We are here with you hands in hands to facilitate your learning & don't appreciate the idea of copying or replicating solutions. Read More>>

Looking For Something at vustudents.ning.com? Click Here to Search

www.bit.ly/vucodes

+ Link For Assignments, GDBs & Online Quizzes Solution

www.bit.ly/papersvu

+ Link For Past Papers, Solved MCQs, Short Notes & More


Dear Students! Share your Assignments / GDBs / Quizzes files as you receive in your LMS, So it can be discussed/solved timely. Add Discussion

How to Add New Discussion in Study Group ? Step By Step Guide Click Here.

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. 02
Semester: 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. 1.      Divide: Divides the problem into a small number of pieces
  2. 2.      Conquer: Solves each piece by applying divide and conquer to it recursively
  3. 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. 

+ How to Follow the New Added Discussions at Your Mail Address?

+ How to Join Subject Study Groups & Get Helping Material?

+ How to become Top Reputation, Angels, Intellectual, Featured Members & Moderators?

+ VU Students Reserves The Right to Delete Your Profile, If?


See Your Saved Posts Timeline

Views: 17817

.

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

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

+ Click Here to Search (Looking For something at vustudents.ning.com?)

+ Click Here To Join (Our facebook study Group)

Replies to This Discussion

Please Discuss here about this assignment.Thanks

Our main purpose here discussion not just Solution

We are here with you hands in hands to facilitate your learning and do not appreciate the idea of copying or replicating solutions.

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.

can u plz explain it? i hve problem in algo

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 , 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.

 

first we should find the recurrence relation of sum of the first n squares
1^2 + 2^2 + . . . + n^2.

T(N)= T(n-2)+n^2
there is mistake in above recurrence relation. pls find it.
now it is easy to solve with iteration method.

is it comlete solution .?

Dear Students Don’t wait for solution post your problems here and discuss ... after discussion a perfect solution will come in a result. So, Start it now, replies here give your comments according to your knowledge and understandings....

I think asey hi ho ga 

koi sloution ki form me upload kreen plz

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 

any one got the complet solution

RSS

Latest Activity

٥ دن posted a discussion
21 minutes ago
Gulzar Ahmed joined + M.Tariq Malik's group
45 minutes ago
+ ՏhehαrZααD + liked + !! "AS" !!'s discussion Jis Tarah ..
1 hour ago
Pronoun liked zobialatif's discussion hazrat ali says
2 hours ago
٥ دن updated their profile
2 hours ago
+ !! "AS" !! replied to + !! "AS" !!'s discussion Jis Tarah ..
3 hours ago
Siddiq khan kakar liked + M.Tariq Malik's discussion PAK301 Pakistan Studies Short Notes, PAK301 Solved Subjective Questions, PAK301 Solved MCQs
3 hours ago
Siddiq khan kakar liked + M.Tariq Malik's group PAK301 Pakistan Studies
3 hours ago
+ ! ! JS ! ! + posted a discussion
3 hours ago
Siddiq khan kakar liked Siddiq khan kakar's discussion RIP
3 hours ago
Kashif Iqbal added 2 discussions to the group FIN624 Islamic Mode of Financing
3 hours ago
+ ! ! JS ! ! + liked + Iuuoɔǝut +'s discussion جلوۂ عشق حقیقت تھی حسن مجاز بہانہ تھا
3 hours ago
+ ! ! JS ! ! + liked + !! "AS" !!'s discussion Baat Karna ...
3 hours ago
+ ! ! JS ! ! + liked + !! "AS" !!'s discussion Ghalti...
3 hours ago
+ ! ! JS ! ! + liked + !! "AS" !!'s discussion Yaha Har Cheez ..
3 hours ago
+ ! ! JS ! ! + liked +!!!StRaNGeR!!! +'s discussion ﺁﭖ ﺩﻝ ﺟﻮﺋﯽ ﮐﯽ ﺯﺣﻤﺖ ﻧﮧ ﺍﭨﮭﺎﺋﯿﮟ ، ﺟﺎﺋﯿﮟ
3 hours ago
+ ! ! JS ! ! + liked + !! "AS" !!'s discussion Alfaaz Ki Nisbat..
3 hours ago
+ ! ! JS ! ! + liked + !! "AS" !!'s discussion Jis Tarah ..
3 hours ago
Siddiq khan kakar posted discussions
3 hours ago
+ ! ! JS ! ! + replied to + !! "AS" !!'s discussion Jis Tarah ..
3 hours ago

© 2019   Created by + M.Tariq Malik.   Powered by

Promote Us  |  Report an Issue  |  Privacy Policy  |  Terms of Service