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

Application packages, APPLICATION PACKAGES : There are two options. You ca...

APPLICATION PACKAGES : There are two options. You can either write your own program or buy an applications package, i.e. a proprietary program, 'off-the-shelf. The former option i

Compare cisc with risc cpus, Question 1 Define the following terms        ...

Question 1 Define the following terms                           1) Pipelining 2) Super Pipelining 3) Dynamic Execution 4) Multiprocessing 5) Multimedia Extensions Question 2

Explain what is rmi, QUESTION (a) Explain what is RMI? (b) Draw a di...

QUESTION (a) Explain what is RMI? (b) Draw a diagram showing the different parts of the Java RMI architecture. (c) What is the function of the RMI security manager and RM

Find shortest path in network, Find shortest path from node 1 to node 10 in...

Find shortest path from node 1 to node 10 in the network shown in figure, also find shortest path from node 3 to node 10. Please write all steps to finding shortest path mechanism

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

Impact printers and non - impact printers, Impact Printers and non - Impact...

Impact Printers and non - Impact Printers: Impact Printers: These are printers in which the print-head strikes a ribbon, and include the daisywheel and thimble printer

Digital logic design, Find the complement of the following decimal 7

Find the complement of the following decimal 7

Communications programs , Communications Programs : By communications prog...

Communications Programs : By communications programs, we mean those programs which allow a computer to communicate via a transmission cable to another electronic device. Here we d

Variables and constants, Variables and Constants: These are the smalle...

Variables and Constants: These are the smallest components of a programming language.  For writing a program, one must know how to use the internal memory of a computer. A Com

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