Problem 3 [40 points] Suppose you are given an (undirected, unweighted) graph G = (V, E). The graph has colored edges, and so you are also given a partition of the edges E = RUB into two sets, the red edges and the blue edges. (a) Give a polynomial time algorithm to compute a spanning tree of G with as many red edges as possible. Prove your algorithm is correct and analyze its running time