Design a dynamic leaderboard with rank queries

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.