Dynamic Programming GATE 2015 Question #6819 with Solution

GATE 2015 · Set-1

AlgorithmsDynamic ProgrammingmediumMCQ2 marks

Consider the problem of finding a maximum weight independent set in a path graph G = (V, E), where V = {v1, v2, ..., vn} and edges connect vi to vi+1 for each 1 <= i < n. Let w(vi) denote the non-negative weight of vertex vi. Which of the following recurrence relations correctly computes the maximum weight M(i) of an independent set in the prefix path {v1, ..., vi}?

AM(i) = max(M(i - 1), M(i - 2) + w(vi))BM(i) = M(i - 1) + M(i - 2) + w(vi)CM(i) = max(M(i - 1) + w(vi), M(i - 2))DM(i) = M(i - 2) + w(vi)

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