Solution Explanation: Design a Leaderboard

This problem requires designing a data structure to efficiently manage a leaderboard with three operations: addScore, top, and reset. The optimal approach leverages the strengths of both hash tables and ordered data structures.

Core Idea:

The solution combines a hash table (or dictionary) for fast lookups of player scores and an ordered data structure (e.g., a sorted list or a balanced binary search tree) to efficiently retrieve the top K players.

• Hash Table (d or record_map): Stores player IDs as keys and their scores as values. This provides O(1) average-case time complexity for addScore and reset.

• Ordered Data Structure (rank or implicitly sorted record_map): Stores player scores, allowing for quick retrieval of the top K scores. The choice of data structure impacts performance.

Data Structure Choices and Trade-offs:

Several ordered data structures could be used for rank:

1. Sorted List (Python's SortedList, similar implementations in other languages): Offers logarithmic time complexity for insertion, deletion, and retrieval of elements. This is a good balance between efficiency and simplicity.

2. Binary Search Tree (BST) (e.g., TreeMap in Java, std::map in C++, BTreeMap in Rust): Another good option providing logarithmic time complexity for operations. It's particularly efficient in languages where a well-implemented balanced BST is readily available.

3. Sorted array or Vector (unsorted in C++): This solution requires sorting the entire array each time you access it, making top relatively inefficient.

Algorithm:

1. addScore(playerId, score):

   • Check if the playerId exists in the hash table.
   • If it exists, update the score in the hash table and update the score in the ordered data structure (remove old score and add new score).
   • If it doesn't exist, add the player and score to both the hash table and the ordered data structure.

2. top(K):

   • Retrieve the top K scores from the ordered data structure. This is very efficient due to the ordering. Sum the top K scores and return the sum.

3. reset(playerId):

   • Remove the player from the hash table.
   • Remove the player's score from the ordered data structure.

Time Complexity Analysis:

• addScore: O(log n) - dominated by insertion/deletion in the ordered structure (assuming a balanced BST or sorted list).
• top: O(K) - retrieving K elements is linear, provided the data structure is already sorted. In some solutions, sorting is involved, influencing overall runtime.
• reset: O(log n) - removing from the ordered structure.

Space Complexity: O(n) - to store the scores of all players in both the hash table and the ordered structure.

Code Examples (with explanations):

The code examples provided earlier demonstrate the implementation using different languages and appropriate data structures. The Python solution uses SortedList for efficient sorted-list functionality. Java, C++, and Rust use different approaches but achieve the same outcome. Note that the Rust solution doesn't use a separate ordered structure; BTreeMap implicitly handles sorting. This might seem to offer O(log n) for top, but because iteration and summing are still O(k), this difference is inconsequential unless k is consistently much smaller than n.

Choosing the Right Data Structure:

The choice of the ordered data structure is important. If simplicity is paramount and the language provides an efficient sorted list implementation (like Python's SortedList), it is a good choice. If you're working in a language with a readily available and well-implemented balanced BST (like Java's TreeMap or C++'s std::map), that might be slightly more efficient in specific scenarios. Avoid using a simple unsorted array or vector since it leads to O(n log n) sorting complexity for the top operation.