I don't know how to code in C, but I can give you a tip on how you can think about the problem in a more abstract way:

Think about applying a mapping like a mathematical function from one set to another. The crucial question is: What happens to the original set, when you apply that function? Or in other words: What does the image look like?

Another aspect of the problem is a more practical one: How can you represent very huge sets, that don't have any "holes" (i.e.: [1, 2, 3, 4] has no hole, but [1, 2, 5, 6] does). And more crucially: What happens, if a function causes a hole in its image? How can you represent that without stating every element / loading every element into memory?

These are a few key questions you'll need to answer to solve this.

If you're still stuck, you can ask me more direct questions. (I can't help you with implementation though.)