How to get all subsets of an array?

Question

Given an array: [dog, cat, mouse]

what is the most elegant way to create:

[,,]
[,,mouse]
[,cat,]
[,cat,mouse]
[dog,,]
[dog,,mouse]
[dog,         


        

Answer 1

Here's an easy-to-follow solution along the lines of your conception:

private static void Test()
{
    string[] test = new string[3] { "dog", "cat", "mouse" };

    foreach (var x in Subsets(test))
        Console.WriteLine("[{0}]", string.Join(",", x));
}

public static IEnumerable<T[]> Subsets<T>(T[] source)
{
    int max = 1 << source.Length;
    for (int i = 0; i < max; i++)
    {
        T[] combination = new T[source.Length];

        for (int j = 0; j < source.Length; j++)
        {
            int tailIndex = source.Length - j - 1;
            combination[tailIndex] =
                ((i & (1 << j)) != 0) ? source[tailIndex] : default(T);
        }

        yield return combination;
    }
}

Answer 2

You can use the BitArray class to easily access the bits in a number:

string[] animals = { "Dog", "Cat", "Mouse" };
List<string[]> result = new List<string[]>();
int cnt = 1 << animals.Length;
for (int i = 0; i < cnt; i++) {
   string[] item = new string[animals.Length];
   BitArray b = new BitArray(i);
   for (int j = 0; j < item.Length; j++) {
      item[j] = b[j] ? animals[j] : null;
   }
   result.Add(item);
}

Answer 3

static IEnumerable<IEnumerable<T>> GetSubsets<T>(IList<T> set)
{
    var state = new BitArray(set.Count);
    do
        yield return Enumerable.Range(0, state.Count)
                               .Select(i => state[i] ? set[i] : default(T));
    while (Increment(state));
}

static bool Increment(BitArray flags)
{
    int x = flags.Count - 1; 
    while (x >= 0 && flags[x]) flags[x--] = false ;
    if (x >= 0) flags[x] = true;
    return x >= 0;
}

Usage:

foreach(var strings in GetSubsets(new[] { "dog", "cat", "mouse" }))
    Console.WriteLine(string.Join(", ", strings.ToArray()));

Answer 4

Here's a solution similar to David B's method, but perhaps more suitable if it's really a requirement that you get back sets with the original number of elements (even if empty):.

static public List<List<T>> GetSubsets<T>(IEnumerable<T> originalList)
{
    if (originalList.Count() == 0)
        return new List<List<T>>() { new List<T>() };

    var setsFound = new List<List<T>>();
    foreach (var list in GetSubsets(originalList.Skip(1)))
    {                
        setsFound.Add(originalList.Take(1).Concat(list).ToList());
        setsFound.Add(new List<T>() { default(T) }.Concat(list).ToList());
    }
    return setsFound;
}

If you pass in a list of three strings, you'll get back eight lists with three elements each (but some elements will be null).

Answer 5

Guffa's answer had the basic functionality that I was searching, however the line with

BitArray b = new BitArray(i);

did not work for me, it gave an ArgumentOutOfRangeException. Here's my slightly adjusted and working code:

string[] array = { "A", "B", "C","D" };
int count = 1 << array.Length; // 2^n

for (int i = 0; i < count; i++)
{
    string[] items = new string[array.Length];
    BitArray b = new BitArray(BitConverter.GetBytes(i));
    for (int bit = 0; bit < array.Length; bit++) {
        items[bit] = b[bit] ? array[bit] : "";
    }
    Console.WriteLine(String.Join("",items));
}

Answer 6

I'm not very familiar with C# but I'm sure there's something like:

// input: Array A
foreach S in AllSubsetsOf1ToN(A.Length): 
    print (S.toArray().map(lambda x |> A[x]));

---

Ok, I've been told the answer above won't work. If you value elegance over efficiency, I would try recursion, in my crappy pseudocode:

Array_Of_Sets subsets(Array a) 
{
    if (a.length == 0) 
         return [new Set();] // emptyset
    return subsets(a[1:]) + subsets(a[1:]) . map(lambda x |> x.add a[0]) 
}