### Problem 1: Merge overlapping intervals You are given a list of closed intervals `intervals`, where `intervals[i] = [start_i, end_i]` and `start_i <= end_i`. **Task:** Merge all overlapping intervals and return a new list of non-overlapping intervals that cover the same ranges. **Input:** - `intervals`: an array/list of `[start, end]` pairs (not necessarily sorted) **Output:** - A list of merged, non-overlapping intervals (order can be by increasing start) **Follow-up:** - Support inserting one additional interval `newInterval` into the existing set and return the merged result efficiently. --- ### Problem 2: Implement agent-rating APIs with ordering by average Design and implement a data structure that supports the following APIs for rating “agents” by name. - `rateAgent(name, score)`: record a new rating for the agent `name`. - `name` is a string identifier. - `score` is an integer in `[1, 5]`. - `getTopAgents()`: return a list of agent names sorted by their **current average score** in **descending** order. **Details / requirements:** - Each agent can receive many ratings over time. - The average for an agent is computed over all ratings recorded so far for that agent. - `getTopAgents()` may be called many times; aim for an efficient approach across many operations. - Define a deterministic tie-breaker for equal averages (e.g., by name ascending). **Constraints (assume typical interview scale):** - Up to ~`10^5` total API calls. - Many repeated `getTopAgents()` calls should not require excessive recomputation each time.