Earn Higher Grades With Instant Assignment Help.Ask Question!

Data structures & Algorithms
(5/5)

Consider a collection of n closed intervals with distinct endpoints [Si, ti]; you can assume without loss of generality that the Si's and ti's are all distinct integers

INSTRUCTIONS TO CANDIDATES
ANSWER ALL QUESTIONS

Consider a collection of n closed intervals with distinct endpoints [Si, ti]; you can assume without loss of generality
that the Si's and ti's are all distinct integers (in particular you can simply assume that the Si's and the ti's comprise the numbers 1, 2., '2n).

a) Give an algorithm for finding the largest possible subset of non-overlapping intervals. For example, in Figure
1, an optimal subset is {c, e, h, k, o, q}.

b) Consider a related problem of finding the smallest possible subset of points such that each interval overlaps at
least one point. For example, the points labeled (I) through in Figure I accomplish this. Is it a coincidence
that both problems happen to have the same objective value (i.e. 6)?

Let k > 2 be fixed and suppose you are given a matrix M whose columns consist of a single consecutive block of
an integer between 1 and k — 1, and where every row of M sums to a multiple of k, as shown below (for the case k=8);

Prove that it is possible to select a subset of columns and subtract k from their positive elements so that the rows
Of the new matrix sum to zero. For example, if we select columns l, 2, 3, 5, 9, and II in the above, the resulting
matrix

Attachments:
(5/5)

Expert's Answer

9 Times Downloaded

Related Questions

CSI 1420 Introduction to C Programming & Unix Fall 2018, CRN 44882, Oakland University Homework Assignment 6 - Using Arrays and Functions in C

DescriptionIn this final assignment, the students will demonstrate their ability to apply two majorconstructs of the C programming language – Fu

The standard path finding involves finding the (shortest) path from an origin to a destination, typically on a map. This is an

Path finding involves finding a path from A to B. Typically we want the path to have certain properties,such as being the shortest or to avoid going t

Develop a program to emulate a purchase transaction at a retail store. This program will have two classes, a LineItem class and a Transaction class. The LineItem class will represent an individual

Develop a program to emulate a purchase transaction at a retail store. Thisprogram will have two classes, a LineItem class and a Transaction class. Th

SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of Sea Ports. Here are the classes and their instance variables we wish to define:

1 Project 1 Introduction - the SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of

Project 2 Introduction - the SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of Sea Ports. Here are the classes and their instance variables we wish to define:

1 Project 2 Introduction - the SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of

9 Times Downloads

Ask This Assignment To Be Done By Our ExpertsGet A+ Grade Solution Guaranteed

expert
joyComputer science
(4/5)
12 Answers Hire Me
expert
Robert DLaw
(4.8/5)
560 Answers Hire Me
expert
Dr Samuel BarberaStatistics
(5/5)
519 Answers Hire Me
expert
Tutor For YouEconomics
(5/5)
958 Answers Hire Me