Support room moves and query top-k fastest

Problem

There are R rooms labeled 0..R-1 (in increasing order), and P people labeled 0..P-1.

• Initially, all people are in room 0 .
• Operation move(personId) moves that person from room i to room i+1 , if i < R-1 . (If already in the last room, they stay there.)
• Within each room, maintain the arrival order of people (FIFO by the time they entered that room).

Design a data structure that supports:

1. countInRoom(roomId) -> int
   • Return how many people are currently in roomId .
   • Must be O(1) time.
2. topKFastest(k) -> list[int]
   • Return the k fastest people , where “faster” means:
     1. People in higher-numbered rooms are faster (closer to the end).
     2. For people in the same room , the one who entered that room earlier is faster.
   • Return fewer than k people if k > P .

Example

R = 5, P = 5.

Operations:

• move(1) , move(2) , move(1)

State:

• Person 1 is in room 2
• Person 2 is in room 1
• Others are in room 0

So:

• countInRoom(1) == 1 , countInRoom(2) == 1
• topKFastest(2) returns [1, 2] (order can be [1,2] given the definition above).

Complexity expectations

Explain the time complexity of each operation and aim for efficient updates (especially avoiding scanning all people for countInRoom or topKFastest).