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

Write a long note letters to the editor, Question 1 What is meant by typog...

Question 1 What is meant by typography? Describe the process in which one can choose and use type Question 2 What is investigative reporting? Write a long note Question 3

Explain TCP and UDP features in detail and compare, Which applications requ...

Which applications require TCP and why? Also specify which applications require UDP and why? A4) TCP is also known as connection-oriented: setup required between client and server

Differentiate between a dynamic and a static web site, QUESTION a) Diff...

QUESTION a) Differentiate between a dynamic and a static web site. b) Why are electronic mails (e-mails) preferred to the post office mails? How do they affect the modern of

Unix Shell, Write a shell script, change-lines, which will substitute a str...

Write a shell script, change-lines, which will substitute a string for a replacement string for each occurance of the string in files specified. The original file will be saved,

With an example, Question 1 With an example, illustrate the concept of ext...

Question 1 With an example, illustrate the concept of extern variable Question 2 What is the difference between pointer variable and simple variable? Question 3 Give the

What is heuristic evaluation, Question 1: (a) How would you describe h...

Question 1: (a) How would you describe human reasoning? (b) Describe the different types of human reasoning? Question 2: (a) What are the computational factors affec

Sequential-access memory device, Sequential-access memory device: A  S...

Sequential-access memory device: A  Sequential-access  memory device reads data in sequence. In other words, information on a serial device can only be retrieved in the same s

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