Algorithms, Basic Computer Science

Assignment Help:
1. In each of the following situations, indicate whether f = O(g), or f = O(g), or both (in which case f = T(g)). Briefly explain why.
(a) f(n)=10n5 +8n2,g(n)=20n4 +7n3 +300 (b) f(n) = log 8n, g(n) = log(n2)
(c) f(n)=n3logn,g(n)=13n 5
(d) f(n) = (3)n, g(n) = 6n3 2
2. We introduced in class that when analyzing algorithm complexity, we can ignore the lower-order terms and the coefficient of the leading term. For example, 3n + 5 ? n. Using the formal definition of the big-O notation, show that 3n + 5 = O(n) and n = O(3n + 5), in other words, 3n + 5 = T(n).
3. The Fibonacci numbers F0, F1, F2, . . ., are defined by the rule F0 =0,F1 =1,Fn =Fn-1 +Fn-2.
Use induction to prove that Fn = 20.5n for n = 6.
4. Write a python program to compute the Fibonacci numbers F8, F28, F48. What are the three values? What is the total number of additions needed by your program? Provide your answers as well as your source code.

Related Discussions:- Algorithms

Some CPUs provide multiple modes of operation, even though most systems onl...

even though most systems only distinguish among user and kernel modes, some CPUs provide multiple modes. Multiple modes could be used to provide a finer-grained security strategy.

Advantages of computerized record-keeping, Advantages of Computerized Reco...

Advantages of Computerized Record-keeping Less manpower is required for upkeep.  Recording, storing, and retrieving are all much faster: easier and with little practice

Encoder, What is an encoder? Draw the logic circuit of Decimal to BCD encod...

What is an encoder? Draw the logic circuit of Decimal to BCD encoder and explain its working.?

Flowcharts, what is a dry running of flow chart?

what is a dry running of flow chart?

Reflex agent-artificial intelligence, Reflex agent-Artificial Intelligence ...

Reflex agent-Artificial Intelligence If an agent decides and executes an action in response to a sensor input without consultation of its world, then it may be considered a ref

Explain briefly about gnome desktop, Question 1 Brief about the shells of ...

Question 1 Brief about the shells of Linux operating system Question 2 Explain briefly about GNOME desktop Question 3 Write note on the following Encryption Sig

Pyhon''s Multi-Line Statements , Statements in Python classically end with ...

Statements in Python classically end with a new line. Python does, though, permit the use of the line continuation character (\) to denote that the line should continue. Illustrati

Data input , Data Input : There are several aspects of data input that nee...

Data Input : There are several aspects of data input that need careful consideration. We shall assume that in a laboratory environment you are mainly concerned with entering data

Introduction to laboratory organisation and management, INTRODUCTION : In ...

INTRODUCTION : In the earlier units of this block you learnt the importance of proper filing and record keeping. You are also aware that in laboratory organisation and management,

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd