Algorithm

We need to schedule as many meetings as possible in a single room without overlaps. The key observation is that once we choose a meeting that ends earliest, it leaves the room available for more potential meetings afterward. This naturally leads to a greedy approach, where instead of testing all possible combinations we pick meetings in an order that maximizes free time for future meetings. The greedy choice is to always select the meeting that finishes earliest among the available ones.

Sort meetings by end time so that the ones that finish earliest are considered first.
Select the first meeting in the sorted list and mark its end time as the last occupied time.
Iterate through remaining meetings, and for each, check if its start time is strictly greater than the last occupied end time.
If condition holds, include that meeting in the schedule and update the last occupied end time to this meeting’s end time.
Continue until all meetings are checked, resulting in the maximum possible non-overlapping meetings in the room.