Combination Generator in Linq

Question

Hi,

Is it possible to create some Linq that generates a List containing all possible combinations of a series of numbers??

If you enter "21" it would generate a list with the elements:

list[0] = "21"
list[1] = "22"
list[2] = "11"
list[3] = "12"

(Not nessesarily in that order)

I understand you can use range to do things like:

List<char> letterRange = Enumerable.Range('a', 'z' - 'a' + 1).Select(i => (Char)i).ToList(); //97 - 122 + 1 = 26 letters/iterations

Which generates the alphabet from a-z. But I can not seem to transfer this knowledge to make a combination generator

I have been able to figure it out with the following code, but it seems way too bulky and I am sure it can be done with a few lines. It really does feel like a bad solution I have made.

Imagine I have called GetAllCombinations("4321") if it helps

public static String[] GetAllCombinations(String s)
{
    var combinations = new string[PossibleCombinations(s.Length)];

    int n = PossibleCombinations(s.Length - 1);

    for (int i = 0; i < s.Length; i++)
    {
        String sub;
        String[] subs;

        if (i == 0)
        {
            sub = s.Substring(1); //Get the first number
        }
        else if (i == s.Length - 1)
        {
            sub = s.Substring(0, s.Length - 1);
        }
        else
        {
            sub = s.Substring(0, i) + s.Substring(i + 1); 
        }

        subs = GetAllCombinations(sub);

        for (int j = 0; j < subs.Length; j++)
        {
            combinations[i * n + j] = s[i] + subs[j];
        }
    }

    return combinations;
}
public static int PossibleCombinations(int n) //Combination possibilities. e.g 1-2-3-4 have 24 different combinations
{
    int result = 1;

    for (int i = 1; i <= n; i++)
        result *= i;

    return result;
}

Answer 1

What you're looking for are actually permutations. In short, permutations means that order is relevant (ie, 12 is different from 21) whereas a combination means order is irrelevant (12 and 21 are equivalent). For more information see Wikipedia.

See this thread.

As for doing is in pure LINQ, that sounds like using LINQ for the sake of using LINQ.

Answer 2

Here's a nice example on how to that: Permutations, Combinations, and Variations using C# Generic

Answer 3

For what it's worth, try something like this:

public static IEnumerable<string> GetPermutations(string s)
{
    if (s.Count() > 1)
        return from ch in s
               from permutation in GetPermutations(s.Remove(s.IndexOf(ch), 1))
               select string.Format("{0}{1}", ch, permutation);

    else
        return new string[] { s };
}

Answer 4

Take a look at this

http://fsharpcode.blogspot.com/2010/04/c-permutations-using-rx.html