Data Scientist, gTech Ads Professional Services

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

Tell me about a time you had to work with a signed contract. Describe the situation, your role, and the outcome. What were the key clauses or provisions that were most relevant to the situation? What challenges, if any, did you face in interpreting or adhering to the contract terms? How did you ensure that your actions were in compliance with the contract, and what steps did you take to mitigate potential risks or disputes? For example, consider a scenario where you were managing a project with a vendor, and the contract outlined specific deliverables, timelines, and payment terms. A conflict arose when the vendor failed to meet a critical deadline, potentially impacting the project's overall timeline and budget. How did you leverage the contract to address the issue, protect your company's interests, and find a resolution that was fair to both parties? Or, imagine you were involved in a negotiation where the other party wanted to change certain terms after the contract was signed. How did you handle the situation, ensuring that any modifications were properly documented and agreed upon by all parties involved? What did you learn from this experience, and how has it influenced your approach to working with contracts in subsequent projects or situations?