@above
Many ways to do this problem

One will be to find the bfs (there will be many and this will lead to
a forest )
This , in turn can be done in O(e+v) , using adjancy list or matrix .
Whenever , we cannot go further , start from any new uncovered node ,
and keep exploring recursively .Keep a boolean flag array for the
elements you have already covered .

Also  , this looks like a union find problem .So one can also do this
using disjoint set data structure .

http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=disjointDataStructure

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