Algorithms Question, thanks

Let G = (V, E) be an undirected graph with n nodes. A subset of the nodes is called an independent set if no two of them are joined by an edge. Finding large indepenedent sets is difficult in general; but here we will see that it can be done efficiently in a graph which is "simple" enough. Recall that a graph (V. E) a path if its nodes can be written as ui,V2, . . . , Vn, with an edge between v, and v if and only if i and j differ by 1. Let each node v, have a positive integer weight w, The goal of this question is to find an independent set in a path G whose total weight is as large as possible. (a) Show that the following "heaviest first" algorithm does not always find the max- imum weight independent set While there are nodes in G, add the heaviest remaining node to the independent set and delete it and its neighbors from G