What is the Interval Scheduling problem and how can it be solved using a greedy algorithm?

What is the Interval Scheduling problem and how can it be solved using a greedy algorithm?

The Interval Scheduling problem involves selecting the maximum number of non-overlapping intervals from a given set of intervals. The goal is to find a schedule that maximizes the number of intervals selected.

A greedy algorithm can be used to solve this problem. The algorithm works as follows:

1. Sort the intervals based on their finishing times in ascending order.
2. Initialize an empty set to store the selected intervals.
3. Iterate through the sorted intervals.
4. For each interval, check if it overlaps with any of the previously selected intervals. If it does not overlap, add it to the selected set.
5. Continue this process until all intervals have been considered.
6. Return the selected set of intervals as the solution.

The greedy algorithm works by always selecting the interval with the earliest finishing time that does not overlap with any previously selected intervals. This ensures that the maximum number of intervals can be scheduled without any overlaps.