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Given a list of train arrival and departure times, you need to find the minimum number of platforms required so that no train waits. Which approach guarantees an optimal solution for this problem?

easy🔍 Pattern Recognition Q11 of Q15
Intervals - Minimum Number of Platforms Required
Given a list of train arrival and departure times, you need to find the minimum number of platforms required so that no train waits. Which approach guarantees an optimal solution for this problem?
AUse a greedy algorithm that assigns platforms as trains arrive without sorting times.
BUse a sweep line algorithm by creating events for arrivals and departures, sorting them, and tracking concurrent trains.
CUse dynamic programming to find the maximum overlap of intervals by building a state table.
DUse nested loops to check every pair of trains for overlap and count maximum overlaps.
Step-by-Step Solution
Solution:

  1. Step 1: Understand the problem requires tracking concurrent trains

    The key is to find the maximum number of trains present at the station simultaneously.

  2. Step 2: Recognize that sorting events and sweeping through them tracks concurrency efficiently

    By creating arrival and departure events and sorting them, we can increment or decrement the count of trains present, capturing the peak count.

  3. Final Answer:

    Option B -> Option B

  4. Quick Check:

    Sweep line tracks concurrency optimally [OK]
Quick Trick: Sort events and sweep to track concurrency [OK]
Common Mistakes:
MISTAKES
  • Assuming greedy assignment without sorting works
  • Trying DP which is unnecessary overhead
  • Using nested loops which is inefficient
Trap Explanation:
PITFALL
  • Nested loops or greedy without sorting seem intuitive but fail on overlapping intervals and efficiency.
Interviewer Note:
CONTEXT
  • Tests if candidate can identify the correct pattern beyond brute force or naive greedy.
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