Your boss asks you to decide which of two algorithms to use in a

new software system. The runtimes of the two algorithms are given

by the following recurrences $($remember that when the base case of a

recurrence is not given, assume $T(c)=(1)$ for any constant $c)$:

Algorithm $1$: $T(n)=5T(\frac{n}{2})+n$

Algorithm $2$: $T(n)=3T(\frac{n}{2})+n^2$

Which algorithm has the better asymptotic cost? Justify your answer

by solving both recurrences $($using recursion trees$)$ and comparing the

solutions.