Product Manager I, Google Ads

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 web proxy. Consider the following requirements: Basic Functionality: The proxy should be able to forward HTTP and HTTPS requests from clients to web servers and return the responses. Caching: Implement caching to reduce latency and bandwidth usage for frequently accessed resources. How would you handle cache invalidation? Security: The proxy should support HTTPS and protect client data. How would you handle SSL/TLS certificates? Scalability: The proxy should be able to handle a large number of concurrent connections. What architectural choices would you make to ensure scalability? Authentication: Implement basic authentication (username/password) to control access to certain websites. Logging: Log requests and responses for debugging and monitoring purposes. What information should be logged, and how would you manage log files? Blocking: Implement the functionality to block access to certain websites based on a blacklist. Discuss the architecture, components, and algorithms involved in building such a web proxy. Include considerations for performance, security, and maintainability. Provide example scenarios and solutions to potential challenges.

Google

Tell me about the most challenging project you have ever handled. To provide more context, please consider the following aspects in your response: Describe the project briefly: What were the project's goals, and what was your role? What made it challenging? Was it a technical hurdle, a difficult deadline, a complex team dynamic, ambiguous requirements, or something else? Provide specific examples of the challenges you faced. How did you overcome these challenges? What steps did you take to address the issues? What resources did you utilize? Did you have to learn new skills or technologies on the fly? What was the outcome? Were you able to successfully complete the project? If not, what were the lessons learned? What would you do differently next time? What was your biggest takeaway from the project? How did this experience shape your approach to future projects? Did it change your perspective on teamwork, problem-solving, or project management? For instance, perhaps you led a project to migrate a legacy system to a new cloud-based platform, and you encountered unexpected compatibility issues that required you to develop innovative workarounds. Or maybe you were part of a team that was tasked with developing a new feature for a popular product, but the requirements changed frequently, and the timeline was extremely tight. Sharing these types of details will help me understand the scope and complexity of the project and how you responded to the challenges involved.