Explain CAP, indexing, locks, and logs

You are interviewing for a general software engineering role. Answer the following conceptual questions: 1. What does the CAP theorem state in distributed systems, and what trade-offs do real systems make in practice? 2. What is a database index? Compare common index types such as B-tree and hash indexes, and discuss their effects on read performance, write performance, storage cost, and query patterns. 3. How do concurrency control and locks work in databases or multithreaded systems? Explain shared vs. exclusive locks, deadlocks, and common isolation problems such as dirty reads, non-repeatable reads, and phantom reads. 4. What is the purpose of logs in software systems and databases? Distinguish between application logs, audit logs, and database recovery logs, and explain how logging helps with debugging, observability, and crash recovery.