Give a polynomial-time algorithm for the following problem. We are given a binary tree T = (V, E) with an even number of nodes, and a nonnegative weight on each edge. We wish to find a partition of the nodes V into two sets of equal size so that the weight of the cut between the two sets is as large as possible (i.e., the total weight of edges with one end in each set is as large as possible). Note that the restriction that the graph is a tree is crucial here, but the assumption that the tree is binary is not. The problem is NP-hard in general graphs.