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CS702 - Advanced Algorithms Analysis and Design Assignment No. 2 Solution and Discussion Spring 2017 Due Date: May 25, 2017

CS702 - Advanced Algorithms Analysis and Design Assignment No. 2 Solution and Discussion Spring 2017 Due Date: May 25, 2017

1

Virtual University of Pakistan

Spring 2017

Answer the following questions in your own words. Plagiarism will be checked for each question. Marks will be awarded on the basis of answer and plagiarism report.

Question 1                                                                                                            (15 Marks)

Consider the recurrence

t

n = n

if n = 0, 1, 2

t

n  = 6.tn-1 - 11.t n-2  +  6.t n-3       otherwise

Find the general solution of the recurrence above.

Question 2                                                                                                            (15 Marks)

Prove that 5.n2  + 10.n + 16         Î Q(n2 )

Question 3                                                                                                            (20 Marks)

There are two assembly lines, as shown in the diagram below, each with 6 stations. The auto is required to go through from all of these 6 stations from left to right. Nodes represent stations. The assembly time at each station is shown at each node. The entering and exit times for an auto are also given. The transfer time is represented at the edges when an auto moves to next station on a different line. There is no transfer time if it stays on the same line. Determine which stations to choose from lines 1 and 2 to minimize total time through the factory. Also compute the optimal value in terms of time. Use Dynamic

Programming Approach. You need to calculate    f

optimal path.                                     i[j], li[j], f*, l* and the

5                     5 3                                         6                     8                    7

3                                                                                                                                            3

5

4 1

3

In

6

Out

2

4

5

3

1

1

3                     4

8                      6

4                     7

6

For  the  sequence  of  matrices,  given  below,  compute  the  order  of  the  product,

A

1.A2.A 3.A 4, in such a way that minimizes the total number of scalar multiplications,

using Dynamic Programming.

Order of A

1  =  20 x 10

Order of A

Order of A2 =  10 x 30

Order of A

3  =  30 x 15

4  =  15 x 25

2

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