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

Computer, hitory and genration of computer

hitory and genration of computer

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

Multiple allocations, You can also allocate a single value to several varia...

You can also allocate a single value to several variables at the same time. For instance: X=y=z =1 Now, an integer object is generated with the value 1, and all three variables are

Data communications, Data communication as a need developed in the 1960s wi...

Data communication as a need developed in the 1960s with the interconnection of peripheral devices to mainframe computers. Within the immediate vicinity of the mainframe computer t

Logic instructions , They are used to act upon logic operations on the oper...

They are used to act upon logic operations on the operators. AND OR, NEG NOT TEST XOR AND INSTRUCTION Function: It acts upon the conjunction of the operators bit by bit. Syntax: A

Digital transmission, Digital Transmission: In digital transmission, w...

Digital Transmission: In digital transmission, wave patterns are translated into discrete bits and are separated by intervals. Bits (contraction for binary digits) are the sma

Immediate addressing, These addressing modes are: With immediate addressing...

These addressing modes are: With immediate addressing, no lookup of data is essentially required. The data is located in the operands of the instruction itself, not in a different

Telephobn directory, #que1) Create telephone directory. • The heading shoul...

#que1) Create telephone directory. • The heading should be 16-point Arial font in bold • The rest of the document should use 10-point font size • Other headings should use 10-point

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