Homework Help is Here – Start Your Trial Now!
Engineering
Computer Science
Exercise 7.11 Suppose you are the "algorithmatician" of your company and the manager comes to you with the following problem. The company has to buy n different software products. Due to various constraints, the company can only buy at most one software product per month. Each software is currently selling for a price of $100. However, they become expensive cach month according to the following formula: the cost of software j increases by a factor ry >1 cach month, where ry is a known parameter. This means that if software j is purchased t months from now, it will cost $100(r,)". It is given that all price growth rates are distinct: that is, rr, for software i fj (even though at the start they all have the same price of $100). The question the manager poses for you is this: Given that the company can only buy at most one software product a month, in which order should it buy the products so that the total amount of money apent is as amall as possiblel? In particular he has the following questions: (1) Consider the following example to get started. Suppose ri = 2, a=3, and ra= 4. What is the best order to buy the three products and why? (H) Give a greedy algorithm to find the optimal order assuming that we have n products to buy and the growth rate of product i is r, 1sisn. What is the time complexity of your algorithm? (Hi) Prove that your greedy algorithm always gives the optimal ordering. (Hint: Use exchange argument.)

Exercise 7.11 Suppose you are the "algorithmatician" of your company and the manager comes to you with the following problem. The company has to buy n different software products. Due to various constraints, the company can only buy at most one software product per month. Each software is currently selling for a price of $100. However, they become expensive cach month according to the following formula: the cost of software j increases by a factor ry >1 cach month, where ry is a known parameter. This means that if software j is purchased t months from now, it will cost $100(r,)". It is given that all price growth rates are distinct: that is, rr, for software i fj (even though at the start they all have the same price of $100). The question the manager poses for you is this: Given that the company can only buy at most one software product a month, in which order should it buy the products so that the total amount of money apent is as amall as possiblel? In particular he has the following questions: (1) Consider the following example to get started. Suppose ri = 2, a=3, and ra= 4. What is the best order to buy the three products and why? (H) Give a greedy algorithm to find the optimal order assuming that we have n products to buy and the growth rate of product i is r, 1sisn. What is the time complexity of your algorithm? (Hi) Prove that your greedy algorithm always gives the optimal ordering. (Hint: Use exchange argument.)

Database System Concepts
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
See similar textbooks
icon
Related questions
Question
Exercise 7.11 Suppose you are the "algorithmatician" of your company and the manager comes to you with the following problem. The company has to buy n different software products. Due to various constraints, the company can only buy at most one software product per month. Each software is currently selling for a price of $100. However, they become expensive each month according to the following formula: the cost of software j incresses by a factor ry > 1 each month, where r, is a known parameter. This means that if software j is purchased t months from now, it will cost $100(r,). It is given that all price growth rates are distinct: that is, r, #r, for software i + j (even though at the start they all have the same price of $100). The question the manager poses for you is this: Given that the company can only buy at most one software product a month, in which order shoukd it buy the products so that the total amount of money spent is as small as poasible? In particular he has the following questions: (1) Consider the following example to get started. Suppose ri = 2, ra = 3, and ra = 4. What is the best order to buy the three products and why? (ii) Give a greedy algorithm to find the optimal order assuming that we have n products to buy and the growth rate of product i is r, 1<i< n. What is the timne complexity of your algorithm? (iii) Prove that your greedy algorithm always gives the optimal ordering. (Hint: Use exchange argument.)
Transcribed Image Text:Exercise 7.11 Suppose you are the "algorithmatician" of your company and the manager comes to you with the following problem. The company has to buy n different software products. Due to various constraints, the company can only buy at most one software product per month. Each software is currently selling for a price of $100. However, they become expensive each month according to the following formula: the cost of software j incresses by a factor ry > 1 each month, where r, is a known parameter. This means that if software j is purchased t months from now, it will cost $100(r,). It is given that all price growth rates are distinct: that is, r, #r, for software i + j (even though at the start they all have the same price of $100). The question the manager poses for you is this: Given that the company can only buy at most one software product a month, in which order shoukd it buy the products so that the total amount of money spent is as small as poasible? In particular he has the following questions: (1) Consider the following example to get started. Suppose ri = 2, ra = 3, and ra = 4. What is the best order to buy the three products and why? (ii) Give a greedy algorithm to find the optimal order assuming that we have n products to buy and the growth rate of product i is r, 1<i< n. What is the timne complexity of your algorithm? (iii) Prove that your greedy algorithm always gives the optimal ordering. (Hint: Use exchange argument.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Topological Sort
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Database System Concepts
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS