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CS721 Advanced Algorithms Fall 2016 Assignment 03
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.
E 3. Weight (lbs)
5 Price ($)
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
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.
October 19, 2016, 1:59 PM
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