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COSC 3333HW4Homework 4Due Date: 7/31/16 11:59pm1.Use thedynamic programming techniqueto find an optimal parenthesization ofa matrix-chain product whose sequence of dimensions is <8, 5, 10, 30, 20, 6>.MatrixDimensionA18 * 5A25*10A310*30A430*20A520*6You may do this either by implementing the MATRIX-CHAIN-ORDERalgorithm in the text or by simulating the algorithm by hand. In either case, showthe dynamic programming tables at the end of the computation.2.We have 5 objects, and the weights and values areNo.12345w1020304050v2030666055The knapsack can carry a weight not exceeding 90, find a subset items and give thetotal weight and value for following algorithms:1)By using the algorithm of greedy of value for 0-1 knapsack problem? By selectingthehighestvalue first.2)By using the algorithm of greedy of weight for 0-1 knapsack problem? Byselectinglightestitem first.3)By using the algorithm of greedy of density for 0-1 knapsack problem? Byselecting the highestdensityitem first.4)By using the algorithm of greedy of density forfractional knapsackproblem?By selecting the highest density item first.3.Using Floyd’s algorithm (See Algorithm2 slide 54), calculate the length of theshortest path between each pair of nodes in the graph by constructing a matrix.Give the each step of the adjacency matrix.

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