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What is the time complexity of the optimal two pointers approach for finding intersections of two sorted interval lists of sizes m and n?

medium🪤 Complexity Trap Q5 of Q15
Intervals - Interval List Intersections
What is the time complexity of the optimal two pointers approach for finding intersections of two sorted interval lists of sizes m and n?
AO(m * n)
BO(m + n)
CO(max(m, n) * log(min(m, n)))
DO(m^2 + n^2)
Step-by-Step Solution
Solution:

  1. Step 1: Analyze pointer increments

    Each pointer i and j only moves forward through their respective lists once.

  2. Step 2: Sum of pointer moves

    Total moves ≤ m + n, so time complexity is linear in combined input size.

  3. Final Answer:

    Option B -> Option B

  4. Quick Check:

    Two pointers scan each list once [OK]
Quick Trick: Two pointers -> linear time [OK]
Common Mistakes:
MISTAKES
  • Confusing with nested loops O(m*n)
Trap Explanation:
PITFALL
  • Many think nested loops are needed, leading to O(m*n) misconception.
Interviewer Note:
CONTEXT
  • Tests understanding of two pointers time complexity.
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