Question

Could you please help me to solve the problem. Also, could you please answer questions in clear hand-writing and show me the full process, thank you (Sometimes I get the answer which was difficult to read).Thanks a lot

Suppose we are comparing implementations of two algorithms on the same machine. For input size of n, Algorithm A runs in 8n^2 steps, while Algorithm B runs in 64nlog₂(n) steps. For what value n>2, where n is an integer, does Algorithm A run in fewer steps than Algorithm B? (give your answer in whole number(s)).

Answer 1

GRAPH:

We can also manually check the validity of this interval by taking a value of n out of this range. For example :

Let n=44, then:

A: 8n2 = 8 x 44^2 = 15488 steps

B: 64nlog2(n) = 64 x 44 x log2(44) = 15374 steps

Thus at this point, A>B and hence our interval holds true.

NOTE: Writing the interval 3<=n<=43 is same as 2<n<=43 as n as supposed to be an integer greater than 2, as mentioned in the question