CS502 Assignment 3 Solution 2022

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CS502 ASSIGNMENT 3 SOLUTION FALL 2021 

Provide by VU Answer


Total Marks: 20

Due Date: 10 Feb 2022



Question 1: 

A thief enters in a Gold shop carrying knapsack (bag). Knapsack (bag) capacity is 33KG of weight. The shop has only 10 gold bricks; each brick has a specific weight and price. Now, the thief’s dilemma is to make such a selection of bricks that it maximizes the profit (i.e. total price) without exceeding the knapsack (bag) weight. 


https://miro.medium.com/max/1000/1*TSMpfYmY3HnB03TqONbVrQ.jpeg

You are required to do the following task:


1. Help the thief for the selection of bricks using greedy method for getting maximum profit.


Solution:



Bricks

Weight (KG)

Price

Price / Weight Ratio

1

4

$120

$30

2

3

$110

$36.66

3

9

$130

$1.4

4

7

$140

$20

5

5

$200

$40

6

1

$50

$50

7

2

$70

$35

8

11

$160

$14.54

9

6

$153

$25.5

10

13

$170

$13.07


Weight(KG):

1+5+3+2+4+6+7+(11-6)

1+5+3+2+4+6+7+5

33KG

Price:

$50 + $200+ $110+ $70+ $120+ $153+ $140+ (160/11*5)

$50 + $200+ $110+ $70+ $120+ $153+ $140+ $72.72

$915.72

Maximum Profit = $915.72


2. Which approach will be used for this scenario (write only name)?


Solution:


Greedy Method About Price/Weight Ratio



Question 2:


A well-known Network Solution company that deals with large volumes of data over the network wants to use a data compression technique that reduces the coding redundancy without loss of data quality. For trial/test execution the company has decided to use Huffman encoding algorithm to encode the given string "allamaiiii” before transmitting over the network. 

 

You are required to do the following task:


  1. Calculate the frequency of characters.

  2. Generate Huffman Tree

  3. Write the code of every character

  4. Required total no of bits


Solution:

Giving String “allamaiiii”



Character

Frequency

a

3

i

4

l

2

m

1


2. Generate Huffman Tree


Solution:





3. Write the code of every character


Solution:

Character

Frequency

Character code

Character Bits

a

3

10

(3*2) =6

i

4

0

(4*1) =4

l

2

111

(2*3) =6

m

1

110

(1*3) =3


4. Required total no of bits


Solution:


Required Total No of Bits = 19




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