Given a sequence A formed by n positive numbers and a positive integer d, we are interested in a distant max-product subsequence (MPS) of A, which is a subsequence of A formed by elements whose indices are at least d units apart and have the maximum product. Describe a dynamic programming algorithm that reports the product of the MPS of A. For example, if A = [2, 10, 12, 9, 1, 3, 5] and d = 2, the output should be 10 × 9 × 5 = 450. In your solution, it suffices to complete the first two steps of the DP algorithm. That is, define subproblems, describe the optimal for a larger subproblem as a function of the optimal solution for smaller subproblems, and write a recursive formula for the optimal value of a subproblem (remember to include the base case). Assume the indices start at 1.

Given a sequence A formed by n positive numbers and a positive integer d, we are interested in a distant max-product subsequence (MPS) of A, which is a subsequence of A formed by elements whose indices are at least d units apart and have the maximum product. Describe a dynamic programming algorithm that reports the product of the MPS of A. For example, if A = [2, 10, 12, 9, 1, 3, 5] and d = 2, the output should be 10 × 9 × 5 = 450. In your solution, it suffices to complete the first two steps of the DP algorithm. That is, define subproblems, describe the optimal for a larger subproblem as a function of the optimal solution for smaller subproblems, and write a recursive formula for the optimal value of a subproblem (remember to include the base case). Assume the indices start at 1.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

Given a sequence A formed by n positive numbers and a positive integer d, we are interested
in a distant max-product subsequence (MPS) of A, which is a subsequence of A formed by
elements whose indices are at least d units apart and have the maximum product. Describe
a dynamic programming algorithm that reports the product of the MPS of A.
For example, if A = [2, 10, 12, 9, 1, 3, 5] and d = 2, the output should be 10 × 9 × 5 = 450.
In your solution, it suffices to complete the first two steps of the DP algorithm. That is,
define subproblems, describe the optimal for a larger subproblem as a function of the optimal
solution for smaller subproblems, and write a recursive formula for the optimal value of a
subproblem (remember to include the base case). Assume the indices start at 1.

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