That's to say, if it's relevant now (at time of speaking) that you still don't cross paths, present tense don't is appropriate. But if you're reminiscing (perhaps decades later) about your schooldays, say, then it's all in the past - so you'd use didn't.

Which is correct did not or didn t?

In terms of when you should use did not as opposed to didn't, I think it depends on the situation, and on your relationship with the intended audience. If you're writing a dissertation or a report to your boss, maybe use did not; if you're writing a text or email to your friend, I'm sure didn't would be just fine.

When to use did not and does not?

Did is used for past tense. Doesn't is the contracted (short) form of does not. Don't is the contracted form of do not. 1.