(1) Use Dynamic programming technique to solve the set-partition problem. See the problem definition below. (Define the object function, write the recursive relation, give the initial condition, illustrate the table, indicate where the answer is, and estimate the time complexity and space complexity.)

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
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Please refer to this textbook: “Cormen et al., Introduction to Algorithms, 3rd Edition”

 

And answer the following questions:

Question:21

1.
(1) Use Dynamic programming technique to solve the set-partition problem.
See the problem definition below.
(Define the object function, write the recursive relation, give the initial condition, illustrate the table,
indicate where the answer is, and estimate the time complexity and space complexity.)
(2) Is the algorithm in part(1) a polynomial time algorithm? Explain.
Set-partition problem:
Given a set S ofn positive integers, S= {s,s2,S3..., S „},
is there a partition of S into two disjoint subsets A and S - A such that
Es; = E s; ?
s,EA
s, ES-A
Transcribed Image Text:1. (1) Use Dynamic programming technique to solve the set-partition problem. See the problem definition below. (Define the object function, write the recursive relation, give the initial condition, illustrate the table, indicate where the answer is, and estimate the time complexity and space complexity.) (2) Is the algorithm in part(1) a polynomial time algorithm? Explain. Set-partition problem: Given a set S ofn positive integers, S= {s,s2,S3..., S „}, is there a partition of S into two disjoint subsets A and S - A such that Es; = E s; ? s,EA s, ES-A
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