4. Given a weighted, undirected graph G, the product-weight of a spanning tree T of G is the product of the weights of edges in the tree T. (For example, for the graph shown below on the left, the product-weight of the spanning tree shown on the right is 2.3 4 = 24.) @2. 0 . . B200 4.0 4.0 Design an algorithm that takes as input any weighted, undirected graph G such that edge weights are positive and outputs a spanning tree of G with maximum product-weight. (a) (1 point) Give pseudocode for your algorithm. (b) (1 point) Prove that your algorithm always outputs a spanning tree with maximum product-weight