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CS502 Assignment No. 02 Solution & Discussion Due Date: Dec 07, 2015
Assignment No. 02 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:
Objective
The objective of this assignment is to enable students:
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:
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. 
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Slove of Question 2 divide and conquer technique
Algorithm to find minimum number
If (p=r) // here we supposing n is equal to one
Then return A[p]
Else < Choose_Pivot (A, p, r) //if n is not equal to 1 then select a pivot
q < Partition (A, p, r, x) ...................//then divide the array
if rank_x= 1 ................../// if the rank of pivot element after partition is 1
then return x ... //then this pivot element is the minimum number in array
else //if rank_x > 1 //// otherwise proceed recursively
then return Select( A, p, q1, 1)
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