Question

An algorithm takes 5 seconds for input size 200. How long will it take for input size 1000 if the running time is linear (assume low-order terms are negligible)?

Answer 1

The running time for an input size of 1000 will be 25 seconds.

To calculate the runtime of the Algorithm we need to know what an Algorithm is and how its runtime works.

What is the runtime of an Algorithm?

A finite sequence of rigorous instructions, used to solve a critical problem of a specific class or for computational purposes is called an Algorithm. The time taken to complete the said task is called the runtime of an Algorithm.

Let us now solve the question about linear running time of an algorithm.

Input size($N_{1}$)=200

Time taken($T_1$)=5 seconds

Final input size($N_2$)=1000

Let the final time taken be T.

Now we know that: $\frac{N_1}{T_1}=\frac{N_2}{T_2}$

Substituting the values we get $T_2=25$ seconds .

Therefore the linear running time for an input size of 1000 is 25 seconds.

To know more about Algorithm:

brainly.com/question/17780739

#SPJ4