Suppose trains can arrive and depart multiple times (reusing platforms), or the station allows fractional arrival/departure times (e.g., 10:00.5). How does this affect the minimum platforms problem and which approach is best suited?
AGreedy sorting by integer times only works; problem becomes unsolvable with fractional times
BMin-heap approach remains optimal as it dynamically tracks earliest departure times even with fractional or repeated intervals
CTwo-pointer approach fails due to fractional times; brute force is best
DThe problem reduces to maximum non-overlapping intervals; use interval scheduling DP
Step-by-Step Solution
Solution:
Step 1: Understand fractional and repeated intervals impact
Fractional times do not break the logic of min-heap approach, which dynamically tracks earliest departure times.
Step 2: Min-heap approach handles fractional and repeated intervals correctly
Since min-heap compares actual times, it can handle fractional values and multiple arrivals/departures gracefully.
Step 3: Two-pointer approach also works if sorting supports fractional times
But min-heap is more flexible for dynamic intervals.
Final Answer:
Option B -> Option B
Quick Check:
Min-heap handles fractional and repeated intervals well [OK]
Quick Trick:Min-heap dynamically tracks earliest departure even with fractional times [OK]
Common Mistakes:
MISTAKES
Assuming min-heap handles fractional times unchanged
Thinking brute force is best
Ignoring complexity of repeated intervals
Trap Explanation:
PITFALL
Candidates often assume fractional times break greedy sorting, but min-heap approach remains valid.
Interviewer Note:
CONTEXT
Tests candidate's ability to adapt or recognize limits of greedy approaches.
Master "Minimum Platforms (Train Stations)" in Greedy Algorithms
3 interactive learning modes - each teaches the same concept differently
