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Computers and Technology

1 answer:

Thepotemich [5.8K]3 years ago

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Narrative, Content

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a program p takes time proportional to log where nlogn is the input size. if the program takes 100 ms to process input of size 1

Eddi Din [679]

Answer:

The time is $4 \times 10^7 \ microseconds.$

Explanation:

$\ The \ requires \ time \ be \ t \ microseconds, \\\\\ \ formula: \\\\ time \propto \ nlog_n \Rightarrow \ time \ = \ knlogn \\\\$

$\ 10 \ = \ 100 \ log(100) \ \ \ \ \ \ \ \ \ k= 10^2 \ log\ ( \ 10^2\ ) \ k\\\\t=100,000,000 \log \ ( \ 100,000,000\ ) \ k = \ 10^8 \ log\ (\ 10^8\ )\ k \\\\\rightarrow \frac{t}{10} \ =\frac{10^8\ log \ (10^8)k}{10^2\ log\(10^2\ ) k} \\\\\rightarrow \frac{t}{10} \ =\frac{10^8\ log \ (10)\times 8 \times k}{10^2\ log\(10) \times 2 k} \\\\\rightarrow \frac{t}{10} \ =\ 4\times 10^6\\\\\rightarrow \ t \ =\ 4\times 10^6 \times 10 \\\\\rightarrow \ t \ =\ 4\times 10^7 \ microseconds \\\\$