Hi Everyone!

I haven't been active lately because of interviews going on. Recently I appeared for Amazon Interview for Internship and there was a problem that I still have doubts with:

I confirmed with the interviewer that there is a formation of the cycle in this, he told me that cycle formation is possible and whenever it happens you have to break the chain there since you don't want to repeat the same elements

As you can see the graph is not an unweighted DAG, Hence, the problem became finding acyclic longest chain in a directed cyclic graph.

I wasn't able to come with a clear solution (O(n)) because it didn't feel right that how I can take care of cases with a cycle using maybe topological sort? So I wanted to ask what is the best possible complexity answer for this.

Thanks!

UPD: The problem might not even be of a graph, I have mentioned the original problem in the exact words as by the interviewer, not that you have to follow the graph approach, I just want to find any possible views on this.