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Question: let m1 m2 mn be a...

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Let M1, M2, . . . , Mn be a sequence of matrices. Each matrix Mi has dimension ri-1 × ri, The minimum cost of multiplying matrices Mi x M2 x... x Mn can be computed as follows. Let cij, i Sj, be the minimum cost of multiplying matrices M x Mi+x... x Mj. Then we can show that if j i (a) (10) Design an efficient algorithm to compute these cijs in a way that when cij is to be computed, all the ciks and all the ck+lýs which are needed have already been computed. (b) (5) Use n 8 as an example to show the order of the cis are computed by your algorithm. (c) (5) Which cij is the minimum cost to multiply these matrices?

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