Staff Software Engineer, Network Acceleration, High Performance Computing

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 simplified distributed key-value store. Assume we need to handle a high volume of read and write requests. The key-value store should support the following operations: get(key): Retrieves the value associated with the given key. put(key, value): Stores the value associated with the given key. Here are some specific considerations for the design: Scalability: The system should be able to scale horizontally to handle increasing amounts of data and traffic. Consider how data will be distributed across multiple servers. Consistency: Discuss the consistency model you would implement. Would you choose strong consistency or eventual consistency? What are the trade-offs? Provide a rationale for your choice. Elaborate on how your design ensures that reads return the most up-to-date data (or how it handles potential inconsistencies, if any). Fault Tolerance: How would the system handle server failures? Describe the mechanisms you would implement to ensure data durability and availability in the face of node failures. Explain the role of replication and how it impacts consistency. Data Partitioning: Describe your data partitioning strategy. Consider using techniques like consistent hashing or range-based partitioning. Explain how your chosen strategy affects load balancing and data locality. Provide a concrete example of how keys would be mapped to specific servers in your design. Caching: Where would you incorporate caching in your system to improve read performance? Discuss different caching strategies (e.g., client-side caching, server-side caching) and their implications. Walk me through the architectural components of your key-value store, including the roles of different servers, the communication protocols used, and the data flow for get and put operations. Explain any potential bottlenecks and how you would address them. For example, if consistent hashing is used, how do you handle nodes being added or removed from the cluster?

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.