took ~ 1 second.