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

Super computers, Super Computers: The specialised demands and requirem...

Super Computers: The specialised demands and requirements of science, industry and military have led to the creation of powerful super computers. For numerically intensive com

Assembly, can you help me to do my assembly program homework

can you help me to do my assembly program homework

CAI, What is CAI? Explain its pitfalls

What is CAI? Explain its pitfalls

Enterprise resource planning, ENTERPRISE RESOURCE PLANNING What ...

ENTERPRISE RESOURCE PLANNING What has football got to do with it? asks management guru Michael Hammer in his latest best seller Beyond Reengineering. The answer is almos

Database, Q1: ER modelling & logical design. An information system is requi...

Q1: ER modelling & logical design. An information system is required for an online auction site, based on the following speci?cation: Only registered users can use the site. Privat

About execution cycle, One time a program is in memory it has to be execut...

One time a program is in memory it has to be executed. To do this, each instruction must be appeared at, decoded and acted upon in turn until the program is finished. This is accom

What is Semaphore and explain with example?, Description A semaphore is a...

Description A semaphore is a confined variable whose value can be accessed and changed only by the operations P and V and initialization operation known as ''Semaphoiinitislize''.

C++, Ask question #MiniA string S is said to be "Super ASCII", if it contai...

Ask question #MiniA string S is said to be "Super ASCII", if it contains the character frequency equal to their ascii values. String will contain only lower case alphabets (''''a''

What technical challenges must be overcome, QUESTION a) Clearly explain...

QUESTION a) Clearly explain three main issues arising in the design of components for use in Intranets. b) Explain the term "location-aware Computing". c) The Internet en

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