= You are given a set of n positive numbers A {a₁,..., an} and a positive integer t. Design a dynamic programming algorithm running in O(nt) time that decides whether there exists a subset A' C A such that x = t. Note that each element of A can be xЄA' used at most once. Is the run-time of your algorithm polynomial with respect to the size of the input?

= You are given a set of n positive numbers A {a₁,..., an} and a positive integer t. Design a dynamic programming algorithm running in O(nt) time that decides whether there exists a subset A' C A such that x = t. Note that each element of A can be xЄA' used at most once. Is the run-time of your algorithm polynomial with respect to the size of the input?

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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Concept explainers

Linear Programming Concepts

Linear programming is a famous mathematical modeling tool for determining the best distribution of scarce resources among competing demands. Machinery, time, personnel, raw materials, money, and space are all resources. It is used to find the most optimal solution to a problem with given constraints. The real-life situations can be formulated using linear programming concepts into a mathematical model. Linear programming problems consist of an objective function and linear equalities subjected to constraints.

Question

5. You are given a set of n positive numbers A = {a₁,..., an} and a positive integer t.
Design a dynamic programming algorithm running in O(nt) time that decides whether
there exists a subset A' CA such that Σ x = t. Note that each element of A can be
xЄA'
used at most once. Is the run-time of your algorithm polynomial with respect to the
size of the input?

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