Respuesta :

CPED

Answer:

Given that:

A= 40n^2

B = 2n^3

By given scenario:

40n^2=2n^3

dividing both sides by 2

20n^2=n^3

dividing both sides by n^2 we get

20 = n

Now putting n=20 in algorithms A and B:

A=40n^2

= 40 (20)^2

= 40 * (400)

A= 16000

B= 2n^3

= 2 (20)^3

= 2(8000)

B= 16000

Now as A and B got same on n = 20, then as given:

n0 <20 for n =20

Let us take n0 = 19, it will prove A is better than B.

We can also match the respective graphs of algorithms of A and B to see which one leads and which one lags, before they cross at n= 20.

Lanuel

Based on the calculations, algorithm A would be better than algorithms B for [tex]n\geq 21[/tex]

Given the following data:

  • Number of operations A = [tex]40n^2[/tex]
  • Number of operations B = [tex]2n^3[/tex]

What is an algorithm?

An algorithm refers to a standard formula (procedures) which contains a set of finite steps and instructions (operations) that must be executed while proffering solutions to a problem on a computer under appropriate conditions.

In this scenario, we would determine the point of intersection for the graphs describing the behavior of these two algorithms as follows:

[tex]A=B\\\\40n^2=2n^3\\\\[/tex]

n = 20.

Therefore, [tex]n_0=21[/tex]

Note: For all [tex]n\geq 21[/tex], algorithm A would be faster than algorithms B.

In conclusion, algorithm A would be better than algorithms B for [tex]n\geq 21[/tex]

Read more on algorithm here: brainly.com/question/24793921

Otras preguntas