1) In the matrix chain multiplication algorithm, specify the dynamic programming solution in terms of the...

 

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1) In the matrix chain multiplication algorithm, specify the dynamic programming solution in terms of the number of scalar multiplications that are carried out to multiply n matrices, denoted by C [1, n]. 2) Apply the dynamic programming algorithm to the following instance of the matrix chain multiplication algorithm: M: 54 M2: 46 M3: 62 M4: 27 M5:7 6 3) Determine the order of matrix multiplications that gives the least number of scalar multiplications when multiplying i) The five matrices. ii) The first four matrices (MM2 M3 M4). Note: Show all your work. Consider the optimization problem max 4u1+5u2+4u3+8u4+6u5 4u1+6u2+5u3+9u4+7u5 19 uj0, j=1,...,5. (a) Assume that all u; may take only values 0 or 1. Solve the problem by dynamic programming. Draw the graph of the equivalent longest path problem. (b) Assume that all u; may take nonnegative integer values. Solve the problem by dynamic programming. In both cases, use the backward version of dynamic programming, calculating the value functions VN(x), VN1(x), ., V(x) for all possible states x. 1) In the matrix chain multiplication algorithm, specify the dynamic programming solution in terms of the number of scalar multiplications that are carried out to multiply n matrices, denoted by C [1, n]. 2) Apply the dynamic programming algorithm to the following instance of the matrix chain multiplication algorithm: M: 54 M2: 46 M3: 62 M4: 27 M5:7 6 3) Determine the order of matrix multiplications that gives the least number of scalar multiplications when multiplying i) The five matrices. ii) The first four matrices (MM2 M3 M4). Note: Show all your work. Consider the optimization problem max 4u1+5u2+4u3+8u4+6u5 4u1+6u2+5u3+9u4+7u5 19 uj0, j=1,...,5. (a) Assume that all u; may take only values 0 or 1. Solve the problem by dynamic programming. Draw the graph of the equivalent longest path problem. (b) Assume that all u; may take nonnegative integer values. Solve the problem by dynamic programming. In both cases, use the backward version of dynamic programming, calculating the value functions VN(x), VN1(x), ., V(x) for all possible states x.