Question 1: (50 pts) Consider the Differentiated Set Coverage Problem: Input: n items, U=1,2,,n, coverage requirements of the items f=f1,f2,,fn, m sets, S1,S2,,Sm, price of the sets p=p1,p2,,pm. Let x=x1,x2,,xm be the selection decisions of the sets, xi{0,1}. Output: A minimum price selection x of the sets S1,S2,,Sm that can cover the items in U at least f times. Ex: Let n=5 and U=1,2,3,4,5 having coverage requirements f=1,2,1,2,1. Let m=5 and S1={1,2},S2={2,3,4},S3={2,5},S4={3,4},S5={1,4} with prices p=5,6,10,2,4. For instance, item j=2U should be covered by at least f2=2 different sets Si. We note that item 2 can be covered by S1 with price p1=5, by S2 with price p2=6 and by S3 with price p3=10. 1. (20 pts) Determine a greedy selection rule for the sets. Design a greedy algorithm for the Differentiated Set Coverage Problem and report the pseudocode. 2. (10 pts) Discuss the time complexity of your greedy algorithm. Is it efficient? Can your algorithm find the optimum solution? 3. (20 pts) Implement your algorithm in Java. Use the input given in the example and report the console outputs. Report your Java code scripts