Equivalence relation and the resulting subsets

[Melvik12]

I wanna write a program which should give me the resulting subsets according to an Equivalence relation what I should do?
thanks!

[mehdi62b]

you should use Disjoint Set
you should merge the pair elements which have common elemts for making the resulting subsets!

[mehdi62b]

BTW an implemeted DisjiontSet includes two main functions

1. Merge O(1)
2. Find O(n)

public class DisjointSet
  {
   int[] inner=new int[12];
   public void Add(int a,int b)
   {
	if(inner[a]==0 && inner[b]==0)
	{
	 if(a<b){inner[a]=a;inner[b]=a;}
	 else
	 {inner[a]=b;inner[b]=b;}
	}
	else
	{
	 if(inner[a]!=0 && inner[b]!=0)
	 {
	  int t1=findx(inner[a]);
	  int t2=findx(inner[b]);
	  merge(t1,t2);
	 }
	 else
	 {
	  if(inner[a]!=0 )
	  {
	   int t=findx(inner[a]);
	   merge(t,b);
	  }
	  else
	  {
	   int t=findx(inner[b]);
	   merge(t,a);
	  }
	 }
	}
   }
   public string output()
   {
	int[] innerTemp=new int[12];
	ArrayList ar=new ArrayList();
	
	for(int j=inner.Length-1;j>0;j--)
	{
	 if(inner[j]!=0 && innerTemp[j]!=-1)
	 {
	  ArrayList innerar=new ArrayList();
	  int root=this.findx(j);
	  for(int i=inner.Length-1;i>0;i--)
	  {
	   if(inner[i]!=0 && innerTemp[i]!=-1 
		&& root==findx(i))
	   {
		int d=i;
		while(d!=root)
		{
		 
		 int t=d;
		 d=inner[d];
		 innerTemp[t]=-1;
		 innerar.Add(t);
		}
	   }
	  }
	  innerar.Add(root);
	  innerTemp[root]=-1;
	  ar.Add(innerar);
	 }
	}
	string result="";
	foreach(ArrayList ar1 in ar)
	{
	 for(int i=ar1.Count-1;i>=0;i--)
	 {
	  result+=ar1[i].ToString()+",";
	 }
	 result+=Environment.NewLine;
	}
	return result;
   }
   private int findx(int a)
   {
	while(inner[a]!=a){a=inner[a];}
	return a;
   }
   private void merge(int a,int b)
   {
	if(a<b)
	 inner[b]=a;
	else
	 inner[a]=b;
   }
  }
  private string testDisjointset()
  {
   DisjointSet dsj=new DisjointSet();
   dsj.Add(1,5);
   dsj.Add(1,6);
   dsj.Add(6,2);
   dsj.Add(7,3);
   dsj.Add(4,10);
   return dsj.output();
  }