We know that there is a Greedy algorithm for scheduling of $n$ jobs which each job has its own deadline and profit.
In greedy algorithm, we sort the set by their profit descendant, And if a job can add to a
possible set of jobs, we add it to the set.
A job can be added to the set, if it starts before its deadline and each work need 1 time slot for doing.
Is there any $O(nlogn)$ algorithm for this problem as follows?
- Sorting the set by their profit using merge sort in $O(nlogn)$
- Add the first job to the possibility set.
- For remain jobs, add the job to the set of its deadline is less than its index in possibility set.
- We have to remain the
possible setsorted. Then for each new coming job, we can add it to the set using
binary searchin $O(logn)$
Total cost of the above algorithm is $O(nlogn)+O(n)*O(logn)=O(nlogn)$
Is this algorithm correct?