Implement interval room counter and token manager

You are given two coding questions.

1) Minimum number of rooms for time intervals

You are given a list of meetings, where each meeting is an interval [start, end) with integer times (start < end). A single room can host multiple meetings as long as their time intervals do not overlap.

Task: Return the minimum number of rooms required to schedule all meetings.

Input: intervals: List[List[int]] where intervals[i] = [start_i, end_i]

Output: int = minimum number of rooms

Notes/constraints (reasonable interview assumptions):

• 1 <= len(intervals) <= 2e5
• 0 <= start_i < end_i <= 1e9
• Intervals that end at time t do not overlap with intervals that start at time t (i.e., treat as [start, end) ).

2) Token manager with generate/renew/count

Design a token system with a fixed lifetime timeToLive (TTL).

Each token has an expiration time. A token generated at currentTime expires at currentTime + timeToLive.

Implement a class (or module) supporting the following operations:

• generate(tokenId: string, currentTime: int) -> void
  • Creates a new token with id tokenId that expires at currentTime + timeToLive .
  • If a token with the same tokenId already exists, you may assume it is overwritten with the new expiration (state your assumption).
• renew(tokenId: string, currentTime: int) -> void
  • If tokenId exists and is unexpired at currentTime , update its expiration to currentTime + timeToLive .
  • If it does not exist or is already expired at currentTime , do nothing.
• countUnexpiredTokens(currentTime: int) -> int
  • Return the number of tokens whose expiration time is strictly greater than currentTime .

Constraints (reasonable interview assumptions):

• Up to 2e5 total operations
• currentTime values are non-decreasing across calls

Provide the required outputs with efficient time complexity.