Question

(1 point) you are the head of a division of a big silicon valley company and have assigned one of your engineers, jim, the job of devising an algorithm to sort through an english text of n words and convert it into an esperanto document. jim comes up with an algorithm which takes 2n2 2n bit operations to handle an input text with n words. suppose the computers in your business can handle one bit operation every nanosecond (1 nanosecond

Answer 1

The question asks about the time an algorithm would take to process text, with a focus on Computers and Technology at the College level, involving algorithmic efficiency and Big Data processing.

Step-by-step explanation:

The question is related to the field of Computers and Technology, specifically revolving around the efficiency of an algorithm developed by an engineer named Jim. The algorithm requires 2n2 + 2n bit operations for a text of n words. Assuming a computer can perform one bit operation per nanosecond, the task is to determine how long it will take to process an English text of a certain size and convert it into Esperanto. This involves an understanding of algorithmic complexity and performance measurement in terms of bit operations over time. Additionally, the question touches on the benefits of improved resources and technology in enhancing productivity, accompanied by an example linked to homework production, as well as a reference to the processing and organizing of large amounts of data using advanced computer algorithms, which is a common challenge in modern astronomy and other fields dealing with Big Data.

Answer 2

Step-by-step explanation:

a) 2n^2+2^n operations are required for a text with n words

Thus, number of operations for a text with n=10 words is 2\cdot 10^2+2^{10}=1224 operation

Each operation takes one nanosecond, so we need 1224 nanoseconds for Jim's algorithm

b) If n=50, number of operations required is 2\cdot 50^2+2^{50}\approx 1.12589990681\times 10^{15}

To amount of times required is 1.12589990681\times 10^{15} nanoseconds which is

1125899.90685 seconds (we divided by 10^{9}

As 1$day$=24$hours$=24\times 60$minutes$=24\times 60\times 60$seconds$

The time in seconds, our algortihm runs is \frac{1125899.90685}{24\cdot 60\cdot 60}=13.0312 days

Number of days is {\color{Red} 13.0312}

c) In this case, computing order of number of years is more important than number of years itself

We note that n=100 so that 2(100)^2+2^{100}\approx 1.267650600210\times 10^{30} operation (=time in nanosecond)

Which is 1.267650600210\times 10^{21} seconds

So that the time required is 1.4671881947\times 10^{16} days

Each year comprises of 365 days so the number of years it takes is

\frac{1.4671881947\times 10^{16}}{365}=4.0197\times 10^{13} years

That is, 40.197\times 10^{12}=$Slightly more than $40$ trillion years$

Correct option is E