Implement an LRU cache with O(1) ops

Design and code an LRU cache supporting get(key) and put(key, value) in O(1) average time with capacity N. Specify your data structures, handle updates to existing keys, and define precise eviction behavior when capacity is exceeded. Discuss thread-safety concerns and how you would add an optional per-key TTL without violating big-O guarantees. Provide complexity analysis for time and space, and identify edge cases (e.g., N=1, repeated gets, large values).