Since the set cover problem is NP-Complete you can only use a greedy algorithm for small universes or the algorithm will never finish. But since your example only has 5 sets, it's not too bad.

It can be very simple if you use recursion. I'm guessing this is for an assignment, so I'm not writing the code for you, but I'll help you get started and help you if you get stuck.

Here's how I would approach it. Loop through your sets using a for loop that does this:

Take the current set S

Does S cover the universe?

If so return 1 and the name of the set.

If not, remove the sets in S from the universe and loop through the other sets (only the ones after the current one) and find the minimum that covers the remaining portion of the universe (by calling the same function this code is in). Return 1+the minimum and the set that covered plus this set.

This will give the minimum set cover in a fairly efficient time. To speed it up some, keep track of how many sets have been picked so far and the current minimum so you can just quit if the current set of sets is bigger or equal to the current minimum.

If the above is confusing, try to figure it out and let us know where you are stuck.

It can be very simple if you use recursion. I'm guessing this is for an assignment, so I'm not writing the code for you, but I'll help you get started and help you if you get stuck.

Here's how I would approach it. Loop through your sets using a for loop that does this:

Take the current set S

Does S cover the universe?

If so return 1 and the name of the set.

If not, remove the sets in S from the universe and loop through the other sets (only the ones after the current one) and find the minimum that covers the remaining portion of the universe (by calling the same function this code is in). Return 1+the minimum and the set that covered plus this set.

This will give the minimum set cover in a fairly efficient time. To speed it up some, keep track of how many sets have been picked so far and the current minimum so you can just quit if the current set of sets is bigger or equal to the current minimum.

If the above is confusing, try to figure it out and let us know where you are stuck.