Bird
Raised Fist0

What is the time complexity of the sweep line algorithm for finding the minimum number of platforms required given n trains, and why?

medium🪤 Complexity Trap Q13 of Q15
Intervals - Minimum Number of Platforms Required
What is the time complexity of the sweep line algorithm for finding the minimum number of platforms required given n trains, and why?
AO(n log n) due to sorting arrivals and departures separately and merging them.
BO(n^2) because each event is compared with all others to count overlaps.
CO(n) because we only iterate through arrivals and departures once.
DO(n log n) because events are sorted and then processed in a single pass.
Step-by-Step Solution
Solution:

  1. Step 1: Identify sorting as the main cost

    We create 2n events and sort them by time, which takes O(n log n).

  2. Step 2: Single pass processing after sorting

    After sorting, we iterate through events once, O(n), updating counts.

  3. Final Answer:

    Option A -> Option A

  4. Quick Check:

    Sorting dominates, linear sweep after [OK]
Quick Trick: Sorting events dominates time complexity [OK]
Common Mistakes:
MISTAKES
  • Assuming O(n) because of single pass ignoring sorting
  • Confusing nested loops brute force with sweep line
  • Thinking sorting arrivals and departures separately is enough
Trap Explanation:
PITFALL
  • Sorting all events together is required; sorting separately then merging is less efficient or incorrect.
Interviewer Note:
CONTEXT
  • Checks understanding of sorting cost and linear sweep in event-based algorithms.
Master "Minimum Number of Platforms Required" in Intervals

3 interactive learning modes - each teaches the same concept differently

Try ItSolutionTrace

Want More Practice?

15+ quiz questions · All difficulty levels · Free

Free Signup - Practice All Questions
More Intervals Quizzes
Count of Intervals Containing Each Point - Count of Intervals Containing Each Point - Quiz 1easy Employee Free Time - Employee Free Time - Quiz 12easy Insert Interval - Insert Interval - Quiz 9hard Meeting Rooms II (Minimum Conference Rooms) - Meeting Rooms II (Minimum Conference Rooms) - Quiz 6medium Meeting Rooms II (Minimum Conference Rooms) - Meeting Rooms II (Minimum Conference Rooms) - Quiz 14medium Merge Intervals - Merge Intervals - Quiz 3easy Minimum Interval to Include Each Query - Minimum Interval to Include Each Query - Quiz 10hard Minimum Interval to Include Each Query - Minimum Interval to Include Each Query - Quiz 14medium Non-overlapping Intervals (Max Non-Overlap) - Non-overlapping Intervals (Max Non-Overlap) - Quiz 3easy Remove Covered Intervals - Remove Covered Intervals - Quiz 6medium