Combination

A permutation is a group of generated numbers in an order, but a combination is a group of numbers without an order. As with permutations, we use a combination generation class with a skip function.
Combinatorial generation is basically a class like this:

public class Combination{
    private int N;
    private int R;
    public  int[] Index=null;
    private bool First=false;

    public Combination( int N, int R ){
        this.N=N;
        this.R=R;
        if( R>0 && R<=N ){
            Cmb=new int[R];
            Cmb[0]=0;
            for( int m=1; m<R; m++ ) Index[m]=Index[m-1]+1;
            First=true;
        }
    }
    public bool Successor(int skip=int.MaxValue){
        if(N<=0) return false;
        if(First){ First=false; return (Index!=null); }

        int k;
        if(Index[0]==N-R) return false;
        if(skip<R-1){
            for(k=skip; k>=0; k--){ if(Index[k]<=N-R) break; }
            if(k<0)  return false;
        }
        else{
            for(k=R-1; k>0 && Index[k]==N-R+k; --k);
        }

        ++Index[k];
        for(int j=k; j<R-1; ++j)  Index[j+1]=Index[j]+1;
        return true;
    }
}

Combination is used as follows.
The change position of the next combination generation can be changed dynamically. The position specification is from 0 to (combination size - 1), In other cases, or if the specification is omitted, the skip function will not work.

>var cmb = new Combination (6,3);
int skip=4;
    while(cmb.Successor(skip) ){
      //  (Evaluation process : Set change position skip for next combination generation)
}

Test code

static void Main( string[ ] args ){
    for( int skip=0; skip<5; skip++ ){
        Combination cmb = new Combination(6,4);
        Console.WriteLine("\n ===== Combination(6,4) skip={0}",skip );
        while( cmb.Successor(skip) )  Console.WriteLine(cmb);
        Console.ReadKey();
    }
}

Execution results

(left: combination generation results, right: working data inside the function)

===== Combination(6,4) skip=0
 0 1 2 3
 1 2 3 4
 2 3 4 5

 ===== Combination(6,4) skip=1
 0 1 2 3
 0 2 3 4
 0 3 4 5
 1 2 3 4
 1 3 4 5
 2 3 4 5

 ===== Combination(6,4) skip=2
 0 1 2 3
 0 1 3 4
 0 2 3 4
 0 3 4 5
 1 2 3 4
 1 3 4 5
 2 3 4 5
 
===== Combination(6,4) skip=3
 0 1 2 3
 0 1 2 4
 0 1 2 5
 0 1 3 4
 0 1 3 5
 0 1 4 5
 0 2 3 4
 0 2 3 5
 0 2 4 5
 0 3 4 5
 1 2 3 4
 1 2 3 5
 1 2 4 5
 1 3 4 5
 2 3 4 5

 ===== Combination(6,4) skip=4
 0 1 2 3
 0 1 2 4
 0 1 2 5
 0 1 3 4
 0 1 3 5
 0 1 4 5
 0 2 3 4
 0 2 3 5
 0 2 4 5
 0 3 4 5
 1 2 3 4
 1 2 3 5
 1 2 4 5
 1 3 4 5
 2 3 4 5