How do you count ongoing events for multiple query times?

DSA
Hard
Google
141.8K views

Direct Answer

This question asks candidates to determine the number of active events at specific time points given start and end intervals. It tests algorithmic efficiency and interval handling skills.

Why Interviewers Ask This

Interviewers ask this to evaluate a candidate's ability to optimize solutions beyond brute force methods. They want to see if you can identify patterns in interval data, such as sorting start and end times separately. The core evaluation focuses on time complexity reduction, specifically moving from O(N*Q) to O((N+Q)logN) or better using binary search or sweep line algorithms. This demonstrates deep understanding of data structures and algorithmic thinking required for high-scale systems.

How to Answer This Question

Start by explaining the naive brute-force approach where you check every event against every query, acknowledging its O(N*Q) complexity. Then, propose an optimized solution: separate the start and end times into two sorted arrays. For each query, use binary search (specifically upper_bound) to find how many events have started before or at that time and subtract how many have ended before it. Alternatively, discuss the sweep-line algorithm where you process events chronologically. Clearly state your chosen complexity and justify why it is superior. Ensure you handle edge cases like overlapping boundaries correctly.

Key Points to Cover

  • Identify the inefficiency of brute force O(N*Q)
  • Sort start and end times independently
  • Use binary search to count active intervals
  • Calculate result as (starts <= t) - (ends < t)

Sample Answer

The problem requires counting overlapping intervals for multiple queries. A brute-force approach checks all N events for each Q query, resulting in O(N*Q) time. To optimize, I would separate start and end times into two…

Common Mistakes to Avoid

  • Failing to handle inclusive vs exclusive boundaries correctly
  • Not considering the sorting step for optimization
  • Ignoring the case where no events are ongoing

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