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# ASSIGNMENT NO # 3 FUNDAMENTAL OF ALGORITHM CS 502 DUE DATE 24 JULY

Fundamentals of Algorithms CS502-

Spring 2015

ASSIGNMENT #3

Rules for Marking

It should be clear that your assignment will not get any credit if:

O The assignment is submitted after due date.

O The submitted assignment does not compile or run. Or corrupt file

O The assignment is copied.

O Submit your solution in Microsoft Word document “doc/docx”

Objectives

This assignment will help you to understand the concepts of Knapsack Problem and Huffman encoding.

The grip on these topics will help you to understand the cores of Dynamic Programming and Greedy paradigms and increase your confidence to apply these strategies for real world problems.

Guidelines

1.In order to attempt this assignment you should have full command on Lecture # 17to Lecture # 26

and also read the text book “Introduction to Algorithms” byThomaH.Cormen particularly for Huffman encoding technique for compressing the data.

2.In order to solve this assignment you have strong concepts about following topicsüKnapsack Problem(Dynamic Programming)üRadix Sort Books to read For solution Cormen, Leiserson, Rivest, and Stein (CLRS) 2001, Introduction to Algorithm, (2nd ed.) McGraw Hill.

Estimated Time

4 Hours For Question1 maximum time is 2.5 hours ,divide the time according to your ease 1.5 hour will enough to understand the logics0/1 Dynamic Programming and in 1 hour can design your problem solution according to given scenario; and for second problem focus on the radix sort and you can develop all this in 1.5 hour.

It all depends upon your sheer concentration.

Question# 1(10) Let’s assume,

You are working in Multinational Organization XYZ and your company is going to launch projects at broader level. Your Company has 140 Billion \$ for investment. You area Business analyst in your company and you have to develop the strategy to maximize the earned profit following the given limits; projects Are to be launched in the year 2016.

•First project is about Research and Development of underdeveloped countries which has cost 40 billion \$ and the profit earned will be54 Billion \$, and

•The second project is to launch the Software Industries for security Enhancements in different countries which has cost 60 billion\$ and profit earned will be 40billion \$.

•The Third project is relating to Launch the Industry Plants Nano Technology design for the computing purposes the cost is 70 Billion \$ giving the profit of

72 billion \$

.

•The fourth project is to launch quality Medicine Formation

(Pharmaceutical Oriented) project to serve Humanity and has cost 76

billion

\$ and profit is 84 billion \$ and

•There is also fifth project which is relating to Chemical Industries in many countries which has cost 36 billion \$ giving the profit of 40 billion \$

.

Find out the projects to be selected to earn the maximum profit using

0-1 Knapsack you may assign explicit simple variables for your ease to proceed the calculations.

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Attachments:

### Replies to This Discussion

Project 1 and 4 will be selected

Yes you are right there will be 94 instead of 84 at last line under 80 and 90 columns

Thanks for correction ShariqMayo

Hadi bro guide me about project no3 72,94 and then 126 where come from how to calculate this plz help me .

Get idea from file i upload under here

Attachments:

hadi can u tell how you conclude project 1 and 4

AM I RIGHT HERE

Not Right when we have only 140 \$ dollar then how we can spend 176 \$ dollar to get complete three project you mentioned as 1, 2 and 4.

Get idea help from file which i uploaded above.

it is very simple we will chose 4th and 5th :)

http://viewtube.tv/video/PLJHuErj-Tw/dynamic-programming0-1-knapsac...

Aslam o alaikum

Guizee ye table bna k is ka Algo code b likhna hay ya bas yahi table bana k send krna hay.

Complete Solution this

V[i,j] = max {V[i − 1, j], vi + V[i − 1, j − wi]}
Project/Weights 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
C=40, P=54 0 0 0 0 54 54 54 54 54 54 54 54 54 54 54
C=60, P=40 0 0 0 0 54 54 54 54 54 54 94 94 94 94 94
C=70, P=72 0 0 0 0 54 54 54 72 72 72 72 126 126 126 126
C=76, P=84 0 0 0 0 54 54 54 72 84 84 84 126 138 138 138
C=36, P=40 0 0 0 0 54 54 54 72 84 84 94 126 138 138 138

Yeh assignment kis file ma upload kerni hai

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