[Solved] You are given a list of trips, each with a number of passengers, a start location, and an end location.... Which algorithmic approach best guarantees an optimal and efficient solution? | Intervals

Intervals - Car Pooling

You are given a list of trips, each with a number of passengers, a start location, and an end location. You need to determine if a vehicle with a fixed capacity can carry all passengers without exceeding capacity at any point along the route. Which algorithmic approach best guarantees an optimal and efficient solution?

ABrute force simulation by incrementing passenger count at every location for each trip

BGreedy algorithm that picks trips with earliest end location first

CDynamic programming to find maximum passengers at each location using state transitions

DSweep line algorithm that processes passenger count changes at trip start and end points

Step-by-Step Solution

Solution:

Step 1: Understand problem constraints
The problem requires tracking passenger counts over intervals defined by start and end locations.
Step 2: Identify suitable algorithm
Sweep line processes events (passenger changes) in sorted order, efficiently tracking capacity usage without simulating every location.
Final Answer:
Option D -> Option D
Quick Check:
Sweep line handles interval events optimally [OK]

Quick Trick: Intervals with start/end events -> sweep line [OK]

Common Mistakes:

MISTAKES

Assuming greedy earliest end works for capacity constraints
Thinking DP is needed for counting passengers
Using brute force for large location ranges

Trap Explanation:

PITFALL

Greedy and DP approaches seem plausible but fail to efficiently track overlapping intervals and capacity changes.

Interviewer Note:

CONTEXT

Tests if candidate can recognize interval event processing pattern under capacity constraints.

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Which algorithmic approach best guarantees an optimal and efficient solution?

Step 1: Understand problem constraints

Step 2: Identify suitable algorithm

Final Answer:

Quick Check:

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