Question

The runtime of a program is proportional to n^1.5 where n is the input size.  For input size 100 the runtime is 51 ms.  What is the new runtime when the input size is quadrupled?

Answer 1

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Answer :

Runtime = 408 ms

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Explanation:

Runtimes means the time taken by a program to run completely.

If a program has Runtime of 10ms , it means that it takes 10 ms for this program to be run completely.

Input is processed by program while its running. If the size or amount of input increases , the runtimes also increases in most cases.

Here in the question it is given : 'runtime of a program is propotional to  n^{1.5 '}

So,     ∝    ,  where is Runtime.

we can write this as , = k (    ) , where k is a constant.

So, k = /   n^1.5

It is given in the question that when input size is 100 , the runtime is 51ms

So,    = k (    )

=> 51 = k ()

=> k = 51/ ()

It is asked in the question that if runtime is quadrupled, whats new runtime.

So, n = 100*4 = 400.

   = k   (    )

= k ( )

   = 51/ () * ( )

    = 51/1000 * 8000

   = 408 ms

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