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Ex.5 (Dynamic Programming on Trees) Let G=(V,E) be an undirected graph. If G is connected and acyclic, then it is called a tree. A subset I of the vertices V is called an independent set if no two vertices of I are adjacent. Assume that a positive weight w(i) is associated with each vertex i. We define the weight w(I) of an independent set I to be the sum of the weights of all the vertices in I. That is, w(I)=iIw(i). Further, an independent set is called a maximum weight independent set if it has the maximum possible weight among all independent sets. Give an O(n) time algorithm, which finds the maximum weight independent set of a graph G for the case that G is a tree. (Hint: we solved the same problem in class when we were doing dynamic programming, for the case that the graph was a path, instead of a tree.)