Question: Let G=(V, E) be a undirected graph (in fact, a path), where V={v1, v2, ..., vn} contains n nodes and E={(vi, vi+1), (vi, vi+2)|i=1, 2,

Let G=(V, E) be a undirected graph (in fact, a path), where V={v1, v2, ..., vn} contains n nodes and E={(vi, vi+1), (vi, vi+2)|i=1, 2, ..., n-2} {(vn-1, vn) . Each node vi V has a weight w(vi) 0. An independent set V' V of the graph is a subset of V such that for any pair of nodes vi V' and vj V', (vi, vj) is not in E. The weight of the independent set V' is the total weight of the nodes in V'. Design a DP algorithm that finds the maximum weight independent set V' in G.\

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