c# - How to generate all subsets of a given size? -

given number n, , subset size, want possible subsets of specified size of set {1, ..., n}.

expected result for n = 5 , subsetsize = 4:

{{1,2,3,4}, {1,2,3,5}, {1,3,4,5}, {1,2,4,5}, {2,3,4,5}} 

(that list<list<int>>)

that means need (subsetsize choose n) subsets (newton's symbol).

any idea algorithm find me such list of lists of integers? i'm implementing in c#, if matters.

internal class program {     private static ienumerable<ienumerable<int>> subsets(int n, int subsetsize)     {         ienumerable<int> sequence = enumerable.range(1, n);          // generate list of sequences containing 1 element e.g. {1}, {2}, ...         var oneelemsequences = sequence.select(x => new[] { x }).tolist();          // generate list of int sequences         var result = new list<list<int>>();         // add initial empty set         result.add(new list<int>());          // generate powerset, skip sequences long         foreach (var oneelemsequence in oneelemsequences)         {             int length = result.count;              (int = 0; < length; i++)             {                 if (result[i].count >= subsetsize)                     continue;                  result.add(result[i].concat(oneelemsequence).tolist());             }         }          return result.where(x => x.count == subsetsize);     }      private static void outputsubset(int n, ienumerable<ienumerable<int>> subsets)     {         console.writeline("n: {0}", n);         foreach (var subset in subsets)         {             console.writeline("\t{0}", string.join(" ", subset.select(x => x.tostring())));         }     }      private static void main()     {         (int n = 1; n < 500; n++)         {             var subsets = subsets(n, subsetsize: 4);             outputsubset(n, subsets);         }     } } 

output:

n: 1 n: 2 n: 3 n: 4         1 2 3 4 n: 5         1 2 3 4         1 2 3 5         1 2 4 5         1 3 4 5         2 3 4 5 n: 6         1 2 3 4         1 2 3 5         1 2 4 5         1 3 4 5         2 3 4 5         1 2 3 6         1 2 4 6         1 3 4 6         2 3 4 6         1 2 5 6         1 3 5 6         2 3 5 6         1 4 5 6         2 4 5 6         3 4 5 6 n: 7         1 2 3 4         1 2 3 5         1 2 4 5         1 3 4 5         2 3 4 5         1 2 3 6         ...