1. Making the arrangements. My garden features a number of flower beds. As a person of particular tastes, I have a rating system for how lovely a pairing of flowers is. I encode these ratings in a huge table: Rose Daisy Tulip Sunflower Rose Daisy Tulip 3 -2 5 Sunflower 0 1 -4 (You may assume that the table can include any (finite) number of types of flowers; loveliness ratings are integers; and that flower names are arbitrary and can be invented.) The loveliness of a flowerbed is the total rating of all pairs of flower types in the flowerbed. The LOVELY-FLOWERBED problem is to determine, given my preferences as a table in the form described above and an integer f, whether I can have a flowerbed whose total loveliness rating is at least l. (a) After ruining my garden path, Alfie suggests that the following greedy approach will solve the LOVELY-FLOWERBED problem: Choose the first flower as the one that has the highest total loveliness with all other flower types. Choose the next flower as the one with the highest loveliness rating with any flower already in the flowerbed. Repeat until a flowerbed with loveliness is achieved, or you run out of flowers. Is Alfie right or wrong? Rigorously justify your answer. (b) Prove that LOVELY-FLOWERBED is complete for NP.

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
icon
Related questions
Question
1. Making the arrangements. My garden features a number of flower beds. As a person of particular
tastes, I have a rating system for how lovely a pairing of flowers is. I encode these ratings in a huge
table:
Rose
Daisy
Tulip
Sunflower
Rose Daisy Tulip
3
-2
5
-
-
Sunflower
0
1
-4
(You may assume that the table can include any (finite) number of types of flowers; loveliness ratings
are integers; and that flower names are arbitrary and can be invented.)
The loveliness of a flowerbed is the total rating of all pairs of flower types in the flowerbed. The
LOVELY-FLOWERBED problem is to determine, given my preferences as a table in the form described
above and an integer , whether I can have a flowerbed whose total loveliness rating is at least l.
(a) After ruining my garden path, Alfie suggests that the following greedy approach will solve the
LOVELY-FLOWERBED problem:
Choose the first flower as the one that has the highest total loveliness with all other flower
types. Choose the next flower as the one with the highest loveliness rating with any
flower already in the flowerbed. Repeat until a flowerbed with loveliness is achieved,
or you run out of flowers.
Is Alfie right or wrong? Rigorously justify your answer.
(b) Prove that LOVELY-FLOWERBED is complete for NP.
Transcribed Image Text:1. Making the arrangements. My garden features a number of flower beds. As a person of particular tastes, I have a rating system for how lovely a pairing of flowers is. I encode these ratings in a huge table: Rose Daisy Tulip Sunflower Rose Daisy Tulip 3 -2 5 - - Sunflower 0 1 -4 (You may assume that the table can include any (finite) number of types of flowers; loveliness ratings are integers; and that flower names are arbitrary and can be invented.) The loveliness of a flowerbed is the total rating of all pairs of flower types in the flowerbed. The LOVELY-FLOWERBED problem is to determine, given my preferences as a table in the form described above and an integer , whether I can have a flowerbed whose total loveliness rating is at least l. (a) After ruining my garden path, Alfie suggests that the following greedy approach will solve the LOVELY-FLOWERBED problem: Choose the first flower as the one that has the highest total loveliness with all other flower types. Choose the next flower as the one with the highest loveliness rating with any flower already in the flowerbed. Repeat until a flowerbed with loveliness is achieved, or you run out of flowers. Is Alfie right or wrong? Rigorously justify your answer. (b) Prove that LOVELY-FLOWERBED is complete for NP.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

Can you give a formal proof for part b?

Solution
Bartleby Expert
SEE SOLUTION
Knowledge Booster
Intelligent Machines
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
  • SEE MORE 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