Technical Program Manager, LearnX 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 system for URL shortening, like TinyURL. Assume that we need to handle a large number of requests, say billions of URLs per day. Consider the following: Functional Requirements: The system should generate a shorter, unique alias for a given URL. Users should be able to enter a shortened URL and be redirected to the original URL. The shortened URLs should be relatively short. Non-Functional Requirements: The system should be highly available. URL redirection should be as fast as possible. The shortened URLs should be unique. The system should be scalable to handle a large number of URLs and requests. Considerations: How would you design the data model to store the mappings between shortened and original URLs? What algorithms would you use to generate the shortened URLs? Consider the trade-offs between different algorithms. How would you handle collisions (when the same shortened URL is generated for two different original URLs)? What kind of database would you use and why? How would you handle the high volume of traffic and ensure low latency for redirection? Consider caching strategies. How would you scale the system to handle future growth? Walk me through your design, explaining your choices and the rationale behind them. Include diagrams and specific technologies where appropriate. Explain how you would ensure the system meets the requirements for availability, performance, and scalability.

Google

Okay, let's delve into your motivations. Why are you interested in working at this company specifically? I'm looking for more than just a generic answer about seeking a new job. I want to understand what resonates with you about our company's mission, values, and the specific role you're applying for. To give you some context, consider our commitment to innovation in the field of AI, particularly our recent work on developing more ethical and transparent algorithms. Or perhaps you're drawn to our collaborative work environment, where cross-functional teams work together to solve complex problems. Maybe you admire our company's dedication to social responsibility, like our initiatives to promote STEM education in underserved communities. When answering, please be specific and show that you've done your research. For instance, you could discuss a particular project that caught your attention, how your skills and experience align with the team's needs, or how you see yourself contributing to our company's long-term goals. Avoid vague statements like I'm a hard worker or I'm a team player without providing concrete examples. Instead, focus on demonstrating a genuine interest in our company and a clear understanding of how you can make a valuable contribution. To summarize, I want to know: What specifically attracts you to our company? How do your skills and experiences align with the requirements of this role and the company's goals? What unique contributions do you believe you can make to our team and our overall mission?