Product Manager I, Search

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

Let's discuss your skillset. To start, can you elaborate on your technical proficiencies, such as your experience with programming languages, frameworks, and tools? For instance, have you worked with Python, Java, or C++? Are you familiar with front-end frameworks like React or Angular, or back-end technologies like Node.js or Django? Can you provide examples of projects where you effectively utilized these skills to overcome technical challenges? Furthermore, how do you approach learning new technologies and integrating them into your existing workflow? In addition to technical skills, can you share examples of your soft skills, such as communication, teamwork, problem-solving, and leadership? For example, describe a situation where you effectively communicated a complex technical concept to a non-technical audience, or a time when you successfully collaborated with a team to achieve a common goal. How do you handle conflicts within a team, and what strategies do you employ to ensure that everyone's voice is heard? Finally, how do you stay up-to-date with the latest industry trends and advancements, and how do you continuously develop your skills to remain competitive in the ever-evolving tech landscape?