Dynamic programming can be used to develop an algorithm for solving the matrix-chain multiplication problem introduced in Section 3.3. This is the problem of determining how the product
a) Show that the brute-force method of determining the minimum number of integer multiplications needed to solve amatrix-chain multiplication problem has exponential worst-case complexity. [Hint: Do this by first showing that the order of multiplication of matrices is specified by parenthesizing the product. Then, use Example 5 and the result of part (c) of Exercise 43 in Section 8.4.)
b) Denote by
c) Explain why part (b)leads to the recurrence relation
e) Show that your algorithm from part (d) has 0(n3) worst-case complexity in terms of multiplications of integers.
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Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
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