3. 20+5 25 points] (Biconnected components) An undirected graph representing an electricity grid should really have the property of being biconnected. This has the effect that if a tree falls on one power line, all the lights are still on. An undirected graph is biconnected, if it is connected and every edge belongs to a simple (a) Design an DFS-based algorithm A that decides whether a graph G is biconnected. Write pseudo-code for A. Use a recursive procedure to describe A. Instead of just identifying which vertices are already visited, your DFS algorithm should compute the depth of each vertex in the DFS tree. Before a vertex is placed in the tree, its depth is ini tialized to oo. Hint: Each vertex v has to learn the depth v.h of the highest vertex in the DFS tree T to which there is an edge from some vertex in the subtree of T rooted at w. (b) Every vertex v knows an increasingly better upper bound on v.h. At which time does v know the proper value of v.h