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 (http://en.wikipedia.org/wiki/Disjoint)
you should merge the pair elements which have common elemts for making the resulting subsets!

[mehdi62b]

BTW an implemeted DisjiontSet includes two main functions

Merge O(1)
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();
}