What is the best way to find all combinations of items in an array?

What is the best way to find all combinations of items in an array in c#?

Solution 1:

UPDATED

Here are a set of generic functions (require .net 3.5 or higher) for different scenarios. The outputs are for a list of {1, 2, 3, 4} and a length of 2.

Permutations with repetition

static IEnumerable<IEnumerable<T>> 
    GetPermutationsWithRept<T>(IEnumerable<T> list, int length)
{
    if (length == 1) return list.Select(t => new T[] { t });
    return GetPermutationsWithRept(list, length - 1)
        .SelectMany(t => list, 
            (t1, t2) => t1.Concat(new T[] { t2 }));
}

Output:

{1,1} {1,2} {1,3} {1,4} {2,1} {2,2} {2,3} {2,4} {3,1} {3,2} {3,3} {3,4} {4,1} {4,2} {4,3} {4,4}

Permutations

static IEnumerable<IEnumerable<T>>
    GetPermutations<T>(IEnumerable<T> list, int length)
{
    if (length == 1) return list.Select(t => new T[] { t });
    return GetPermutations(list, length - 1)
        .SelectMany(t => list.Where(o => !t.Contains(o)),
            (t1, t2) => t1.Concat(new T[] { t2 }));
}

Output:

{1,2} {1,3} {1,4} {2,1} {2,3} {2,4} {3,1} {3,2} {3,4} {4,1} {4,2} {4,3}

K-combinations with repetition

static IEnumerable<IEnumerable<T>> 
    GetKCombsWithRept<T>(IEnumerable<T> list, int length) where T : IComparable
{
    if (length == 1) return list.Select(t => new T[] { t });
    return GetKCombsWithRept(list, length - 1)
        .SelectMany(t => list.Where(o => o.CompareTo(t.Last()) >= 0), 
            (t1, t2) => t1.Concat(new T[] { t2 }));
}

Output:

{1,1} {1,2} {1,3} {1,4} {2,2} {2,3} {2,4} {3,3} {3,4} {4,4}

K-combinations

static IEnumerable<IEnumerable<T>> 
    GetKCombs<T>(IEnumerable<T> list, int length) where T : IComparable
{
    if (length == 1) return list.Select(t => new T[] { t });
    return GetKCombs(list, length - 1)
        .SelectMany(t => list.Where(o => o.CompareTo(t.Last()) > 0), 
            (t1, t2) => t1.Concat(new T[] { t2 }));
}

Output:

{1,2} {1,3} {1,4} {2,3} {2,4} {3,4}

Solution 2:

That's called permutations.

This can give you the permutations of any collection:

public class Permutation {

  public static IEnumerable<T[]> GetPermutations<T>(T[] items) {
    int[] work = new int[items.Length];
    for (int i = 0; i < work.Length; i++) {
      work[i] = i;
    }
    foreach (int[] index in GetIntPermutations(work, 0, work.Length)) {
      T[] result = new T[index.Length];
      for (int i = 0; i < index.Length; i++) result[i] = items[index[i]];
      yield return result;
    }
  }

  public static IEnumerable<int[]> GetIntPermutations(int[] index, int offset, int len) {
    if (len == 1) {
      yield return index;
    } else if (len == 2) {
      yield return index;
      Swap(index, offset, offset + 1);
      yield return index;
      Swap(index, offset, offset + 1);
    } else {
      foreach (int[] result in GetIntPermutations(index, offset + 1, len - 1)) {
        yield return result;
      }
      for (int i = 1; i < len; i++) {
        Swap(index, offset, offset + i);
        foreach (int[] result in GetIntPermutations(index, offset + 1, len - 1)) {
          yield return result;
        }
        Swap(index, offset, offset + i);
      }
    }
  }

  private static void Swap(int[] index, int offset1, int offset2) {
    int temp = index[offset1];
    index[offset1] = index[offset2];
    index[offset2] = temp;
  }

}

Example:

string[] items = { "one", "two", "three" };
foreach (string[] permutation in Permutation.GetPermutations<string>(items)) {
  Console.WriteLine(String.Join(", ", permutation));
}

Solution 3:

It is O(n!)

static List<List<int>> comb;
static bool[] used;
static void GetCombinationSample()
{
    int[] arr = { 10, 50, 3, 1, 2 };
    used = new bool[arr.Length];
    used.Fill(false);
    comb = new List<List<int>>();
    List<int> c = new List<int>();
    GetComb(arr, 0, c);
    foreach (var item in comb)
    {
        foreach (var x in item)
        {
            Console.Write(x + ",");
        }
        Console.WriteLine("");
    }
}
static void GetComb(int[] arr, int colindex, List<int> c)
{

    if (colindex >= arr.Length)
    {
        comb.Add(new List<int>(c));
        return;
    }
    for (int i = 0; i < arr.Length; i++)
    {
        if (!used[i])
        {
            used[i] = true;
            c.Add(arr[i]);
            GetComb(arr, colindex + 1, c);
            c.RemoveAt(c.Count - 1);
            used[i] = false;
        }
    }
}

Solution 4:

Regarding Pengyang answer: Here is my generic function which can return all the combinations from a list of T:

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

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

Example 1:n=3,k=2

IEnumerable<IEnumerable<int>> result =
    GetCombinations(Enumerable.Range(1, 3), 2);

Output - a list of integer-lists:

{1, 1} {1, 2} {1, 3} {2, 1} {2, 2} {2, 3} {3, 1} {3, 2} {3, 3}

.............................................................................

I ran this example and I am not quite sure about the rightness of the results.

Example 2:n=3, k=3

IEnumerable<IEnumerable<int>> result =
    GetCombinations(Enumerable.Range(1, 3), 3);

Output - a list of integer-lists:

{1, 1, 1} {1, 1, 2} {1, 1, 3} 
{1, 2, 1} {1, 2, 2} {1, 2, 3} 
{1, 3, 1} {1, 3, 2} {1, 3, 3}
{2, 1, 1} {2, 1, 2} {2, 1, 3} 
{2, 2, 1} {2, 2, 2} {2, 2, 3} 
{2, 3, 1} {2, 3, 2} {2, 3, 3}
{3, 1, 1} {3, 1, 2} {3, 1, 3} 
{3, 2, 1} {3, 2, 2} {3, 2, 3} 
{3, 3, 1} {3, 3, 2} {3, 3, 3}

This should not happen with combinations otherwise it should specify it is with repetition.See article http://en.wikipedia.org/wiki/Combinations