Senior Product Manager, Geo

Google

Given n pairs of parentheses, what is the total number of different, valid combinations of those parenthesis? For example: For n = 1, the only valid combination is (), so the answer is 1. For n = 2, the valid combinations are ()() and (()), so the answer is 2. For n = 3, the valid combinations are ((())), (()()), (())(), ()(()), and ()()(), so the answer is 5. Calculate the number of valid parenthesis combinations for a given n. Explain the formula or method used to arrive at the answer. What is the underlying mathematical concept at play here, and how does it ensure that we only count valid combinations, avoiding invalid ones such as )()(? Detail the relationship between this problem and Catalan numbers, and discuss how this relationship can be utilized to efficiently compute the number of valid combinations, even for relatively large values of n.

Google

Let's design a rate limiter for an API. The rate limiter should: Limit the number of requests a user can make to an API within a given time window. Support different rate limits for different users or API endpoints. For example, a free tier user might be limited to 10 requests per minute, while a premium user can make 100 requests per minute. Similarly, some API endpoints might have lower rate limits than others due to resource constraints. Be highly performant to avoid adding significant latency to API requests. Be scalable to handle a large number of users and API requests. Be reliable and prevent accidental overloads that could cause service disruptions. Describe the architecture, algorithms, and data structures you would use to implement such a rate limiter. Consider the following: How would you store the rate limit counters for each user or endpoint? What algorithm would you use to determine whether a request should be allowed or throttled? How would you handle distributed rate limiting across multiple servers? How would you ensure the rate limiter is resilient to failures? As an example, imagine a scenario where a social media platform wants to prevent users from spamming their API with excessive requests to post updates. The platform has millions of users and thousands of API endpoints. Some users pay for premium access with higher request limits. How would you design a robust and efficient rate limiter to handle this scale and these varying requirements?

Google

Describe a time you faced a tough technical problem. What made it so difficult, and how did you approach solving it? What resources did you consult, and what was the final outcome? What did you learn from this experience, and how has it shaped your problem-solving skills since then? For example, perhaps you were tasked with optimizing a slow-running query in a large database. The initial attempts to improve performance, such as adding indexes, didn't yield the desired results. You then had to dive deep into the query execution plan, identify bottlenecks, and rewrite the query using more efficient techniques, like leveraging window functions or temporary tables. You could also describe the challenges faced while integrating a new feature into a legacy system with poorly documented code. You might have had to reverse engineer parts of the system, deal with unexpected dependencies, and carefully test the integration to avoid breaking existing functionality. Elaborate on the specific tools and methodologies you employed during these challenges, such as debuggers, profilers, or version control systems. Also, explain how you collaborated with team members or sought assistance from external resources like online forums or documentation to overcome the obstacles.