[Solved] Consider two approaches to solve the car pooling problem: (1) Sorting events and sweep line, and (2) Difference array... When is the sorting events approach preferable over the difference array? | Intervals

Intervals - Car Pooling

Consider two approaches to solve the car pooling problem: (1) Sorting events and sweep line, and (2) Difference array with prefix sums. When is the sorting events approach preferable over the difference array?

AWhen the maximum location L is very large but number of trips n is small

BWhen capacity is very large and no capacity checks are needed

CWhen trips have overlapping start and end locations only

DWhen the maximum location L is small and n is very large

Step-by-Step Solution

Solution:

Step 1: Analyze difference array approach
Difference array uses O(L) space and time; inefficient if L is large.
Step 2: Analyze sorting events approach
Sorting events is O(n log n), independent of L, better when L is large and n is small.
Step 3: Identify when sorting is better
When L is small and n is large, difference array is efficient; sorting events is preferable when L is large and n is small.
Final Answer:
Option D
Quick Check:
Sorting better when L large and n small -> Option D

Quick Trick: Sorting events better when L large, n small; difference array better when L small [OK]

Common Mistakes:

MISTAKES

Confusing which approach depends on L or n
Assuming difference array always better

Trap Explanation:

PITFALL

Candidates often mix up which approach scales better with L or n.

Interviewer Note:

CONTEXT

Tests trade-off reasoning between two common approaches.

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More Intervals Quizzes

When is the sorting events approach preferable over the difference array?

Step 1: Analyze difference array approach

Step 2: Analyze sorting events approach

Step 3: Identify when sorting is better

Final Answer:

Quick Check:

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