Suppose you are working with a $2\mathrm{.}5$ GHz dual core PC that can do

$2$ flops per core per clock cycle. Given an input size of n$,$ suppose that some

algorithm requires n$2$ flops to compute a desired quantity.

$($i$)$ Estimate how long it would take the algorithm to compute the desired quan

tity for n $=20,000.$

$($ii$)$ Estimate the largest input size n for which the algorithm can compute the

desired quantity in one minute