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

Perverse software, Perverse software: Perverse software is a program w...

Perverse software: Perverse software is a program which causes hindrances in other programs execution in such a way resulting in modification or complete destruction of data w

The central processing unit (cpu), THE CENTRAL PROCESSING UNIT (CPU): T...

THE CENTRAL PROCESSING UNIT (CPU): The CPU is the heart of any computing system.  It executes the individual machine instructions, which make up a program. The CPU is formed fr

Design problem, Design Problem 1. Implement a basic file system managed fr...

Design Problem 1. Implement a basic file system managed from within a file. The file system should have the following capabilities: i. List files stored along with their sizes.

Define internet and explain its working, Question 1 Define Internet and ex...

Question 1 Define Internet and explain its working Question 2 Explain page format specifiers and page content specifiers of XSL-FO Question 3 Write a note on HTML

Explain the construction of hard drive, Question 1 Classify and explain th...

Question 1 Classify and explain the different types of computers Question 2 List and explain the commonly used input devices Question 3 What is binary number system? Exp

Fourth generation of computers, THE FOURTH GENERATION (1975 ONWARDS) ...

THE FOURTH GENERATION (1975 ONWARDS) This generation of computers have one or more of the following characteristics:     Semi-conductor memory instead of core memo

Generic techniques in artificial intelligence, G e ne ric Techniques Dev...

G e ne ric Techniques Developed: In  the  pursuit  of  solutions  to  many   problems  in  the  above  categories,  serval specific  techniques have sprung up which have bee

DATA STRUCTURE, WHAT IS DATA STRUCTURE AND EXPLAIN ME.

WHAT IS DATA STRUCTURE AND EXPLAIN ME.

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