We have been working very hard since 2009 to facilitate in your learning Read More. We can't keep up without your support. Donate Now.

www.vustudents.ning.com

 www.bit.ly/vucodes + Link For Assignments, GDBs & Online Quizzes Solution www.bit.ly/papersvu + Link For Past Papers, Solved MCQs, Short Notes & More

# CS502 Assignment No. 02 Solution & Discussion Due Date: Dec 07, 2015

CS502 Assignment No. 02 Solution & Discussion Due Date: Dec 07, 2015

# CS502 - Fundamentals of Algorithms Assignment No. 02 Solution Fall 2015 Due Date Dec 07, 2015

 Assignment No. 02Semester: Fall 2015 CS502: Fundamentals of Algorithms Due Date:07/12/2015 Instructions Please read the following instructions carefully before submitting assignment:   It should be clear that your assignment will not get any credit (zero marks) if: The assignment is submitted after due date. The submitted assignment is other than .doc file. The submitted assignment does NOT open or file is corrupted. The assignment is copied (from other student or ditto copy from any other source).   Objective   The objective of this assignment is to enable students:   Write and solve recurrence relations of recursive algorithms using iteration method Design algorithm using Divide and conquer approach   Submission   You are required to submit your solution through LMS as MS Word document.   For any query about the assignment, contact at CS502@vu.edu.pk                                                              GOOD LUCK Question 1:   Consider the following recursive algorithm for computing the sum of the first n squares: Sum(n) = 12 + 22 + . . . + n2.   Algorithm: SUM(n) if n = 1 return 1 else return SUM(n − 1) + n ∗ n   Write recurrence relation for above algorithm and solve it using Iteration Method.   Question 2:   In Divide and conquer strategy, three main steps are performed:   1.      Divide: Divides the problem into a small number of pieces 2.      Conquer: Solves each piece by applying divide and conquer to it recursively 3.      Combine: Combines/merges the pieces together into a global solution.   Write an algorithm to find minimum number from a given array of size ‘n’ using divide and conquer approach. Lectures Covered:  This assignment covers first 15 Lectures. Deadline:             Your assignment must be uploaded/submitted at or before 07 Dec, 2015.

+ http://bit.ly/vucodes (Link for Assignments, GDBs & Online Quizzes Solution)

+ http://bit.ly/papersvu (Link for Past Papers, Solved MCQs, Short Notes & More)

Views: 17906

### Replies to This Discussion

anyone plssssssssssssssssssss share your complete solution here....

solution plz

koi 2 question ka idea b de den plz

``def find_min(arr):     """ Return the least number in nonempty list `arr`.     """     len_arr = len(arr)     assert len_arr > 0     # Base case:     if len_arr == 1:         return arr[0]     # Divide...     mid = len_arr // 2        # floor of len_arr/2; thus, mid ≥ 1     m1 = find_min(arr[0:mid])     m2 = find_min(arr[mid:len_arr])     # ... and conquer:     return min(m1,m2)kya yh thek hy???``

Important Announcement Regarding Assignment 2 Due Date Dated: Dec 07, 15
Dear Students,

This is to inform you that Deadline of Assignment 2 submission has been extended to 08-12-2015.

By considering your problems in solving Assignment 2, we are going to conduct tomorrow’s (08-12-2015) Adobe Connect Sessions on Assignment 2. If you are facing any difficulty to solve assignment, you are advised to attend the sessions. Detailed announcement on these sessions schedule has already been made on LMS.

In case of any query, you can contact at cs502@vu.edu.pk.

Good Luck!

Regards,

Instructor CS502

kindly koi to sol btaye.bht togh assignment h kch smj ni ara

idea

First of all, if n == 1 you should probably return 1. And yes, this recursive function computes 1 + 2^3 + 3^3 + ... + n^3. How do we know that?

Well, take an example like n = 5;

• R(5) returns R(4) + 5^3
• R(4) returns R(3) + 4^3
• ....
• R(2) returns R(1) + 2^3
• R(1) returns 1

If you add them up => R(5) returns 5^3 + 4^3 + .. + 2^3 + 1.

EXPLANATION:

Denoting S(n) the sum of the first n cubes, S(n) must be a polynomial of the fourth degree in n, let

S(n) = an^4+bn³+cn²+dn.

This is because

1) S(0)= 0, so there is no independent term,

2) When computing S(n)-S(n-1), which must equal n³, you get a polynomial of the third degree, by cancellation of the quartic term:

S(n)-S(n-1) = a(n^4-(n-1)^4)+b(n³-(n-1)³)+c(n²-(n-1)²)+d(n-(n-1)).

Developing and simplifying,

a(4n³-6n²+4n-1)+b(3n²-3n+1)+c(2n-1)+d = n³.

Let us identify the coefficients:

n³:  4a        =1
n²: -6a+3b     =0
n:   4a-3b+2c  =0
1:   -a +b -c+d=0
Solving this triangular system is straigthforward:

a=1/4
b=1/2
c=1/4
d=0.

and finally

S(n) = (n^4+2n³+n²)/4 = n²(n+1)²/4.

Check iteration method of power 2 k=log n

T(n) = 2kT (n/(2k)) + (n+n+n+....+n)

= n + n log n

see on page 31

Lecture number 8 the solution s given

EXAMPLE FROM BOOK:

plz guide us ya working to nahe karne

T(n) = 2kT(n/(2k)) + (n + n + n + · · · + n) | {z }
k times
= 2kT(n/(2k)) + kn
= 2(logn)T(n/(2(logn))) + (log n)n
= 2(logn)T(n/n) + (log n)n
= nT(1) + n log n = n + n log n

bot easy assignment ha i done :D

plz give me solution

Solution

SEe Aach file

Attachments:

## Latest Activity

mahwish anwer Ellahi and Ali shah joined Virtual University of Pakistan
7 minutes ago
1 hour ago
1 hour ago
1 hour ago
1 hour ago
1 hour ago

1

2

3

## HELP SUPPORT

This is a member-supported website. Your contribution is greatly appreciated!