Design LRU cache and pick k closest points

1) Design a fixed-capacity in-memory cache that evicts the least recently used key when full. Support get(key) and put(key, value) in O( 1) average time. Describe the data structures you would use, how recency is updated on get/put, how evictions occur, and analyze time and space complexity. 2) Given an array of 2D points and an integer k, return the k points closest to the origin by Euclidean distance. First outline a straightforward approach using sorting. Then discuss improvements using Quickselect and a max-heap, including their time and space complexity and when you would choose each approach.