/*
* The problem of scheduling unit-time tasks with deadlines and penalities for a single processor has following inputs
* S={a1,a2,...,an} of n unit-time task.
* A unit-time task requires exactly 1 unit of time to complete
* deadlines d1,d2,...,dn, 1<=di<=n
* penalities w1,w2,...,wn.
* A penality wi is incurred if task ai is not finished by time di, and no penality if task finishes at deadline
* The problem is to find a schedule for S that minimizes the total penalty incurred for missed deadlines
*
* Complexety: O(n*log(n))
*/
public static List <Tuple <Sequencing_Job, bool> > FindSequence3(Sequencing_Job[] jobs)
{
List <Tuple <Sequencing_Job, bool> > sequence = new List <Tuple <Sequencing_Job, bool> >();
if (jobs.Length <= 0)
{
return(sequence);
}
Array.Sort(jobs, new Sequencing_ReverseComparerPenalty());
int maxDeadline = Int32.MinValue;
foreach (Sequencing_Job job in jobs)
{
if (job.Deadline > maxDeadline)
{
maxDeadline = job.Deadline;
}
}
Sequencing_DisjointSet disjointSet = new Sequencing_DisjointSet(maxDeadline);
List <Sequencing_Job> penalised = new List <Sequencing_Job>();
Sequencing_Job[] tmpSequence = new Sequencing_Job[jobs.Length];
foreach (Sequencing_Job job in jobs)
{
int slot = disjointSet.Find(job.Deadline);
if (slot > 0)
{
disjointSet.Merge(disjointSet.Find(slot - 1), slot);
tmpSequence[slot - 1] = job;
}
else
{
penalised.Add(job);
}
}
foreach (Sequencing_Job job in tmpSequence)
{
if (job != null)
{
sequence.Add(new Tuple <Sequencing_Job, bool>(job, false));
}
}
foreach (Sequencing_Job job in penalised)
{
sequence.Add(new Tuple <Sequencing_Job, bool>(job, true));
}
return(sequence);
}
/*
* Given a set of n jobs where each job i has a deadline di >=1 and profit pi>=0.
* Only one job can be scheduled at a time. Each job takes 1 unit of time to complete.
* We earn the profit if and only if the job is completed by its deadline.
* The task is to find the subset of jobs that maximizes profit.
*
* Complexety: O(n*log(n))
*/
public static List <Sequencing_Job> FindSequence2(Sequencing_Job[] jobs)
{
List <Sequencing_Job> jobSequence = new List <Sequencing_Job>();
if (jobs.Length <= 0)
{
return(jobSequence);
}
Array.Sort(jobs, new Sequencing_ReverseComparerProfit());
int maxDeadline = Int32.MinValue;
foreach (Sequencing_Job job in jobs)
{
if (job.Deadline > maxDeadline)
{
maxDeadline = job.Deadline;
}
}
Sequencing_DisjointSet disjointSet = new Sequencing_DisjointSet(maxDeadline);
Sequencing_Job[] results = new Sequencing_Job[maxDeadline + 1];
for (int i = 0; i < jobs.Length; i++)
{
int slot = disjointSet.Find(jobs[i].Deadline);
if (slot > 0)
{
int parentSlot = disjointSet.Find(slot - 1);
disjointSet.Merge(parentSlot, slot);
results[slot] = jobs[i];
}
}
foreach (Sequencing_Job job in results)
{
if (job != null)
{
jobSequence.Add(job);
}
}
return(jobSequence);
}
