Solution Explanation

This problem involves designing a file-sharing system. The system needs to manage user IDs, track which chunks of a file each user owns, and handle user join/leave requests and chunk requests. The key challenge is efficiently managing user IDs, reusing them when users leave, and quickly retrieving users who own a specific chunk.

Approach

The solution uses several data structures to efficiently manage the system:

1. cur (Integer): Keeps track of the next available user ID. It increments whenever a new user joins and there are no reused IDs.

2. reused (Min-Heap/TreeSet): Stores the IDs of users who have left the system. A min-heap (or TreeSet in Java) is used to efficiently retrieve the smallest available ID when a new user joins. This ensures ID allocation is optimized.

3. user_chunks (Hash Table/TreeMap): A hash table (or TreeMap in Java) maps user IDs to sets of chunk IDs they own. This provides efficient lookups for both assigning chunks to users and finding users who own a specific chunk.

The join, leave, and request methods implement the core functionality:

• join(ownedChunks): Assigns a unique ID to a new user. It first checks the reused heap/set; if it's not empty, it reuses the smallest available ID. Otherwise, it assigns the next available ID (cur). The user's owned chunks are stored in user_chunks.

• leave(userID): Removes the user from the system. Their ID is added to the reused heap/set to be reused later.

• request(userID, chunkID): Returns a sorted list of user IDs that own the requested chunk. It iterates through user_chunks to find matching users, adding the requested chunk to the requesting user's owned chunks if found.

Time and Space Complexity

Time Complexity:

• join: O(log k) where k is the number of reused user IDs (due to heap operations). In the worst case, it becomes O(1) if there are no reused IDs.
• leave: O(log k) where k is the number of reused user IDs (due to heap operations).
• request: O(n log n) where n is the number of users (because of sorting the result). The search through user_chunks takes O(n) time.

Space Complexity:

• O(n + m), where n is the number of users and m is the number of chunks. This is due to storing user IDs and their chunk ownership in user_chunks and potentially storing reused IDs in reused.

Code in Python and Java

The code provided in the problem description accurately implements this approach. The Python code uses heapq for the min-heap and defaultdict for the hash table, while the Java code uses TreeSet and TreeMap for their respective functionalities. Both versions ensure efficient ID management and chunk requests. The use of appropriate data structures is crucial for achieving the desired time complexity.