Given a weighted digraph $G$, and collections of vertices $R, S \subset V$ , consider the problem of finding a shortest length path joining a vertex $r\in R$ to a vertex $s\in S$. Reduce this to the shortest path problem from a given vertex to all other vertices.
I have been looking at this question for a while and I'm struggling to articulate what I am thinking. Clearly I should start by taking some fixed $a\in R$ and finding all the shortest paths from a to every other vertex, but I am unsure how to create the paths from any other $r\in R \setminus a$ to $s\in S$ since I cannot guarantee they are the shortest.