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

RMO CSMS marketing subsystem, I need to write a narrative n overview of the...

I need to write a narrative n overview of the diagram and an analysis of the actors

Kids, how do you let kids learn on it

how do you let kids learn on it

Definition of Internal hardware interruptions, Internal interruptions are...

Internal interruptions are produced by convinced events which come during the execution of a program. These types of interruptions are handled on their totality by the hardware and

Digital computer, Digital computer: In the digital computer there are b...

Digital computer: In the digital computer there are basically two types of input, namely Instructions, and Data from the various radio and non-radio sensors, which will be refe

Database management help, Suppose that you are writing a stored procedure t...

Suppose that you are writing a stored procedure to record new purchases. Suppose that you know that while your procedure is running, another stored procedure that records shipment

Variable - concept of programming language, Variable - Concept of programmi...

Variable - Concept of programming language: Variable: As referencing memory by its physical address is very tedious, variable names are used. A variable is a symbolic name giv

Computer generations, Computer Generations: From the early 1940's to t...

Computer Generations: From the early 1940's to the present, computer scientists have been able to identify clear-cut stages in the development of computer technology. With eac

Image processing, Image Processing: This technology is quite advanced ...

Image Processing: This technology is quite advanced and devices are now available for routine scanning and storage of printed pages, graphics, etc., which can then be retrieve

Components of a digital computer , COMPONENTS OF A DIGITAL COMPUTER: A...

COMPONENTS OF A DIGITAL COMPUTER: A digital computer is an electronic device that receives data, performs arithmetic and logical operations and produces results according to a

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