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You have a list of intervals and a list of points. You want to efficiently find, for each point, how many intervals contain it. Which algorithmic pattern best fits this problem?

easy🔍 Pattern Recognition Q1 of Q15
Intervals - Count of Intervals Containing Each Point
You have a list of intervals and a list of points. You want to efficiently find, for each point, how many intervals contain it. Which algorithmic pattern best fits this problem?
ALine sweep algorithm using event sorting of interval starts, ends, and points
BTwo pointers on sorted intervals and points without event processing
CDynamic programming on interval subsets to count coverage
DGraph traversal to find connected components representing coverage
Step-by-Step Solution
Solution:

  1. Step 1: Identify problem requirements

    The problem requires counting how many intervals cover each point efficiently, which suggests processing interval boundaries and points in sorted order.

  2. Step 2: Match to known patterns

    The line sweep algorithm processes interval start and end events plus points in a single sorted pass, maintaining active intervals count, which fits perfectly.

  3. Final Answer:

    Option A -> Option A

  4. Quick Check:

    Line sweep handles intervals and points together efficiently [OK]
Quick Trick: Line sweep handles intervals and points in one sorted pass [OK]
Common Mistakes:
MISTAKES
  • Confusing interval coverage with graph connectivity
  • Thinking DP is needed for counting coverage
  • Ignoring event sorting order in line sweep
Trap Explanation:
PITFALL
  • Candidates often pick DP or graph approaches because they confuse coverage counting with other interval problems.
Interviewer Note:
CONTEXT
  • Tests candidate's ability to recognize interval coverage pattern and appropriate algorithm.
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