Homework Help is Here – Start Your Trial Now!
Engineering
Computer Science
(Dynamic Programming.) Recall the problem presented in Assign- ment 3 where given a list L of n ordered integers you're tasked with removing m of them such that the distance between the closest two remaining integers is maxi- mized. See Assignment 1 for further clarification and examples. As it turns out there is no (known) greedy algorithm to solve this problem. However, there is a dynamic programming solution. Devise a dynamic programming solution which determines the maximum distance between the closest two points after removing m numbers. Note, it doesn't need to return the resulting list itself. Hint 1: Your sub-problems should be of the form S(i, j), where S(i, j) returns the maximum distance of the closest two numbers when only considering removing j of the first i numbers in L. As an example if L [3, 4, 6, 8, 9, 12, 13, 15], then S(4, 1) = 2, since the closest two values of L' = [3,4,6,8] are 6 and 8 after removing 4 (note, 8-6 = = 2). = Hint 2: For the sub-problem S(i, j), assuming j < i−2, you know there's always an optimal solution which leaves the values L[1] and L[i] in the list. Give a mathematical definition of S(i, j) including all its base cases

(Dynamic Programming.) Recall the problem presented in Assign- ment 3 where given a list L of n ordered integers you're tasked with removing m of them such that the distance between the closest two remaining integers is maxi- mized. See Assignment 1 for further clarification and examples. As it turns out there is no (known) greedy algorithm to solve this problem. However, there is a dynamic programming solution. Devise a dynamic programming solution which determines the maximum distance between the closest two points after removing m numbers. Note, it doesn't need to return the resulting list itself. Hint 1: Your sub-problems should be of the form S(i, j), where S(i, j) returns the maximum distance of the closest two numbers when only considering removing j of the first i numbers in L. As an example if L [3, 4, 6, 8, 9, 12, 13, 15], then S(4, 1) = 2, since the closest two values of L' = [3,4,6,8] are 6 and 8 after removing 4 (note, 8-6 = = 2). = Hint 2: For the sub-problem S(i, j), assuming j < i−2, you know there's always an optimal solution which leaves the values L[1] and L[i] in the list. Give a mathematical definition of S(i, j) including all its base cases

C++ Programming: From Problem Analysis to Program Design
C++ Programming: From Problem Analysis to Program Design
8th Edition
ISBN:9781337102087
Author:D. S. Malik
Publisher:D. S. Malik
Chapter10: Classes And Data Abstraction
Section: Chapter Questions
Problem 19PE
See similar textbooks
icon
Related questions
Question
100%
(Dynamic Programming.) Recall the problem presented in Assign- ment 3 where given a list L of n ordered integers you're tasked with removing m of them such that the distance between the closest two remaining integers is maxi- mized. See Assignment 1 for further clarification and examples. As it turns out there is no (known) greedy algorithm to solve this problem. However, there is a dynamic programming solution. Devise a dynamic programming solution which determines the maximum distance between the closest two points after removing m numbers. Note, it doesn't need to return the resulting list itself. Hint 1: Your sub-problems should be of the form S(i, j), where S(i, j) returns the maximum distance of the closest two numbers when only considering removing j of the first i numbers in L. As an example if L [3, 4, 6, 8, 9, 12, 13, 15], then S(4, 1) = 2, since the closest two values of L' = [3,4,6,8] are 6 and 8 after removing 4 (note, 8-6 = = 2). = Hint 2: For the sub-problem S(i, j), assuming j < i−2, you know there's always an optimal solution which leaves the values L[1] and L[i] in the list. Give a mathematical definition of S(i, j) including all its base cases
Transcribed Image Text:(Dynamic Programming.) Recall the problem presented in Assign- ment 3 where given a list L of n ordered integers you're tasked with removing m of them such that the distance between the closest two remaining integers is maxi- mized. See Assignment 1 for further clarification and examples. As it turns out there is no (known) greedy algorithm to solve this problem. However, there is a dynamic programming solution. Devise a dynamic programming solution which determines the maximum distance between the closest two points after removing m numbers. Note, it doesn't need to return the resulting list itself. Hint 1: Your sub-problems should be of the form S(i, j), where S(i, j) returns the maximum distance of the closest two numbers when only considering removing j of the first i numbers in L. As an example if L [3, 4, 6, 8, 9, 12, 13, 15], then S(4, 1) = 2, since the closest two values of L' = [3,4,6,8] are 6 and 8 after removing 4 (note, 8-6 = = 2). = Hint 2: For the sub-problem S(i, j), assuming j < i−2, you know there's always an optimal solution which leaves the values L[1] and L[i] in the list. Give a mathematical definition of S(i, j) including all its base cases
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
C++ Programming: From Problem Analysis to Program…
C++ Programming: From Problem Analysis to Program…
Computer Science
ISBN:
9781337102087
Author:
D. S. Malik
Publisher:
Cengage Learning
C++ for Engineers and Scientists
C++ for Engineers and Scientists
Computer Science
ISBN:
9781133187844
Author:
Bronson, Gary J.
Publisher:
Course Technology Ptr
Systems Architecture
Systems Architecture
Computer Science
ISBN:
9781305080195
Author:
Stephen D. Burd
Publisher:
Cengage Learning
Operations Research : Applications and Algorithms
Operations Research : Applications and Algorithms
Computer Science
ISBN:
9780534380588
Author:
Wayne L. Winston
Publisher:
Brooks Cole
Programming Logic & Design Comprehensive
Programming Logic & Design Comprehensive
Computer Science
ISBN:
9781337669405
Author:
FARRELL
Publisher:
Cengage
LINUX+ AND LPIC-1 GDE.TO LINUX CERTIF.
LINUX+ AND LPIC-1 GDE.TO LINUX CERTIF.
Computer Science
ISBN:
9781337569798
Author:
ECKERT
Publisher:
CENGAGE L
SEE MORE TEXTBOOKS