Merge intervals and design rating APIs

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.