1. (a) Find the best possible relationship using one of the notations: O, Ω, Θ, o, w, for the following pairs of functions: n3 + 7n1.5-3 and nlog8 – 10n°.5 + 7; nlgn and n11; 5″ and (5.1)”; 4″ and n!. Justify each answer (b) Function f(n) = n3 + 5000n-60000 when n 〈 50 and f(n) = nlog n+ 100n for n 〉 50. Write f(n) in asymptotic notation in the simplest possible form.

Solution:

a)

n^3+7(n^1..5)-3 and n^(log 8 -10(n^0.5)+7)

we already know how Big- O, Big-Omega, Theta works but here is an overview to go through once again,

By looking at functions we can observe that

n^3+7(n^1..5)-3 <= c1* ( n^(log 8 -10(n^0.5)+7))

and Please note that log2 8= log 2^3= 3 log 2= 3*1= 3, so n^log 8= n^3

n^3+7(n^1..5)-3 >= c2* (n^(log 8 -10(n^0.5)+7))

So we can say that

n^3+7(n^1..5)-3= $\Theta$(n^(log 8 -10(n^0.5)+7) )

Now,

n log n and n^1.1

Now we will compare by putting very large value of n and see the relation between these two

if n=2^256, then n log n= 2.9642775e+79 and

n^1.1= 5.8890708e+84

this means that n^1.1 is greater than n log n

Hence n log n= O(n^1.1).

5^n and 5.1^n

Only by looking at the function we can say that

5^n= o(5.1^n)

4^n and n!

We know that n! is almost equivalent to n^n

So here we can say that 4^n= o(n!)

b)

When we write generalized form of asymptotic notation then we only consider very large value of n, so the function which is taken at n>50 is going to be considered here,

f(n)= n log n + 100n

n log n + 100n <= c * (n log n )

for c= 2.

So, f(n)= O(n log n)

Pages (550 words)
Approximate price: -

Help Me Write My Essay - Reasons:

Best Online Essay Writing Service

We strive to give our customers the best online essay writing experience. We Make sure essays are submitted on time and all the instructions are followed.

Our Writers are Experienced and Professional

Our essay writing service is founded on professional writers who are on stand by to help you any time.

Free Revision Fo all Essays

Sometimes you may require our writers to add on a point to make your essay as customised as possible, we will give you unlimited times to do this. And we will do it for free.

Timely Essay(s)

We understand the frustrations that comes with late essays and our writers are extra careful to not violate this term. Our support team is always engauging our writers to help you have your essay ahead of time.

Customised Essays &100% Confidential

Our Online writing Service has zero torelance for plagiarised papers. We have plagiarism checking tool that generate plagiarism reports just to make sure you are satisfied.

Try it now!

## Calculate the price of your order

Total price:
\$0.00

How it works?

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

HOW OUR ONLINE ESSAY WRITING SERVICE WORKS

Let us write that nagging essay.

By clicking on the "PLACE ORDER" button, tell us your requires. Be precise for an accurate customised essay. You may also upload any reading materials where applicable.

Pick A & Writer

Our ordering form will provide you with a list of writers and their feedbacks. At step 2, its time select a writer. Our online agents are on stand by to help you just in case.

Editing (OUR PART)

At this stage, our editor will go through your essay and make sure your writer did meet all the instructions.