Greedy Algorithms Questions Medium
The job sequencing problem is a combinatorial optimization problem where a set of jobs with associated deadlines and profits needs to be scheduled in a way that maximizes the total profit. Each job has a specific deadline by which it needs to be completed, and if a job is not completed by its deadline, it incurs a penalty.
To solve the job sequencing problem using a greedy algorithm, we follow these steps:
1. Sort the jobs in descending order based on their profits. This ensures that we prioritize the jobs with higher profits.
2. Initialize an array or list to keep track of the time slots for each job. Initially, all time slots are set to zero.
3. Iterate through the sorted jobs and for each job, find the latest available time slot before its deadline. If a time slot is available, assign the job to that time slot and update the time slot accordingly. If no time slot is available, skip the job.
4. Repeat step 3 for all the jobs.
By following this greedy approach, we ensure that the jobs with higher profits are scheduled first, maximizing the total profit. Additionally, by assigning jobs to the latest available time slots, we minimize the penalty incurred for missing deadlines.
It is important to note that the greedy algorithm for the job sequencing problem may not always provide an optimal solution. There can be cases where a different scheduling approach could yield a higher total profit. However, the greedy algorithm provides a simple and efficient solution in many practical scenarios.