What is the Minimum Number of Platforms problem and how can it be solved using a greedy algorithm?

What is the Minimum Number of Platforms problem and how can it be solved using a greedy algorithm?

The Minimum Number of Platforms problem is a scheduling problem that involves finding the minimum number of platforms required to accommodate all given train arrivals and departures at a railway station. The problem assumes that each train arrival and departure is represented by a time interval.

To solve this problem using a greedy algorithm, we can follow these steps:

1. Sort the train arrival and departure times in ascending order.
2. Initialize two variables: "platforms" to keep track of the minimum number of platforms needed, and "currentPlatforms" to keep track of the number of platforms currently in use.
3. Iterate through the sorted time intervals:
a. If the current interval represents a train arrival, increment "currentPlatforms" by 1.
b. If the current interval represents a train departure, decrement "currentPlatforms" by 1.
c. Update "platforms" with the maximum value between "platforms" and "currentPlatforms".
4. Return the value of "platforms" as the minimum number of platforms required.

By following this greedy approach, we consider each train arrival and departure in a sorted order and increment or decrement the number of platforms accordingly. The maximum number of platforms in use at any given time will give us the minimum number of platforms required to accommodate all train schedules.