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

medium🪤 Complexity Trap Q13 of Q15
Intervals - Car Pooling
What is the time complexity of the optimal car pooling solution using the difference array and prefix sum approach, given n trips and maximum location L?
AO(n * L) because we must simulate passenger count at every location for each trip
BO(n + L) because we process each trip once and then sweep through the difference array once
CO(n log n) due to sorting trips by start location before processing
DO(L) because the difference array size dominates and trips are processed in constant time
Step-by-Step Solution
Solution:

  1. Step 1: Analyze trip processing

    Each of the n trips updates two positions in the difference array -> O(n)

  2. Step 2: Analyze prefix sum sweep

    We iterate over the difference array of size L once -> O(L)

  3. Final Answer:

    Option B -> Option B

  4. Quick Check:

    Sum of O(n) + O(L) operations [OK]
Quick Trick: Difference array updates O(n), prefix sum O(L) [OK]
Common Mistakes:
MISTAKES
  • Confusing brute force O(n*L) with optimal
  • Assuming sorting is required
  • Ignoring prefix sum sweep cost
Trap Explanation:
PITFALL
  • Option A looks plausible as brute force but is inefficient; sorting is unnecessary here.
Interviewer Note:
CONTEXT
  • Checks if candidate understands difference between brute force and optimized complexities.
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