Implement LRU Cache.

Focus on understanding the core principles of the Least Recently Used (LRU) caching mechanism. You should be prepared to discuss the data structures you would use, such as a combination of a hash map for fast access and a doubly linked list for maintaining the order of usage. Be ready to explain how you would handle cache hits and misses, including the logic for evicting the least recently used item. Additionally, consider edge cases, such as what happens when the cache is empty or full, and discuss the time and space complexity of your implementation.