CS502 Fundamentals of Algorithms Assignment No.1 Solution Spring Semester 2013

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[SIZE="3"]CS502 Fundamentals of Algorithms Assignment No.1 Solution Spring Semester 2013[/SIZE]


Assignment No. 01
Semester: Spring 2013

CS502-Fundamentals of Algorithms
Total Marks: 20

Due Date: 29/04/2013

Lectures Covered: 1 to 6

Objective
To analyze pseudo code and solve using summations; understand and prove asymptotic notations.

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Question: 1 marks : 10

Analyze the following pseudo code containing nested loops by computing its worst-case running time complexity. Perform all the steps by writing out the loops as summations and then solve the summations.

for i = 1 to log n
{ set j = 1 ; // ignore its constant time in analysis
while ( j <= i )
{ for k = 1 to j
{ k=k+1;
} j = j * 2 ; // ignore its constant time in analysis}}

[Note: Consider log as base 2 log and computing model as RAM (Random Access Machine) like one used in lectures ]

Question: 2 Marks: 10

Part (a)

What is the Asymptotic equivalence ( ) of the below function f(n)?

f(n) = 2n3 + 3n2 – 2n

Part (b)

Prove the Asymptotic equivalent of function in Part (a) by its lower and upper bounds.

[Note: You do not need to draw the graph, only show lower and upper bounds with c1,c2 and n0]

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