Show me the steps to solve Consider Algorithm $2$ in lec$3.$pdf$,$ slide $5.$

$1$

$1.$ Modify the algorithm to cube b instead of squaring it in every re$-$

cursive call.

$[0\mathrm{.}5$ point$]$

$2.$ Given inputs b and p in Z$+,$ what are the best$-$case, worst$-$case, and

average$-$case complexity of the modified algorithm? $[0\mathrm{.}5$ point$]$

$3.$ Identify the inputs for which your algorithm performs the minimum

and those for which the algorithm performs the maximum number

of computations in terms of your inputs $($not exact numbers, but the

properties that have to be satisfied by the said inputs$).[0\mathrm{.}5$ point$]$

$4.$ Use big$-$O$,$ big$-\backslash$theta $,$ and big $$ notation to measure the performance of

your algorithm. Justify your answers. $[0\mathrm{.}5$ point$]$

$5.$ How does your algorithm perform compared to Algorithm $2$ in the

notes