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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


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).




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




You are required to submit your solution through LMS as MS Word document.


For any query about the assignment, contact at

                                                             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. 

Views: 18059

Replies to This Discussion

by iteration it doesn't take the required algo

koi 2nd question b discuss kar dy 

apka first ho gia hai ?

Is Question no.2 answer is Selection Sort Algorithm.?

divide n con

Yeh Assignment ajeeb and tuff  hai.

sab students sa request hai k woh sir ko mail kar ka boley k 2nd Assignment ko cancel kar ka koi aur  assignment dey.


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.



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:

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 

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

first question ka exact answer kia hai.?

iteration method sy krna hai question but jo problem arhi wo sum ki hai

how to solve n convert that into exact format 

Itni mushkil assignment :(
aik lafz ki bhi samajh nahi aa rahi :(


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