Practice Problem 3

You have n events. Each event can be in slot $1$ or slot $2$. Some pairs conflict in slot $1$, others conflict in slot $2$, some conflict in both slots. Model: x_i is true if event i is in slot $1$. Conflicts give you clauses based on which slots they conflict in.

Implement $2$-SAT to find a valid schedule or report impossible. This is a practical scheduling application. Test with different conflict patterns to understand the algorithm's behavior and when solutions exist.