Combinations Algorithm for 3 groups of more values

Question

I need to create a procedure that will allow me to get the full set of combinations of three repeated values ​​uniquely for three or more groups.

For example I can have 3 groups (R1 - R2 - R3) and three values ​​(A - AB - B) and I have to get all the possible combinations divided into 3 groups.

Like this:

Groups    1°   2°   3°   4°   5°   .......

R1        A -  A -  AB - AB - AB   ...
R2        A -  A -  A  - A  - BB   ...
R3        A -  AB - A  - A  - A    ...

I have to be sure that all possible sequences are present and never repeated.

Unfortunately I'm new in the world of programming and I have no knowledge of combinatorics. I could not figure out how to handle it...

I apologize if I was unclear, and thank you in advance to anyone who can give me some help.

Answer 1

I think you want all combinations for your values....

Here is the generic way to do it in C#...

static IEnumerable<IEnumerable<T>> Combinations<T>(IEnumerable<T> list, int length)
{
    if (length == 1) return list.Select(t => new T[] { t });

    return Combinations(list, length - 1)
        .SelectMany(t => list, (t1, t2) => t1.Concat(new T[] { t2 }));
}

And you call it like this...

    var groups = new List<string>() { "R1", "R2", "R3" };
    var values = new List<string>() { "AA", "AB", "BB" };
    var combinations = Combinations(values, groups.Count);
    var i = 0;
    var stringFormat =  string.Join(", ", groups.Select(x => x +"={"+ i++ +"}"));
    // stringFormat looks like "R1={0}, R2={1}, R3={2}"
    foreach (var value in combinations)
    {
        var arrayOfValues = value.ToArray();  // each value is a list of the combinations.
        Console.WriteLine(string.Format(stringFormat, arrayOfValues));
    }

You mentioned your inexperience so I've included doing it the hard coded way which is easier to follow...

    var values = new List<string>() { "AA", "AB", "BB" };
    foreach (var value1 in values)
    {
        foreach (var value2 in values)
        {
            foreach (var value3 in values)
            {
                Console.WriteLine(string.Format("R1 = {0}, R2 = {1}, R3 = {2}", value1, value2, value3));
            }
        }
    }

With the output looking like so...

R1=AA, R2=AA, R3=AA
R1=AA, R2=AA, R3=AB
R1=AA, R2=AA, R3=BB
R1=AA, R2=AB, R3=AA
R1=AA, R2=AB, R3=AB
R1=AA, R2=AB, R3=BB
R1=AA, R2=BB, R3=AA
R1=AA, R2=BB, R3=AB
R1=AA, R2=BB, R3=BB
R1=AB, R2=AA, R3=AA
R1=AB, R2=AA, R3=AB
R1=AB, R2=AA, R3=BB
R1=AB, R2=AB, R3=AA
R1=AB, R2=AB, R3=AB
R1=AB, R2=AB, R3=BB
R1=AB, R2=BB, R3=AA
R1=AB, R2=BB, R3=AB
R1=AB, R2=BB, R3=BB
R1=BB, R2=AA, R3=AA
R1=BB, R2=AA, R3=AB
R1=BB, R2=AA, R3=BB
R1=BB, R2=AB, R3=AA
R1=BB, R2=AB, R3=AB
R1=BB, R2=AB, R3=BB
R1=BB, R2=BB, R3=AA
R1=BB, R2=BB, R3=AB
R1=BB, R2=BB, R3=BB