Greedy Algorithms Questions
The Activity Selection problem is a problem in which we are given a set of activities, each with a start time and finish time, and we need to select the maximum number of non-overlapping activities.
A greedy algorithm can be used to solve the Activity Selection problem. The algorithm works by selecting the activity with the earliest finish time as the first activity. Then, it iteratively selects the activity with the earliest finish time among the remaining activities that does not overlap with the previously selected activities. This process is repeated until no more activities are left.
The steps of the greedy algorithm for the Activity Selection problem are as follows:
1. Sort the activities based on their finish times in ascending order.
2. Select the first activity with the earliest finish time.
3. For each remaining activity, if its start time is greater than or equal to the finish time of the previously selected activity, select it as the next activity.
4. Repeat step 3 until no more activities are left.
By following this greedy approach, we can ensure that we select the maximum number of non-overlapping activities. The greedy algorithm works because by selecting the activity with the earliest finish time, we free up more time slots for other activities to be selected.