## Problem: Dynamic Leaderboard You are asked to implement a **leaderboard** that maintains scores for a set of elements (e.g., players/items). Scores can change over time, and you must support efficient ranking queries. ### Data model - Each element has a unique `id` (string or integer). - Each element has a numeric `score` (integer). - Higher score means a better rank. - **Rank 1** is the highest score. - **Ties:** if multiple elements have the same score, break ties by `id` in ascending order (so ordering is total and deterministic). ### Operations to support Implement a data structure (or API) supporting these operations: 1. **Update score** - `update(id, delta)` or `updateTo(id, newScore)` (choose one and clearly document it). - If `id` does not exist, it is created. 2. **Delete element** - `remove(id)` removes the element from the leaderboard. If it doesn’t exist, do nothing. 3. **Get top-K elements** - `topK(k)` returns the `k` highest-ranked element IDs (or `(id, score)` pairs). - If `k` exceeds the number of elements, return all elements. 4. **Get rank of a specific element** - `getRank(id)` returns the 1-indexed rank of `id` under the ordering rules. - If `id` does not exist, return `-1`. ### What to discuss - The time complexity of each operation. - How you would optimize for real-world usage patterns (e.g., frequent updates, frequent top-K queries, many deletes). ### Constraints (assume) - Up to ~1e5 elements. - Up to ~1e5 operations. Define clearly what your `update` operation means (delta vs set), and ensure your design supports all operations correctly.