Senior Software Engineer, AI Innovation and Research

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 discuss Access Control Lists (ACLs). Imagine you're designing a system where you need to control access to various resources. How would you approach assigning ACLs to users and groups? Be specific. For example, consider a scenario with files, directories, and applications. How would you define permissions (read, write, execute, delete) and associate them with individual users (like 'john.doe') or groups (like 'developers' or 'administrators')? What different strategies would you evaluate for managing ACLs, and what are the tradeoffs between them in terms of security, performance, and ease of administration? For example, would you use an identity-based approach, a role-based approach, or a combination of both? Consider also how you would handle inheritance of ACLs in a hierarchical structure, such as a file system. How would you prevent privilege escalation and ensure that users only have the access they need? Finally, how would you audit ACL changes and monitor access attempts to detect potential security breaches?

Google

Where do you see yourself in 5 years?