Course Schedule IV

Because many prerequisite queries must be answered, preprocess reachability instead of running DFS per query. For a DAG, topologically process courses while maintaining for each course the set of its prerequisites. For edge u to v, union prereq[u] and u into prereq[v]; bitsets make this efficient for moderate n. Then query (a,b) is true when a belongs to prereq[b]. Floyd-Warshall is an alternative O(n cubed) closure when n is small and implementation simplicity matters. Be clear about edge direction: u prerequisite of v means u -> v. If cycles are possible, clarify whether they are invalid input or require general reachability. Bitset/topological preprocessing is roughly O((n+e)*n/wordSize) with O(n squared) storage, followed by O(1) queries.