Question

Problem 2. (5 pts.) Algorithms A and B perform the same task. On input of size n, algorithm A executes 10 n 2 steps, and algorithm B executes 100,000 steps. Find the value of n above which algorithm B is more efficient. Show your work.

Answer 1

For input of size n, the algorithm A executes

steps.

For input of size n, the algorithm B executes

100000 steps.

So,for algorithm B to be more efficient then A,

$100000>10n^2$

$n^2<10000$

So,

$n\varepsilon (1,100)$