Question: (a) Suppose that a particular algorithm has time complexity (T(n) = 3 times 2^n), and that executing an implementation of it on a particular machine

(a) Suppose that a particular algorithm has time complexity $T(n) = 3 \times 2^n$, and that executing an implementation of it on a particular machine takes $t$ seconds for $n$ inputs. Now suppose that we are presented with a machine that is 64 times as fast. How many inputs could we process on the new machine in $t$ seconds?

(b) Suppose that another algorithm has time complexity $T(n) = n^2$, and that executing an implementation of it on a particular machine takes $t$ seconds for $n$ inputs. Now suppose that we are presented with a machine that is 64 times as fast. How many inputs could we process on the new machine in $t$ seconds?

(c) A third algorithm has time complexity $T(n) = 8n$. Executing an implementation of it on a particular machine takes $t$ seconds for $n$ inputs. Given a new machine that is 64 times as fast, how many inputs could we process in $t$ seconds?

Step by Step Solution

★★★★★

3.37 Rating (150 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a The time complexity of the first algorithm is Tn 3 times 2n which is an exponential time complexit... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Practical Introduction To Data Structures Questions!

a. Example 13-1: Batch Reactor with an Exothermic Reaction Wolfram 1. Adiabatic Case: Use Wolfram to see whether you can find a trajectory that is ready to ignite and whose trajectory looks like a...

Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...

Write a literature review for your study. See below for an example of a literature review. Your literature review should provide both analysis and synthesis of previous studies as related to the...

Suppose that a particular algorithm has time complexity ( ) = 2 T ( n ) = n 2 and that executing an implementation of it on a particular machine takes t seconds for n inputs. Now suppose that we are...

Can I please get help on the questions above please 3.3 Arrange the following expressions by growth rate from slowest to fastest. 4n2log3nn!3n20n2log2nn2/3 See Stirling's approximation in Section 2.2...

Can I get help with this question please .4 (a) Suppose that a particular algorithm has time complexity T(n)=3 2n, and that executing an implementation of it on a particular machine takes t seconds...

Suppose that a particular algorithm has time complexity T ( n ) = n 2 and that executing an implementation of it on a particular machine takes t seconds for n inputs. Now suppose that we are...

In a class hierarchy, a subclass reimplements an instance method of a superclass to add more functionality with the same name. In object oriented programming, this phenomenon is known as: option 1:...

Python and most Python libraries are free to download or use, though many users use Python through a paid service. Paid services help IT organizations manage the risks associated with the use of...

answer all questions promptly What is the maximum segment length of a 100Base-FX netdwork,Thelast character('X', etc) refers to the line code method used. Line code is a pattern of voltage, current...

At the top of the most popular type lists for social networking, the following are always included: Facebook, LinkedIn, Twitter, Snapchat, Instagram, and YouTube. Each one has a different purpose and...

An orthogonal matrix is cos a 2sina (a) -2sina cosa (c) cos a sina sina cos a (b) cosa -sina (d) [1 sina cos a

The file market penetration contains Facebook penetration values (the percentage of the country population that are Facebook users) for 22 of the worlds largest economies: 56 57 43 55 42 35 7 25 42...

Defi ne sales promotion and discuss its objectives. (AACSB: Communication) LO.1

In Figure 11.12, explain why we need a timer at the sending site, but none at the receiving site. Figure 11.12 Receiving node Network Sending node Network Data-link Data-link Packet Frame Legend...

Redraw Figure 11.21 with the system not using authentication. Figure 11.21 Carrier detection failed Start Dead Carrier detected Establish Carrier dropped Authentication needed Authentication failed...

Does the duplex communication in Figure 11.10 necessarily mean we need two separate media between the two nodes? Explain. Figure 11.10 Receiving node Sending node Frame ACK [CRC Network [CRC Network...

In a production process, reactor exit flow is a mixture of methyl ethyl keton ( MEK ) , secbutanol and n - butanol. The mixture has 0 . 5 % MEK, 6 9 . 2 % sec - butanol, and 3 0 . 3 % n butanol: The...

At 27 C, a silicon substrate has a Fermi level that is 0.4 eV below the conduction band minimum. a) What is the dopant type (p or n-type), b) what is the dopant (i.e. majority carrier) concentration...

A company is expected to have free cash flows of $75 million next year. The weighted average cost of capital is WACC = 10.1%, and the expected constant growth rate is g = 6.4%. The company has $2...