C# LINQ combinatorics: All Combinations of a Set without the Empty Set

Question

I have a set of strings, and I want to find all possible combinations of the strings and add them to a list. I want to end up with a list of a list of each combination of the strings, minus the empty set.

I have created a solution that does this exactly with a nested for loop. However I want to do this more elegantly, preferably with LINQ, and I am not so proficient with it because I'm still pretty new to it.

The solution should have 2^n - 1 lists of combinations where n is the cardinality of the original set. Here is a correct example of what I am looking for:

set = {a, b, c}

completedListOfCombinations = 
{
    {a},
    {b},
    {a, b},
    {c},
    {a, c},
    {b, c},
    {a, b, c}
}

Here is my working, basic but ugly solution that I crafted with help from: https://stackoverflow.com/a/3319652/3371287

List<string> myStrings =  new List<string> { "a", "b", "c" };

var allCombos = new List<List<string>>();

for (int i = 0; i < myStrings.Count; i++)
{
    int subsetCount = allCombos.Count;
    var m = new List<string>();
    m.Add(myStrings[i]);
    allCombos.Add(m);

    for (int j = 0; j < subsetCount; j++)
    {
        string[] subset = new string[allCombos.ElementAt(j).Count + 1];
        allCombos[j].CopyTo(subset, 0);
        subset[subset.Length - 1] = myStrings[i];
        allCombos.Add(subset.ToList());
    }

}

Can someone show me a more elegant solution for this? I have seen similar LINQ solutions that create Cartesian Pairs and lists with a threshold, but I have not been able to tweak them to what I need.

Answer 1

Providing that all the values in the list are unique:

  List <String> list = new List<String> { "a", "b", "c" };

  var result = Enumerable
    .Range(1, (1 << list.Count) - 1)
    .Select(index => list.Where((item, idx) => ((1 << idx) & index) != 0).ToList());

To print out:

Console.WriteLine(String
  .Join(Environment.NewLine, result
     .Select(line => String.Join(", ", line))));

The outcome is

a
b
a, b
c
a, c
b, c
a, b, c