In class (and chapter 5.4) we looked at a greedy algorithm to solve the set cover problem, and proved that if the optimal set cover has size k, then our greedy algorithm willl find a set cover of size at most klog, n. here is a generalization of the set cover problem. input: a set of elements b of size n; sets c b; positive weights w t' output: a selection of the sets s, whose union is b. cost: the sum of the weights w, for the sets that were picked. design an algorithm to find the set cover with approximately the smallest cost. prove that if there is a solution with cost k, then your algorithm will find a solution with cost o(k logn).