Question: 1. Design and analyze an efficient algorithm to solve the following problem: Input: a connected, weighted, undirected graph G = (V, E), and a

1. Design and analyze an efficient algorithm to solve the following problem:

1. Design and analyze an efficient algorithm to solve the following problem: Input: a connected, weighted, undirected graph G = (V, E), and a set ECE such that the graph (V, ) has no cycles. Output: a spanning tree T = (V, E') such that CE', and which has minimum weight among all such trees. In other words, it's like the MST problem, except that certain edges (namely, the members of ) are required to be in the tree. First describe your algorithm informally, using complete sentences, then give pseudo-code if you feel that it would be helpful. Then analyze its running time.

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