Greedy Algorithms Questions Medium
The interval scheduling problem is a classic optimization problem that involves scheduling a set of tasks or activities, each with a start time and an end time, in a way that maximizes the number of non-overlapping activities that can be performed.
To solve this problem using a greedy algorithm, we can follow the following steps:
1. Sort the activities based on their end times in ascending order. This step ensures that we always consider the activity with the earliest end time first.
2. Initialize an empty set, called the "schedule," to store the selected activities.
3. Iterate through the sorted activities. For each activity, check if it overlaps with any of the activities already in the schedule. If it does not overlap, add it to the schedule.
4. Return the schedule, which represents the maximum number of non-overlapping activities that can be performed.
The greedy strategy in this algorithm is to always select the activity with the earliest end time that does not overlap with the previously selected activities. By doing so, we ensure that we maximize the number of activities that can be scheduled without any conflicts.
This greedy algorithm works because it exploits the fact that selecting the activity with the earliest end time leaves more room for scheduling other activities. By always choosing the activity that finishes earliest, we can fit in as many non-overlapping activities as possible, resulting in an optimal solution to the interval scheduling problem.