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

Ricochet wireless data network, The Internet is replete with great success ...

The Internet is replete with great success stories and sad failures. While it is always nice to hear about the successes, more can probably be learned from the failures. In this ca

Coaxial cables, Coaxial Cables: Another metallic transmission medium w...

Coaxial Cables: Another metallic transmission medium which offers a large bandwidth, is the coaxial cable. Such cables consist of an outer protective shell made of copper tube

What isit, what can you do and what and how who can becbgbfbvuidfgvbkjfdhvb...

what can you do and what and how who can becbgbfbvuidfgvbkjfdhvb98dshrnfjkbhqdbnfiubnfdjbhdfiubndfubhfdbhfdiubhdfuibhyfdubhdfbhfbhdf8u

Erp components, What constitutes ERP? ERP typically comprises a client ...

What constitutes ERP? ERP typically comprises a client server architecture, fourth generation language, RDBMS and graphical user interface in an open systems environment. It

Definition of assembler structure, In assembly language code lines have t...

In assembly language code lines have two fractions, the earliest one is the name of the instruction which is to be executed, and the next one are the parameters of the command. For

C++, Write a C++ program that declares three integers and three strings. Th...

Write a C++ program that declares three integers and three strings. The program prompts the user for three characters and three integers and prints them all on one line.

Syntax - programming language, Syntax: Syntax provides the structure a...

Syntax: Syntax provides the structure and how to formulate the phrase or sentence w.r.t grammar of the language. It tells us about which composition is allowed from the charac

What is i-node number, Question 1 Bring out the advantages of Linux Ope...

Question 1 Bring out the advantages of Linux Operating systems Question 2 Match the Symbols with their respective file types              Symbol               File N

What is the definition of instructiion set?, For a processor to be able ...

For a processor to be able to process an instruction, it requires to be able to determine what the instruction is asking to be carried out. For this to take place, the CPU requires

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