FPGA Design Engineer

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Write code to parse regular expressions including * (0 or more characters), + (1 or more characters), and . (1 exact character). For example: parse(a., ab) should return true. parse(a*, aaa) should return true. parse(a+, a) should return true. parse(a+, ) should return false. parse(a.*b, axyzb) should return true. parse(a.*b, axyz) should return false. parse(abc, abc) should return true. parse(abc, abd) should return false. Your function should take two strings as input: the regular expression and the string to match against. It should return a boolean indicating whether the string matches the regular expression. Focus on handling the special characters ., *, and +. Assume that other characters in the regular expression must match literally. Explain your approach and provide a clear, well-documented code implementation. Consider edge cases such as empty strings and null inputs. Also think about the time and space complexity of your solution, and try to optimize it for performance. Can you provide a solution using dynamic programming?

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Let's design a database for a library. Consider the following requirements: Books: The library has a collection of books. Each book has a title, an author (or authors), a publication year, an ISBN, and a genre. A book can have multiple authors. Members: The library has members who can borrow books. Each member has a unique member ID, a name, an address, and a phone number. Borrowing: The library needs to keep track of which books are borrowed by which members and when they are borrowed and returned. A member can borrow multiple books, and a book can be borrowed by multiple members over time. Reservations: Members can reserve books that are currently checked out. The system needs to keep track of reservations and their order. Late Fees: The library charges late fees for overdue books. The system needs to calculate and track these fees. Based on these requirements, design a relational database schema. Include the tables, columns, data types, primary keys, and foreign keys. Provide a brief explanation for each table and the relationships between them. How would you handle the many-to-many relationship between books and authors? How would you handle the many-to-many relationship between members and borrowed books? How would you ensure data integrity, such as preventing a member from borrowing the same book twice at the same time?

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Let's say you are managing a team of five engineers working on a critical feature for an upcoming product launch. One of your engineers, Sarah, consistently delivers high-quality work but has been missing deadlines lately. During a one-on-one meeting, Sarah confides in you that she is feeling overwhelmed with her workload due to personal issues outside of work. Additionally, another engineer, David, has been expressing frustration about the lack of clear direction and feeling that his skills are not being fully utilized. Furthermore, the team is starting to experience conflicts regarding code ownership and integration, leading to delays and tension. As the engineering manager, how would you address these issues to ensure the successful delivery of the feature while maintaining a positive and productive team environment? Please provide specific steps and strategies you would implement to handle each situation, including Sarah's performance, David's concerns, and the team's conflict.