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(solution) CS721 Advanced Algorithms Fall 2016 Assignment 03 Part 1: 1.


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CS721 Advanced Algorithms Fall 2016 Assignment 03

 

Part 1:

 

1. Design a greedy algorithm for the matrix chain multiplication problem. You must clearly show the greedy property used in

 

your algorithm. This algorithm must do better in terms of the number of subproblems to solve and time complexity than

 

the dynamic programming algorithm. Would it always lead to an optimum solution? If not, present a counter example. For

 

example, consider a greedy property that would pick a pair of matrices with the lowest scalar multiplication cost from the

 

available list in each iteration, i.e., a pair that would give the smallest p x q x r value.

 

2. Given the table of items below, find the maximum value that a knapsack of a capacity 100 lbs can hold. Use a greedy

 

algorithm. Note that fractions of items are allowed in the knapsack. Is the maximum value found optimum? You must

 

show all the intermediate steps.

 

Item

 

A

 

B

 

C

 

D

 

E 3. Weight (lbs)

 

20

 

40

 

50

 

10

 

5 Price ($)

 

40

 

40

 

150

 

50

 

30 Solve Exercise 16.3-1 from the book. All the text and diagrams must be electronically produced.

 

Your name and page number should appear on each page.

 

The entire work must be in a single PDF file.

 

The PDF file name must be in the format Assignment03-Part01-LastName-FirstName.pdf. For example,

 

Assignment03-Part01-Kagdi-Huzefa.pdf . Part 2:

 

4. Write a program that encodes a text file (ASCII characters) using the Huffman prefix code algorithm. It must output the

 

encoded, ?compressed? file. Also, output a separate file with characters and their respective codewords. Finally, the

 

program must decode the given compressed file into the text file using the codeword file. For example, you are given input.txt and hpc is the executable of the program you developed.

 

$hpc ?c input.txt output.hpc

 

The above

 

execution generates the file output.hpc, which is the encoded version of input.txt. It also creates the ?hidden?

 

.output.hpc.codeword file with the codewords for the characters. If the second parameter is not specified, it creates the output

 

file with the same name as the input file and adds the .hpc extension.

 

$hpc ?d output.hpc input.txt

 

The above execution generates the file input.txt, which is the decoded version of output.txt. It uses the ?hidden? .

 

output.hpc.codeword file for decoding. If the second parameter is not specified, it creates the output file with the same name as

 

the input file with the extension changed to .txt. Provide a README file that clearly documents how to build (e.g., makefile) and execute your program.

 

Include your source code and sample input.

 

Create a directory named in the format Assignment03-Part02-LastName-FirstName, which includes all your program

 

and documentation files. Submission:

 

Combine parts I and II into a single compressed file and submit on Blackboard. The compressed file must

 

be named in the format Assignment03-LastName-FirstName with the appropriate extension.

 

Due Date:

 

October 19, 2016, 1:59 PM

 

1

 


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