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

Array, Array: Array  :  In programming, when large amount of related d...

Array: Array  :  In programming, when large amount of related data needs to be processed and each data element is stored with different a variable name, it becomes very diffic

Time sharing, Time Sharing Time sharing allows a large number of users ...

Time Sharing Time sharing allows a large number of users at various remote terminals to simultaneously use a centrally located computer for problem solving. Each user operates

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

Determine whether the system is stable or causal, QUESTION (a) For each...

QUESTION (a) For each of the following systems, determine whether the system is (1) stable, (2) causal, (3) linear, (4) time invariant, (5) passive (i) Y[n] = x[-n] (ii)

Network control, Network Control, Engineering and Management Network co...

Network Control, Engineering and Management Network control in this sense involves traffic management, and the engineering of the networks to support varying traffic loads. In

What is Decode or execution cycle?, just the once the instruction has bee...

just the once the instruction has been fetched and is accumulated, the next step is to decode the instruction so as to work out what actions should be performed to execute it. This

Array, An array A is said to be special if all its elements are same. Given...

An array A is said to be special if all its elements are same. Given an array, your task is to convert the array to special array by performing some operations. The allowed operati

Cryptography, For which X,Y in {o, O, Theta, Omega, omega}, do the relation...

For which X,Y in {o, O, Theta, Omega, omega}, do the relationships t(n)+t''(n) = X(min(t(n),t''(n))) and t(n)+t''(n) = Y(max(t(n),t''(n))) hold for all t,t'' such that t(n),t''(n)

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