How do you count ongoing events for multiple query times?

Q: How do you count ongoing events for multiple query times?

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 distinct arrays and sort them. For any query time T, the number of ongoing events equals the count of starts less than or equal to T minus the count of ends strictly less than T. Using binary search on these sorted arrays allows us to find these counts in O(log N) per query. This reduces the total complexity to O(N log N + Q log N). This approach efficiently handles large datasets common in production environments.

DSA

Hard

Google

141.8K views

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 distinct arrays and sort them. For any query time T, the number of ongoing events equals the count of starts less than or equal to T minus the count of ends strictly less than T. Using binary search on these sorted arrays allows us to find these counts in O(log N) per query. This reduces the total complexity to O(N log N + Q log N). This approach efficiently handles large datasets common in production environments.

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

Practice This Question with AI

Answer this question orally or via text and get instant AI-powered feedback on your response quality, structure, and delivery.

Start Practicing

How do you count ongoing events for multiple query times?

Why Interviewers Ask This

How to Answer This Question

Key Points to Cover

Sample Answer

Common Mistakes to Avoid

Practice This Question with AI

Related Interview Questions

What is the optimal path to maximize collected rocks in a grid?

What is the optimal dynamic programming approach to maximize rocks collected in a grid?

How do you find a triplet where a squared equals b squared plus c squared?

Explain the concept of graph components in computer science?

Defining Your Own Success Metrics

What is Object-Oriented Programming in Java?