Lessons from Giant Pizza

Lesson $1$: Recognize $2$-SAT when you see constraints of the form "at least one of two conditions must hold." that is the OR pattern. Lesson $2$: Model carefully. Map problem entities (toppings, courses, nodes) to boolean variables and constraints (customer wishes, conflicts) to clauses.

Lesson $3$: Trust the algorithm. The SCC-based satisfiability check is complete and correct. If it says unsatisfiable, no solution exists. If it says satisfiable, the constructed assignment works.