Learning On the Way

1997. First Day Where You Have Been in All the Rooms

There are n rooms you need to visit, labeled from 0 to n - 1. Each day is labeled, starting from 0. You will go in and visit one room a day.

Initially on day 0, you visit room 0. The order you visit the rooms for the coming days is determined by the following rules and a given 0-indexed array nextVisit of length n:

• Assuming that on a day, you visit room i,
• if you have been in room i an odd number of times (including the current visit), on the next day you will visit the room specified by nextVisit[i] where 0 <= nextVisit[i] <= i;
• if you have been in room i an even number of times (including the current visit), on the next day you will visit room (i + 1) mod n.

Return the label of the first day where you have been in all the rooms. It can be shown that such a day exists. Since the answer may be very large, return it modulo 109 + 7.

class Solution: 
    def firstDayBeenInAllRooms(self, nextVisit: List[int]) -> int: 
        M = 1000000007 
        dp = [0] * len(nextVisit) # The first day to reach i 
         
        for i in range(1, len(nextVisit)): 
            dp[i] = (2 * dp[i - 1] - dp[nextVisit[i - 1]] + 2) % M 
         
        return dp[-1] % M