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What is the space complexity of the difference array approach for car pooling given n trips and maximum location L?

medium🪤 Complexity Trap Q6 of Q15
Intervals - Car Pooling
What is the space complexity of the difference array approach for car pooling given n trips and maximum location L?
AO(n * L) due to simulating all locations for all trips
BO(n + L) due to trips and difference array
CO(L) for the difference array only
DO(n) for storing trips only
Step-by-Step Solution
Solution:

  1. Step 1: Identify space used by difference array

    Difference array size is O(L).

  2. Step 2: Consider auxiliary space in brute force simulation

    Brute force approach uses O(n * L) space for passenger counts per location per trip.

  3. Final Answer:

    Option A -> Option A

  4. Quick Check:

    Brute force simulates all trips over all locations -> O(n * L) space [OK]
Quick Trick: Brute force uses O(n*L) space, difference array only O(L) [OK]
Common Mistakes:
MISTAKES
  • Confusing time and space complexity
  • Forgetting brute force space usage
Trap Explanation:
PITFALL
  • Candidates often forget brute force uses large auxiliary arrays, inflating space complexity.
Interviewer Note:
CONTEXT
  • Tests understanding of space trade-offs between approaches.
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