Suppose trains can arrive and depart multiple times (reusing platforms), or the station allows fractional arrival/departure times. Which modification to the min-heap approach correctly handles these cases?
AUse brute force nested loops to check all overlaps since fractional times break heap ordering
BSort arrivals and departures separately and use two pointers to count overlaps
CKeep the min-heap but change the comparison to strictly less than (<) to handle fractional times
DUse a balanced BST instead of a min-heap to handle fractional times and reuse efficiently
Step-by-Step Solution
Solution:
Step 1: Identify challenges with fractional and multiple reuse
Fractional times and multiple reuse require precise ordering and efficient insertion/removal of intervals.
Step 2: Choose data structure
A balanced BST supports ordered insertions, deletions, and queries with fractional keys better than a min-heap, which assumes discrete ordering.
Step 3: Why other options fail
Two pointers fail with fractional times due to equality checks; changing comparison in heap breaks correctness; brute force is inefficient.
Final Answer:
Option D -> Option D
Quick Check:
Balanced BST handles fractional and reuse efficiently [OK]
Quick Trick:Balanced BST supports fractional keys and dynamic reuse [OK]
Common Mistakes:
MISTAKES
Assuming min-heap works unchanged with fractional times
Using two pointers without handling fractional equality
Resorting to brute force for efficiency
Trap Explanation:
PITFALL
Min-heap ordering breaks with fractional times; two pointers rely on discrete ordering.
Interviewer Note:
CONTEXT
Tests candidate's ability to adapt data structures to relaxed constraints and real-world scenarios.
Master "Minimum Platforms (Train Stations)" in Greedy Algorithms
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