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Problem 12: Railway Station Congestion

Problem Statement

Given arrival and departure times of all trains that reach a railway station, find the minimum number of platforms required for the railway station so that no train has to wait.

Input Format

  • Two arrays: arrival (sorted) and departure (unsorted or sorted).

Output Format

  • An integer representing the minimum number of platforms.

Constraints

  • 1 <= arrival.length <= 10^5
  • arrival.length == departure.length

Example

Input: arrival = [900, 940, 950, 1100, 1500, 1800], departure = [910, 1200, 1120, 1130, 1900, 2000]
Output: 3
Explanation:

  • At 9:00: Train 1 arrives (Platform count 1)
  • At 9:10: Train 1 departs (Platform count 0)
  • At 9:40: Train 2 arrives (Platform count 1)
  • At 9:50: Train 3 arrives (Platform count 2)
  • At 11:00: Train 4 arrives (Platform count 3)
  • ...At peak, 3 trains are in the station.