"Caught" in a plagiarism program for an exam but not actually cheating

Don't panic. If you did nothing wrong, all you need is to explain what you did and everything shall be OK.

Based on some similarity metric (computed automatically or spotted by a naked eye), your lecturer or teaching assistant marked your work as a potential case of collusion (working together on individual exams). Now you are invited to a meeting, whose purpose is simply to investigate what happened. As a lecturer, I attend them routinely (from the other side than the one you find yourself in), and I can tell you that 50%+ of cases are dismissed immediately.

During the meeting, you will be asked a number of questions. One of them is likely going to be "did you work together with someone"? or "did you share your work with someone"? Answer honestly and provide details when they ask you to. Don't stress out and try to remain calm and polite as much as possible. If you need support, you usually can bring a student union representative or a personal counsel with you.

Don't overthink it. You are not accused at this stage, the misconduct is only suspected by the system. This meeting is not a trial, it's more like a routine checkup. There can be similarities between you work and the work of other students, but as you said, if the problems are simple and straightforward, the similarities are quite possible.

Most often than not, when programmers face a common problem, a common software pattern will emerge.

In this case all you need to do is to explain your rationale and defend your choices. If you can explain the rationale behind it, we'll have a better consideration of you and the case will be dismissed right away.

Note: This belongs to comment's section. Unfortunately I don't have enough points to comment under @Dmitry Savostyanov's stellar answer, hence this

While common problems have common solutions individual programmers leave individual fingerprints which get copied and can be the hallmarks of cheating. So, for instance: int a ,b; is distinct from int a,b; and int a, b; to a plagiarism program but identical code.

Never copy-paste other sources because you will bring these tell-tale fingerprints across.

It's likely that these non programmatic tell-tales and style choices are what mark your code as suspiciously similar.