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 on a single machine. The objective is to maximize the total profit by completing the jobs within their respective deadlines.
A greedy algorithm can be used to solve the job sequencing problem. The steps involved in the greedy approach are as follows:
1. Sort the jobs in descending order of their profits. This ensures that the jobs with higher profits are considered first.
2. Initialize an array or list to keep track of the time slots. Initially, all time slots are set to empty.
3. Iterate through each job in the sorted order. 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 mark it as occupied.
4. Repeat step 3 for all the jobs in the sorted order.
By following this greedy approach, the jobs with higher profits are scheduled first, maximizing the total profit. The algorithm ensures that each job is assigned to the latest available time slot before its deadline, preventing any missed deadlines.
It is important to note that the greedy algorithm for the job sequencing problem assumes that the profits associated with the jobs are non-decreasing. If the profits are not sorted in descending order, the algorithm may not provide an optimal solution.