(b) (13 points) Shortest paths through a vertex: You are given a strongly connected directed graph G-(V, E) with positive edge weights, along with a particular node vo E V. Give an efficient algorithm for finding shortest paths between all pairs of nodes in G, with the one restriction that these paths must all pass through vo- (Note technically the algorithm may return a walk, i.e. an edge may be occur once before and once after the vertex vo.) Noi e that listing all these pailu; 4xpliciily is expensive, both m i,(rins ofnu? inno aud storage, as there are O(n2) pairs of vertices (where n = VI). Thus instead you should output some structure with O(n) size such that given a query pair (s,t), where s,t EV, the structure can be used to output the shortest path from s to t which passes through vo, and do so in time proportional to the length of the path