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

Synchronous and asynchronous transmission, Synchronous and Asynchronous Tra...

Synchronous and Asynchronous Transmission: Another method of setting of terminals denotes synchronous or asynchronous transmission. Many terminals can only communicate in one

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

Protocol, what protocol is used by DNS name server

what protocol is used by DNS name server

Describe different kinds of registers used for register arra, Different kin...

Different kinds of registers are general between most microprocessor designs. These are: Program Counter (PC) This register is utilized to hold the memory address of the next instr

Describe the binary search algorithm, QUESTION 1 Describe the binary se...

QUESTION 1 Describe the binary search algorithm using an example of your own. QUESTION 2 (a) By showing all your workings, give a big-O estimate for f(x) = (x + 1)lo

Rooted tree, Ask qu The figure below shows a rooted tree, 756_Find the hei...

Ask qu The figure below shows a rooted tree, 756_Find the height.png 1.1. Find the height/level of the tree as shown above?estion #Minimum 100 words accepted#

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