Product Manager II, Augmented Reality Perception

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 prototype for a system that answers questions based on financial documents. To make this concrete, imagine a user needs to quickly find information within a company's annual report (a PDF containing financial statements, management discussion, etc.). The user might ask questions like: What was the company's revenue for the last fiscal year? What were the primary risks identified by management? How did operating expenses change compared to the previous year? Describe your approach to building a prototype that can accurately and efficiently answer these types of questions. Consider aspects such as: Document ingestion and processing:** How would you load and pre-process the financial documents (e.g., PDF parsing, text extraction)? Information retrieval:** What techniques would you use to identify the relevant sections of the document that contain the answer? Question answering:** How would you extract the answer from the relevant text (e.g., using rule-based methods, machine learning models)? Data storage:** How would you store the information from the documents to allow for efficient querying? User interface:** How would the user interact with the system to ask questions and receive answers? Evaluation:** How would you evaluate the performance of your prototype?

Google

Tell me about a time you faced a significant challenge and how you overcame it. To provide a detailed response, please consider the following: Describe the challenge:** What specific obstacles did you encounter? What made it difficult to handle? Explain your actions:** What steps did you take to address the challenge? What resources did you utilize? Did you seek help from others? Highlight your thought process:** What were your considerations when deciding on a course of action? What alternatives did you consider, and why did you choose your particular approach? Detail the outcome:** What was the result of your efforts? Did you successfully overcome the challenge? If so, what did you learn from the experience? If not, what would you do differently next time? For example, perhaps you were working on a complex software project with a tight deadline and encountered unexpected technical difficulties. Or, maybe you had to mediate a conflict between team members with differing opinions on how to approach a problem. Another example could involve learning a new programming language or technology in a short timeframe to meet a critical project requirement. When answering, be sure to provide enough context so the interviewer understands the situation and can assess your problem-solving skills, resilience, and ability to learn from challenges.