I knew this one cold so I jumped straight to doubly linked list plus hashmap.
Start by clarifying the requirements and constraints, then propose a design using a hash map and a doubly linked list to achieve O(1) operations. Explain how get and put work, including eviction of the least recently used item when capacity is exceeded, and discuss trade-offs such as concurrency and memory overhead.
Pro tip: Mention that you would use a doubly linked list (not singly) to allow O(1) removal of a node given its reference, and consider using a sentinel head/tail to simplify edge cases. Also, briefly discuss how you would handle thread safety if needed, showing awareness of real-world usage.
Confirm the cache capacity, expected operations (get/put), and whether thread safety is required. Ask about edge cases like capacity 0 or 1.
Select a hash map for O(1) key lookup and a doubly linked list to maintain recency order. Explain why a singly linked list or array would not achieve O(1) for all operations.
Describe get: if key exists, move node to front (most recently used) and return value; else return -1. Describe put: if key exists, update value and move to front; else insert new node at front and evict least recently used (tail) if over capacity.
Discuss handling capacity 0 (no storage), updating existing keys, and ensuring the linked list and hash map stay in sync. Mention using sentinel nodes to simplify insertion/removal.
State that both operations are O(1) average time due to hash map and linked list. Discuss space O(capacity). Mention potential improvements like thread safety or using a different eviction policy.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify that the problem is essentially generating all subset products of the given primes and returning them in sorted order. Discuss a recursive/backtracking approach that builds products incrementally, then sorts the result, or a BFS/priority queue approach that generates products in sorted order without a final sort. Analyze time and space complexity, noting that the output size is 2^n - 1.
Pro tip: Mention that since the primes are distinct, all subset products are unique, so no deduplication is needed; this simplifies the solution and avoids unnecessary overhead. Also, discuss the trade-offs between generating all products and sorting versus using a min-heap to produce sorted output on the fly, especially when the number of primes is large.
Confirm that the input is an array of distinct primes, and the output should be a sorted list of all unique products from non-empty subsets. Ask about constraints like the maximum number of primes (n) to determine if exponential time is acceptable.
Decide between a simple recursive/iterative generation followed by sorting, or a more efficient generation using a min-heap to produce sorted order directly. Explain the trade-offs.
Write code to generate all subset products. For the recursive approach, start with an empty product and for each prime, multiply it with existing products. For the heap approach, initialize with the smallest prime and use a min-heap to generate products in increasing order.
State that the number of products is 2^n - 1, so time complexity is at least O(2^n) and space O(2^n) for the output. If sorting, add O(2^n log 2^n) time. The heap approach can be O(2^n log 2^n) as well but may avoid a full sort.
Test with small arrays (e.g., [2,3] -> [2,3,6]) and consider edge cases like empty array (return empty list) or single prime. Ensure the solution handles large n gracefully if constraints allow.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.