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

Cpu, what is cpu

what is cpu

Flow decomposition technique to list the cycles, QUESTION (a) Consider ...

QUESTION (a) Consider the graph below, use the Flow Decomposition technique to list the cycles and paths produced.                                                (b) Pr

CAI, explain CAI pitfalls

explain CAI pitfalls

Algorithm implementation, Implementing the -Crochemore-Perrin algorithm Th...

Implementing the -Crochemore-Perrin algorithm The software must be functional, code must be clear and including comments and it must have a nice and decent user interface

ICT IN BUSINESS, Explain how ICT can be used for achievement of each of the...

Explain how ICT can be used for achievement of each of the following business objectives, illustrating your answer with examples: 1. Customer intimacy 2. Low-cost leadership

Encoders, compare encoders and multiplers

compare encoders and multiplers

Software development, requirement analysis and specification for online vot...

requirement analysis and specification for online voting

Challenges in building information system, discuss the three major challeng...

discuss the three major challenges in building information system in an organization

Explain initial dynamic model with example, Question 1 Explain initial dyn...

Question 1 Explain initial dynamic model with example Question 2 Discuss the importance of object orientation during system development Question 3 Distinguish between Ob

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