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

What do you mean by an interrupt, Question 1 . Explain briefly the function...

Question 1 . Explain briefly the functional units of a computer Question 2 . What do you mean by an interrupt Question 3 . Explain fetching a word from the memory

Assembly language, Assembly language : Assembly language is a low level...

Assembly language : Assembly language is a low level programming language similar to machine language, but far easier to write and understand because machine language binary in

Data processing, Data Processing In any computer-based system, d...

Data Processing In any computer-based system, data storage and retrieval plays an important role. Data storage involves decision about the encoding of data, assignment o

Cai, What is CAI? Explain its pitfalls.

What is CAI? Explain its pitfalls.

Twisted pairs, Twisted Pairs: Twisted pairs are familiar to all of us ...

Twisted Pairs: Twisted pairs are familiar to all of us as the copper wire telephone lines. These are of low frequency, and support a limited bandwidth (one voice channel) but

#title, what is HMtl stands for, meaning and purpose

what is HMtl stands for, meaning and purpose

Cppm, sum of first 100 integers

sum of first 100 integers

C++, whats the out put of int main(){ int n=310; funcone(n); functwo(&n); ...

whats the out put of int main(){ int n=310; funcone(n); functwo(&n); cout return 0; } void funcone(intn) n=240; } void func two(intn*) { n=120; }

Apple''s rbv, What''s a resource based view of Apple Corporation?

What''s a resource based view of Apple Corporation?

Microwave transmission, Microwave Transmission: Using space as transmi...

Microwave Transmission: Using space as transmission medium, microwave emanates from an origination point on earth, such as telephone exchange, where many individual messages h

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