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What is the time complexity of the difference array and prefix sum approach for the car pooling problem, given n trips and maximum location L?

medium🪤 Complexity Trap Q5 of Q15
Intervals - Car Pooling
What is the time complexity of the difference array and prefix sum approach for the car pooling problem, given n trips and maximum location L?
AO(n * L) because we simulate each location for every trip
BO(n log n) due to sorting events
CO(n + L) because we update difference array and then prefix sum once
DO(L^2) due to nested loops over locations
Step-by-Step Solution
Solution:

  1. Step 1: Analyze difference array updates

    Each trip updates two positions in the diff array -> O(n) operations.

  2. Step 2: Analyze prefix sum computation

    Prefix sum over diff array of length L -> O(L) operations.

  3. Final Answer:

    Option C -> Option C

  4. Quick Check:

    Linear in trips plus linear in max location -> O(n + L) [OK]
Quick Trick: Difference array updates O(n), prefix sum O(L) -> total O(n+L) [OK]
Common Mistakes:
MISTAKES
  • Confusing with sorting approach O(n log n)
  • Assuming nested loops cause O(n*L)
Trap Explanation:
PITFALL
  • Many candidates incorrectly assume sorting or nested loops dominate time complexity.
Interviewer Note:
CONTEXT
  • Tests understanding of time complexity for difference array approach.
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