Consider a single machine that can process jobs. We receive a set of job requests $\{1,2,$dots,$n\},$

and the $i$ th request takes a positive time duration $a_i$ to process. We are able to use the machine

for the period between time $0$ and specified time $T.$ Our goal is to process the jobs so as

to keep the machine busy for the entire time it is available. Give an efficient algorithm to

determine whether the machine can be kept busy for the entire time $T,$ and which jobs should

be processed. You may assume the processing times $a_i$ and total available time $T$ are positive

integers. Also state and justify the running time of your algorithm.