[Solved] You are given arrival and departure times of trains at a station.... Which algorithmic approach guarantees an optimal solution for this problem? | Greedy Algorithms

Greedy Algorithms - Minimum Platforms (Train Stations)

You are given arrival and departure times of trains at a station. You need to find the minimum number of platforms required so that no train waits. Which algorithmic approach guarantees an optimal solution for this problem?

ASort trains by arrival time and use a min-heap to track earliest departure times

BDynamic Programming to find the maximum number of overlapping intervals

CGreedy approach by always assigning the next available platform without sorting

DBrute force nested loops checking all pairs of trains for overlaps

Step-by-Step Solution

Solution:

Step 1: Understand the problem requires tracking overlapping intervals
We need to find the maximum number of trains simultaneously at the station, which corresponds to the maximum overlap of intervals.
Step 2: Identify the optimal approach
Sorting trains by arrival time and using a min-heap to track the earliest departure allows efficient detection of overlaps and platform reuse, guaranteeing an optimal solution.
Final Answer:
Option A -> Option A
Quick Check:
Min-heap approach efficiently tracks platform usage [OK]

Quick Trick: Min-heap tracks earliest departure for platform reuse [OK]

Common Mistakes:

MISTAKES

Assuming greedy without sorting works optimally
Thinking DP is needed for interval overlaps
Using brute force for large inputs

Trap Explanation:

PITFALL

Greedy without sorting or DP approaches seem plausible but fail to handle overlaps efficiently.

Interviewer Note:

CONTEXT

Tests if candidate recognizes the pattern and optimal data structure for interval scheduling.

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More Greedy Algorithms Quizzes

Which algorithmic approach guarantees an optimal solution for this problem?

Step 1: Understand the problem requires tracking overlapping intervals

Step 2: Identify the optimal approach

Final Answer:

Quick Check:

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