Suppose that Algorithm A has runtime complexity O$($n$^2)$ and Algorithm B has runtime complexity

O$($n log n$),$ where both algorithms solve the same problem.

$($a$)$ Assume you started both algorithms simultaneously, and assume that n $=50.$ Is it possible for Algorithm

A to terminate before Algorithm B$?$

$($b$)$ Is it possible, that actual running time of A and B is the function n$?$

$($c$)$ Suppose we also know that Algorithm A has runtime complexity $($n$^2),$ and Algorithm B has runtime

complexity $($n log n$).$ In other words, runtimes of A and B are $\backslash$Theta $($n$^2)$ and $\backslash$Theta $($n log n$),$ respectively. How

do the algorithms compare when n is very large?